Article

On the internal architecture of emergent plants

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Abstract

It remains a puzzling issue why and how the organs in plants living in the same natural environment evolve into a wide variety of geometric architecture. In this work, we explore, through a combination of experimental and numerical methods, the biomechanical morphogenesis of the leaves and stalks of representative emergent plants, which can stand upright and survive in harsh water environments. An interdisciplinary topology optimization method is developed here by integrating both mechanical performance and biological constraint into the bi-directional evolutionary structural optimization technique. The experimental and numerical results reveal that, through natural selection over many million years, these leaves and stalks have been optimized into distinctly different cross-sectional shapes and aerenchyma tissues with intriguing anatomic patterns and improved load-bearing performance. The internal aerenchyma is an optimal compromise between the mechanical performance and functional demands such as air exchange and nutrient transmission. We find that the optimal distribution of the internal material depends on multiple biomechanical factors such as the cross-sectional geometry, hierarchical structures, boundary condition, biological constraint, and material property. This work provides an in-depth understanding of the property–structure–performance–function interrelations of biological materials. The proposed topology optimization method and the presented biophysical insights hold promise for designing highly efficient and advanced structures (e.g., airplane wings and turbine blades) and analyzing other biological materials (e.g., bones, horns, and beaks).

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... Morphological evolution in natural systems underpins a variety of life functions, including growth, locomotion and predation. For example, plants transport water and other minerals through an intricate network of hollow channels, the aerenchyma, whose size and shape change during plant growth (Corson et al., 2009;Zhao et al., 2018). Likewise, skeletal muscles enable us to run and walk via the contraction of multiply innervated (randomly distributed) fibers whose surrounding connective tissue, the extracellular matrix, thickens during motoneuron lesions (Tidball and Wehling-Henricks, 2004;Spyrou et al., 2019). ...
... Over the past two decades, significant efforts have been made to harness computational morphogenesis in synthetic structures. Examples are numerous and can be found in many areas of research including materials science (Portela et al., 2020;Zerhouni et al., 2019;Kumar et al., 2020), mechanobiology (Spyrou et al., 2019;Zhao et al., 2018;Ma et al., 2021), design (Martínez et al., 2016(Martínez et al., , 2018Aage et al., 2017;Baandrup et al., 2020) and architecture (Menges, 2012;Roudavski, 2009). In particular, in the context of materials science and mechanics, today one is able to mimic complex heterogeneous structures that are reminiscent of bone (Portela et al., 2020;Kumar et al., 2020;Martínez et al., 2016Martínez et al., , 2018Aage et al., 2017;Wu et al., 2017), skeletal muscles (Spyrou et al., 2019), plants (Faisal et al., 2012;Zhao et al., 2018) and even particle-reinforced polymers (Segurado and Llorca, 2002;Lopez-Pamies et al., 2013) and geomaterials (Roberts and Teubner, 1995;Roberts and Garboczi, 2001). ...
... Examples are numerous and can be found in many areas of research including materials science (Portela et al., 2020;Zerhouni et al., 2019;Kumar et al., 2020), mechanobiology (Spyrou et al., 2019;Zhao et al., 2018;Ma et al., 2021), design (Martínez et al., 2016(Martínez et al., , 2018Aage et al., 2017;Baandrup et al., 2020) and architecture (Menges, 2012;Roudavski, 2009). In particular, in the context of materials science and mechanics, today one is able to mimic complex heterogeneous structures that are reminiscent of bone (Portela et al., 2020;Kumar et al., 2020;Martínez et al., 2016Martínez et al., , 2018Aage et al., 2017;Wu et al., 2017), skeletal muscles (Spyrou et al., 2019), plants (Faisal et al., 2012;Zhao et al., 2018) and even particle-reinforced polymers (Segurado and Llorca, 2002;Lopez-Pamies et al., 2013) and geomaterials (Roberts and Teubner, 1995;Roberts and Garboczi, 2001). Traditionally, computational morphogenesis has relied on voxel-based algorithms that enable generating complex distributions of Voronoi polyhedra. ...
Article
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The present work introduces a novel and versatile computer-design and experimental strategy to obtain random Voronoi-type geometries, called M-Voronoi (from mechanically grown), with smooth void shapes and variable intervoid ligament sizes that can reach very low relative densities. This is achieved via a numerical, large strain, nonlinear elastic, void growth mechanical process. Originally small circular voids embedded in a cell of arbitrary shape (triangle, circle, rectangle, trapezoid) grow when subjected to displacement (Dirichlet) boundary conditions. The deformed voids evolve into smooth Voronoi-type geometrical shapes leading to macroscopic isotropy or anisotropy depending on the prescribed boundary conditions. The void growth process is a direct consequence of mass conservation and the incompressibility of the surrounding nonlinear elastic matrix phase and the final achieved relative density may be analytically estimated in terms of the determinant of the applied deformation gradient. In order to study the mechanical properties of the M-Voronoi materials, we focus on two-dimensional porous polymer square representative isotropic and anisotropic geometries in terms of void size and realization, which are 3D-printed and experimentally tested under uniaxial compression. For comparison, we also test random polydisperse porous materials with circular voids, standard eroded Voronoi geometries and hexagonal honeycombs. The first two are also isotropic while the latter are only isotropic in the linear elastic regime. We show that the randomness of the M-Voronoi geometry and their non-uniform intervoid ligament size leads to enhanced mechanical properties at large compressive strains with no apparent peak-stress and strong hardening well before densification. By comparing them with the hexagonal geometries, which tend to exhibit a peak-stress and a plateau-type response, we show that the hardening response of the M-Voronoi is mainly due to their geometrical characteristics and less due to the polymer hardening response. Anisotropic M-Voronoi are also produced and tested indicating that anisotropy only enhances the initial stiffness along the longitudinal direction but instead leads to lower buckling loads and hardening rates than the corresponding isotropic M-Voronoi in the nonlinear regime.
... Optimization problems can be solved by using different approaches such as the optimality criteria (OC) method [33,36], the sequential linear/integer programming method [33,39], the method of moving asymptotes [40], and the non-gradient method [41][42][43]. These methods have been used in diverse fields of, for example, additive manufacturing [44,45], metamaterials [46][47][48][49], bionics [32,48,50,51], medical devices [52], flexible electronics [53], soft robotics [54,55] and aerospace [22,27,56]. ...
... f =VðxÞ=V 0 and f* are the material volume fraction and the prescribed volume fraction. The geometric constraint GðxÞ [50,57,58] could be added to equation (2.1) by tuning the maximum component size R max for the local material layout in the optimization module of the software Abaqus. Assume that the veins and leaves are composed of the same material. ...
... The target volume fraction f* of material is set as 20% or 30% in different cases. By changing the maximum geometric size R max defined in equation (2.1), the local accumulation of material can be avoided [50,57,58]. ...
Article
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The growth and development of biological tissues and organs strongly depend on the requirements of their multiple functions. Plant veins yield efficient nutrient transport and withstand various external loads. Victoria cruziana, a tropical species of the Nymphaeaceae family of water lilies, has evolved a network of three-dimensional and rugged veins, which yields a superior load-bearing capacity. However, it remains elusive how biological and mechanical factors affect their unique vein layout. In this paper, we propose a multi-functional and large-scale topology optimization method to investigate the morphomechanics of Victoria cruziana veins, which optimizes both the structural stiffness and nutrient transport efficiency. Our results suggest that increasing the branching order of radial veins improves the efficiency of nutrient delivery, and the gradient variation of circumferential vein sizes significantly contributes to the stiffness of the leaf. In the present method, we also consider the optimization of the wall thickness and the maximum layout distance of circumferential veins. Furthermore, biomimetic leaves are fabricated by using the three-dimensional printing technique to verify our theoretical findings. This work not only gains insights into the morphomechanics of Victoria cruziana veins, but also helps the design of, for example, rib-reinforced shells, slabs and dome skeletons.
... For the designing of a safe and lightweight structure, the structural form with efficient internal force transmission is the goal of structural innovation. The bio-inspired branching structure (BIBS), namely, tree-like structure, is widely used as a support structure in large-span spatial structures, additive manufacturing and internal architecture of plants because of its large supporting space, minimal load path and uniform distribution of internal force with good structural integrity [1][2][3][4][5][6], its structural form determines internal force flow, significantly affects the internal force transfer efficiency (IFTE) and structural behavior. Form finding is a key issue in the design process of tree-like structures, further shape optimization with structural analysis is still required. ...
... clearly shown that the strength of the top surface needs to reach a minimum limit during the topology optimization process for continuum solid materials. Additionally, Fig. 14 comprehensively plots the optimized topologies of the flat-non-design composites and curved-non-design composites with different geometric dimensions and material properties between non-design domain and design domain, and the same solutions were found in the internal architecture of emergent plants [6]. There is a clear trend that when the material properties E 0 of the non-design domain is less than the material properties E 1 of the design domain, the number of the top-level branches of BIBS increases as E 0 gradually decreases to strengthen the bending stiffness of the top surface, in contrast, when the E 0 of the non-design domain is large enough, the optimized topology of the composites is a single straight pillar supporting the top surface and the load-bearing structure has the highest efficiency. ...
Article
Structure’s internal force transfer efficiency is the bases of pursuing the creative structural form. This paper reveals the mechanical mechanisms of the bio-inspired branching structures and further presents a numerical form-finding and shape optimization method for bio-inspired branching structures based on graphic statics with the constraints of strength, stiffness of boundary conditions are considered. Efficient structural form is obtained by connecting the internal force equilibrium and the structural performance in designing process. The reciprocal diagrams in graphic statics are used to solve the form-finding problem to generate compression or tension-only tree-like structure. Establishing the formula of the evaluation criteria of internal force transfer efficiency to characterize the structural performances, the criteria is compared with the continuum topology optimization method, the shape of tree-like structure is optimized by maximizing the structural efficiency under static loads. As a result, suitable external constraints can make a structure efficient and improve the structural redundancy, material properties determine the structural form, which in turn affects the structural behavior. Consequently, the interrelation mechanisms between material-property, structural-form, and structure-performance of the highly efficient bio-inspired branching structures are found. The internal force transfer efficiency and the strength and stiffness of boundary condition are the main factors to determine the optimal solution in the topological design exploration of load-bearing structure, these factors could be controlled to obtain the effective and elegant structural form for practical fabrication. The proposed numerical method could provide intuitive understanding and real-time feedback for the optimal solution, avoid the single solution obtained by the conventional optimization techniques and limited control to modify the output topology. Besides, more structural performance (e.g. buckling, vibration) can be considered in the structural designing process.
... Later, ESO evolved into a method called Bi-directional evolutionary structural optimization (BESO) [7], which in addition to removing elements, also adds them. The use of topological optimization as a computational tool has been successfully applied in biomechanical morphogenesis [8], vehicular structures [9,10], aerospace [11], agriculture [12] and others. ...
... Foz do Iguaçu/PR, Brazil, November [16][17][18][19]2020 of the objective function is illustrated in Fig. 4. The convergence was satisfied in the last ten iterations in both volume and error, as stated in eq. (8). The material removal occurred in a dynamic evolutionary rate, as stated in eq. ...
Conference Paper
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The subsoiler is one of the most used tools in tillage, mainly in the subsurface layers, helping in the availability of nutrients for the plants and reducing soil compaction. In some cases, this tool is oversized due to the lack of engineering tools and technical knowledge. In this aspect, this work aims to apply the topology optimization method to the shank of a subsoiler to decrease the consumption of raw material while maintaining performance during tillage. It was used Ansys, to solve the finite element analysis, in parallel with Matlab based in Bi-directional Evolutionary Structural Optimization (BESO) scheme for the compliance minimization and considering the volume as the constraint. The three-dimensional model of the subsoiler shank was generated on 3D Computer-aided design (CAD). MatLab reads the set parameters, builds an Ansys input file, and sends it to Ansys to perform the finite element analysis. Ansys exports geometry details and elemental strain energy necessary to perform the topology optimization. As a result, the topology optimized subsoiler shank is is 25% lighter than the original part with a 8% increase in the mean compliance. An adaptation of the final geometry was implemented so that the subsoiler could be more easily manufactured after applying the topological optimization method.
... Liu et al. (2018b) studied graded lattice structure design in the topology optimization framework of Moving Morphable Components (MMC) (Guo et al. 2014;Zhang et al. 2016) and Moving Morphable Void (MMV) (Zhang et al. , 2018. Zhao et al. (2018) studied topology optimization for the internal porous architecture of emergent plants using the Bi-directional Evolutionary Structural Optimization (BESO) method (Querin et al. 1998;Yang et al. 1999). Further, porous structures may arise naturally from high-resolution topology optimization which is able to reveal rich structural details (e.g., Wu et al. 2016;Aage et al. 2015Aage et al. , 2017. ...
... where V e s ρ ð Þ denotes the local volume of material measured in the neighborhood of the element e and V e max denotes the maximum allowed local volume of material. Equation (3) and its variants are preferred in porous structural design (e.g., Wu et al. 2018;Zhao et al. 2018). ...
Article
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Porous structures are of valuable importance in additive manufacturing. They can also be exploited to improve damage tolerance and fail-safe behavior. This paper presents a projection approach to design optimized porous structures in the framework of density-based topology optimization. In contrast to conventional constraint approach, the maximum local volume limitation is integrated into the material interpolation model through a filtering and projection process. This paper also presents two extensions of the basic approach, including a robust formulation for improving weak structural features and mesh/design refinement for enhancing computational stability and efficiency. The applicability of the proposed methodology is demonstrated by a set of numerical minimum compliance problems. This approach can be used in a wider range of applications concerning porous structures.
... Some optimized structural designs have been successfully applied in engineering applications such as railway vehicles [26] and aircrafts [27]. Topology optimization is not only used in mechanical design, but also applied in multidisciplinary design, including thermodynamics [28,29], biomechanics [30], acoustics [31,32], micro-structured materials [33][34][35][36], and nano-photonic design [37][38][39]. ...
... In this work, the SCC approach is developed based on the BESO method. The BESO method can be used in multidisciplinary structural optimization, such as stiffness optimization [51,52], natural frequency optimization [53], and the optimal design of functional gradient materials [54], biological materials [30] and concurrent optimization for structures and materials [55]. The BESO method is widely recognized owing to its high-quality topology solutions, simple to understand and implement, and excellent computational efficiency. ...
Article
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Topology optimization is increasingly used in lightweight designs for additive manufacturing (AM). However, conventional optimization techniques do not fully consider manufacturing constraints. One important requirement of powder-based AM processes is that enclosed voids in the designs must be avoided in order to remove and reuse the unmelted powder. In this work, we propose a new approach to realizing the structural connectivity control based on the bi-directional evolutionary structural optimization technique. This approach eliminates enclosed voids by selectively generating tunnels that connect the voids with the structural boundary during the optimization process. The developed methodology is capable of producing highly efficient structural designs which have no enclosed voids. Furthermore, by changing the radius and the number of tunnels, competitive and diverse designs can be achieved. The effectiveness of the approach is demonstrated by two examples of three-dimensional structures. Prototypes of the obtained designs without enclosed voids have been fabricated using AM.
... The BESO method has become a widely used design technique in both academic research (e.g., thermal conduction [15], biomechanics [16,17], acoustics [18], microstructural materials [19,20], and nano-photonic designs [21]) and industrial applications (e.g., architecture [22], automotive [23], aircraft [24] and railway vehicles [25]). ...
Article
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The bi-directional evolutionary structural optimisation (BESO) has attracted much interest in recent decades. However, the high computational cost of the topology optimisation method hinders its applications in large-scale industrial designs. In this study, a parallel BESO method is developed to solve high-resolution topology optimisation problems. An open-source computing platform, FEniCS, is used to parallelise the finite element analysis (FEA) and optimisation steps. Significant improvements in efficiency have been made to the FEA and the filtering process. An iterative solver, a reanalysis approach and a hard-kill option in BESO have been developed to reduce the computational cost of the FEA. An isotropic filter scheme is used to eliminate the time-consuming elemental adjacency search process. The efficiency and effectiveness of the developed method are demonstrated by a series of numerical examples in both 2D and 3D. It is shown that the parallel BESO can efficiently solve problems with more than 100 million tetrahedron elements on a 14-core CPU server. This work holds great potential for high-resolution design problems in engineering and architecture. Keywords: Topology optimisation, Bi-directional evolutionary structural optimisation, FEniCS, Parallel computing, High-resolution
... Among the plentiful methods of topology optimization, four methods have been widely investigated: the solid isotropic material with penalization (SIMP) method [15], the evolutionary structural optimization (ESO) method [16], the bidirectional evolutionary structural optimization (BESO) method [17], and the level-set method [18]. In topology optimization, extended functions and constraints are progressively introduced to overcome challenges in various science and engineering fields, such as biological morphogenesis [19][20][21], advanced manufacturing [22][23][24], and architectural design [25][26][27][28]. For example, the construction field exhibits several outstanding structures and buildings that have been designed using the extended methods of BESO [29]. ...
Article
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Ribbed floor systems, which include ribbed slabs and columns, are used extensively to enhance thestructural performance of buildings. With the emerging topology optimization and advancedmanufacturing techniques, the material usage and construction process of the ribbed floor systems canbe improved significantly to achieve higher efficiency and sustainability. This paper presents a digitaldesign and construction process for ribbed floor systems that combines a modified topologyoptimization method for ribbed slab design with a hybrid digital fabrication process for large-scaleconcrete casting. This new approach is tested through digital design and physical realization of a large-scale ribbed floor unit as proof of concept. The topologically optimized result and the constructed unitare compared with a famous historical floor system designed by Pier Luigi Nervi. The paper shows thatthe proposed design method, based on the bi-directional evolutionary structural optimization framework,can generate a slab design with a continuous rib layout and with higher structural stiffness. The paperalso demonstrates that 3D printing of formworks for casting ribbed slabs and complex-shaped columnsis feasible and sustainable. The new process presented in this paper can be used to design and constructa wide range of structures while minimizing material usage and labor cost.
... Different material properties can also influence the BESO result indirectly. A search illustrates that models with soft material may generate more structural members than the ones with hard material [35]. Therefore, a multimaterial setting is introduced to get more tree-like branches. ...
Article
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This research addresses innovations in building structural components through the generative design technique Bi-directional Evolutionary Structural Optimization (BESO) and the application of large-scale 3D robotic printing to produce efficient and elegant spatial structures. The innovative pavilion discussed in this paper demonstrates a design process and the ambitions of the research group through a full-scale model of large-span spatial structures. The focus of this work is the use of a modified BESO technique to optimize the structure, which features branches of various sizes and then applies ‘skin’ surfaces according to the direction of the main structure. The innovative production, construction, and assembling methodologies are to replace welded ultimately, forged, and cast components with large robotic 3D printed components and bolting methods. The advantages of the new design and construction process are less labor, fewer joints, shorter assembling time, lower cost & more efficient material usage and more complex & elegant large structural form.
... Several optimization techniques have been developed in the past decades, e.g., the solid isotropic material with penalization (SIMP) [10][11][12], the bi-directional evolutionary structural optimization (BESO) [13][14][15], the level set [16,17], and the moving morphable components (MMC) [18,19]. These techniques have been widely used in, e.g., aerospace engineering [20], biological materials [21][22][23], additive manufacturing [24], multi-disciplinary design [25],and architectural design [26,27]. ...
Article
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Shell structures are widely used in architectural design and civil engineering. However, it remains challenging to simultaneously optimize their shape, thickness, and topology under various design constraints and construction requirements. This work presents a method for the shape–thickness–topology coupled optimization of shell structures. In this method, the shape of shells is described by the non-uniform rational B-splines surface. Both shell elements and brick elements are used to discretize the design domain, so that the effect of shell thickness can be accounted for during the form-finding process. The structural self-weight is taken into consideration due to its practical importance. The minimum thickness is constrained to improve the constructability of the obtained designs. Several numerical examples are used to demonstrate the effectiveness of the proposed method. The results show that this method is capable of designing structurally efficient and aesthetically pleasing shells. This work holds potential applications in architectural design.
... The filter techniques can not only solve mesh-dependency and checkerboard problems but also can control the minimum length of the structural members. In addition to the filter techniques, multiple techniques have been developed to realize the length scale control, e.g., the neighborhood based method [28], the Heaviside projection based method [29,30], the structural skeleton concept based method [31][32][33], the structural indicator function based method [34], and the concept of offset surface based method [35]. However, the SCC of continuum structures is more complex. ...
Article
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Shape and topology optimization techniques aim to maximize structural performance through material redistribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. Structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two- and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Numerical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations.
... Through the long history of evolution, biological materials have evolved various degrees of robustness against structural randomness at different length scales (Gao et al., 2003;Zhao et al., 2018Zhao et al., , 2020. For example, Gao et al. (2003) Young's modulus of mineral platelets F Probability distribution function G Elastic strain energy density per area in a cohesive interface k + , k − , k unload Stiffnesses in the stiffening, softening, and unloading stages of the cohesive law l ...
Article
Biological materials have evolved various degrees of robustness against microscopic defects and structural randomness. Of particular interest here is whether and how nacre's brick–mortar microstructure suppresses the adverse effect of microstructural randomness. To this end, a tension–shear–chain (TSC) network model, combined with the virtual internal bond concept, is adopted to investigate the effects of microstructural randomness of nacre, where we show that the ensemble strength and failure behaviors of a larger TSC model exhibit substantially lower randomness. Our results indicate that the staggered brick–mortar microstructure renders nacre insensitive to microstructural randomness, resulting in enhanced resistance to strain localization and crack initiation at weaker interfaces. The influence of microstructural randomness on the size effect of the ensemble mechanical properties of nacre is also revealed. This study provides further insights and guidelines for designing strong and robust nacre-mimic composites.
... By imposing complex constraints in the form-finding process, advanced manufacturing techniques such as 3D-printing can be used directly to fabricate free-form designs generated by structural topology optimization [16,17]. Recently, a transdisciplinary computational framework was established to reveal the developmental mechanisms of animal and plant tissues through biomechanical morphogenesis [18,19]. Besides, much effort has been directed toward increasing the resolutions of the design domain [20,21], enhancing the manufacturability of the optimized results [22], improving the multi-material compatibility of the optimization process [23], and controlling the structural complexity and connectivity [24,25]. ...
Article
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Topology optimization has rapidly developed as a powerful tool of structural design in multiple disciplines. Conventional topology optimization techniques usually optimize the material layout within a predefined, fixed design domain. Here, we propose a subdomain-based method that performs topology optimization in an adaptive design domain (ADD). A subdomain-based parallel processing strategy that can vastly improve the computational efficiency is implemented. In the ADD method, the loading and boundary conditions can be easily changed in concert with the evolution of the design space. Through the automatic, flexible, and intelligent adaptation of the design space, this method is capable of generating diverse high-performance designs with distinctly different topologies. Five representative examples are provided to demonstrate the effectiveness of this method. The results show that, compared with conventional approaches, the ADD method can improve the structural performance substantially by simultaneously optimizing the layout of material and the extent of the design space. This work might help broaden the applications of structural topology optimization.
... The septate pattern is related to the circular culm and larger plants, although the opposite is not verified, since the spongy type occurs in all culm formats and species size. In both the spongy and septate patterns the gaps decrease in size to the periphery improving the load capacity, since the stresses are distributed more evenly (Zhao et al. 2018). Due to the wide distribution in Eleocharis, we can assume that the mixed spongy aerenchyma pattern would be more efficient in resistance, due to the spreading of the vascular bundles, and the septate more efficient in transporting and reserving oxygen due to the large gaps and tissue reduction (see Williams & Barber 1961). ...
Article
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Eleocharis (Cyperaceae) includes more than 300 species of perennial or annual herbs, frequently found on poorly drained soils. The species are morphologicaly similar, and the taxonomy is difficult because their vegetative and reproductive structures are very reduced. Previous study on the stem architecture in the subgenus Limnochloa showed that anatomical features help in the interpretation of the evolution, taxonomy and ecological aspects of the group. Our objectives were to add new characters from the stem (= culm) structure, to explore the characters in a greater number of Eleocharis species, representatives of the other subgenera, and add these data in a new phylogenetic analysis with molecular data. The study covered 68 species obtained from herbaria and fixed material. In addition to the stem architecture, the internal organization of the tissues, the cross-section format, the presence or absence of stretched cells in aerenchyma air gaps and the plant size were included in the morphological analysis. Our data confirm that spongy aerenchyma pattern is the ancestral condition while the mixed and septate patterns occurred independent and punctually. Only the cross-section format was variable among specimens while the other characters were uniform and relevant for taxonomic use.
... Topology optimization reveals the evolutionary logic in nature worlds in some ways (Xie and Steven, 1997;Zhao et al., 2018) and can be used as an analysis instrument to simulate architects' works on classical structures of traditional buildings, such as the Sagrada Familia (Burry et al., 2005) and Palazzeto Dellospori of Rome (Yan et al., 2019). Moreover, several architects and engineers have adopted topology optimization as conceptual form-finding methods in architectural projects (Fig. 1). ...
Article
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With the ability to generate forms with high efficiency and elegant geometry, to-pology optimization has been increasingly used in architectural and structural designs. However , the conventional topology optimization techniques aim at achieving the structurally most efficient solution without any potential for architects or designers to control the design details. This paper introduces three strategies based on Bi-directional Evolutionary Structural Optimization (BESO) method to artificially pre-design the topological optimized structures. These strategies have been successfully applied in the computational morphogenesis of various structures for solving practical design problems. The results demonstrate that the developed methodology can provide the designer with structurally efficient and topologically different solutions according to their proposed designs with multi-filter radii, multi-volume fractions, and multi-weighting coefficients. This work establishes a general approach to integrating objective topology optimization methods with subjective human design preferences, which has great potential for practical applications in architecture and engineering industry.
... Despite for the fact that the discrete nature of BESO makes it high efficient in determining structural boundary compared to density-based methods, research on extending the method to include length scale constraints is rather limited. To the author's best knowledge, only Zhao et al. [45] proposed a maximum length scale control scheme in BESO for inner architecture design of emergent plants, mimicking the internal texture of leaf veins and grass. And Yan et al. [46] achieve the minimum length scale control in BESO with the help of skeleton. ...
Article
This work develops length scale control schemes for Bi-directional Evolutionary Structural Optimization (BESO) method, enabling an enhanced and flexible control of the method on structural member sizes. Specifically, the maximum length scale control is achieved by constraining local material volumes below a threshold value, which is determined upon the allowed maximum length. The massive per-element volume constraints are aggregated by the p-norm global measure. The aggregated volume constraint is augmented to the conventional compliance design objective through a Lagrange multiplier. On the other hand, the minimum length scale control is achieved by a post-processing modification of local feature according to the skeleton detected from a preliminarily optimized topology. The sensitivity numbers of the local structural features that violate the minimum length scale constraint are compensated during the post-processing modification. Both 2D and 3D benchmark design results show that the proposed schemes are effective and efficient in controlling both the maximum and minimum structural length scales.
... The original intention of reducing low efficient materials are the same for both topology optimization and evolution of biological structures in nature. Topology optimization has not only been applied in engineering structural design but also for exploring the optimization mechanisms of biological materials (Zhao et al., 2018;Zhao et al., 2020aZhao et al., , 2020b. Apart from the advantages of achieving high structural performance and low material usage, beautiful structure appearance is also a by-product from topology optimization. ...
Article
Purpose-Furniture plays a significant role in daily life. Advanced computational and manufacturing technologies provide new opportunities to create novel, high-performance and customized furniture. This paper aims to enhance furniture design and production by developing a new workflow in which computer graphics, topology optimization and advanced manufacturing are integrated to achieve innovative outcomes. Design/methodology/approach-Workflow development is conducted by exploring state-of-the-art computational and manufacturing technologies to improve furniture design and production. Structural design and fabrication using the workflow are implemented. Findings-An efficient transdisciplinary workflow is developed, in which computer graphics, topology optimization and advanced manufacturing are combined. The workflow consists of the initial design, the optimization of the initial design, the postprocessing of the optimized results and the manufacturing and surface treatment of the physical prototypes. Novel chairs and tables, including flat pack designs, are produced using this workflow. The design and fabrication processes are simple, efficient and low-cost. Both additive manufacturing and subtractive manufacturing are used. Practical implications-The research outcomes are directly applicable to the creation of novel furniture, as well as many other structures and devices. Originality/value-A new workflow is developed by taking advantage of the latest topology optimization methods and advanced manufacturing techniques for furniture design and fabrication. Several pieces of innovative furniture are designed and fabricated as examples of the presented workflow.
... The original intention of reducing low efficient materials are the same for both topology optimization and evolution of biological structures in nature. Topology optimization has not only been applied in engineering structural design, but also for exploring the optimization mechanisms of biological materials (Zhao et al., 2018;Zhao et al., 2020aZhao et al., , 2020b. ...
Article
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Purpose Furniture plays a significant role in daily life. Advanced computational and manufacturing technologies provide new opportunities to create novel, high-performance and customized furniture. This paper aims to enhance furniture design and production by developing a new workflow in which computer graphics, topology optimization and advanced manufacturing are integrated to achieve innovative outcomes. Design/methodology/approach Workflow development is conducted by exploring state-of-the-art computational and manufacturing technologies to improve furniture design and production. Structural design and fabrication using the workflow are implemented. Findings An efficient transdisciplinary workflow is developed, in which computer graphics, topology optimization and advanced manufacturing are combined. The workflow consists of the initial design, the optimization of the initial design, the postprocessing of the optimized results and the manufacturing and surface treatment of the physical prototypes. Novel chairs and tables, including flat pack designs, are produced using this workflow. The design and fabrication processes are simple, efficient and low-cost. Both additive manufacturing and subtractive manufacturing are used. Practical implications The research outcomes are directly applicable to the creation of novel furniture, as well as many other structures and devices. Originality/value A new workflow is developed by taking advantage of the latest topology optimization methods and advanced manufacturing techniques for furniture design and fabrication. Several pieces of innovative furniture are designed and fabricated as examples of the presented workflow.
... Guest and Prévost initially proposed a maximum length dimension restriction by requiring a minimum void volume in a neighborhood surrounding each voxel, in which a penalty term for the objective function and barrier function was introduced [29][30][31]. The maximum size was also integrated into the bi-directional evolutionary structural optimization method [32,33]. Wu et al. proposed infill formulation by imposing the local volume fraction (LVC) on the given region [34]. ...
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Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such as the p-norm aggregation and implicit porosity control, the violation of the maximum local volume constraint is inevitable. To this end, the primary optimization problem with bounds of local volume constraints is transformed into unconstrained programming by setting up a sequence of minimization sub-problems in terms of the augmented Lagrangian method. The approximation and algorithm using the concept of moving asymptotes is employed as the optimizer. Several numerical tests are provided to illustrate the effectiveness of the proposed approach in comparison with existing approaches. The effects of the global and local volume percentage, influence radius and mesh discretization on the final designs are investigated. In comparison to existing methods, the proposed method is capable of accurately limiting the upper bound of global and local volume fractions, which opens up new possibilities for additive manufacturing.
... Most recently, imposing complicated constraints during the form-finding process has been realized (Chen et al., 2020;He et al., 2020;Xiong et al., 2020;Zhao et al., 2020a). By establishing transdisciplinary computational methods for biomechanical morphogenesis, Zhao et al. (2018Zhao et al. ( , 2020bZhao et al. ( , 2020c 4 have revealed the optimization mechanisms of, e.g., plant leaves and animal stingers. Using topology optimization, a golden ratio distribution rule is found in venation systems (Sun et al., 2018). ...
Article
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The unique, hierarchical patterns of leaf veins have attracted extensive attention in recent years. However, it remains unclear how biological and mechanical factors influence the topology of leaf veins. In this paper, we investigate the optimization mechanisms of leaf veins through a combination of experimental measurements and numerical simulations. The topological details of three types of representative plant leaves are measured. The experimental results show that the vein patterns are insensitive to leaf shapes and curvature. The numbers of secondary veins are independent of the length of the main vein, and the total length of veins increases linearly with the leaf perimeter. By integrating biomechanical mechanisms into the topology optimization process, a transdisciplinary computational method is developed to optimize leaf structures. The numerical results show that improving the efficiency of nutrient transport plays a critical role in the morphogenesis of leaf veins. Contrary to the popular belief in the literature, this study shows that the structural performance is not a key factor in determining the venation patterns. The findings provide a deep understanding of the optimization mechanism of leaf veins, which is useful for the design of high-performance shell structures.
... There has been extensive research on the topology optimization of the single-material continuum based on the BESO method [8,9]. Apart from the applications to architectural design [10] and mechanical design [11], the BESO method has also been introduced to the fields of advanced materials [12], aircraft design [13] and biomechanics [14,15]. ...
Article
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Topology optimization techniques based on finite element analysis have been widely used in many fields, but most of the research and applications are based on single-material structures. Extended from the bi-directional evolutionary structural optimization (BESO) method, a new topology optimization technique for 3D structures made of multiple materials is presented in this paper. According to the sum of each element's principal stresses in the design domain, a material more suitable for this element would be assigned. Numerical examples of a steel-concrete cantilever, two different bridges and four floor systems are provided to demonstrate the effectiveness and practical value of the proposed method for the conceptual design of composite structures made of steel and concrete.
... He took the physical mechanisms such as tension, compression and bending moment as the basis for cataloging the formation of natural forms, and named the morphological generating process as self-forming process (Figure 1; Siegfried 1990). In recent years, some scholars have combined physical model with theoretical model to explore the generating law and physical mechanism of natural morphology by means of computer-aided simulation (Zhao et al. 2018). These studies analyzed the geometric and mechanical principles of natural form from the quantitative perspective, and introduced the potential of the relevant principles applied in the fields of architecture, machinery and so on. ...
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This paper introduces a bioinspired structure design method in the conceptual stage and takes the human femur section as an example, to extract the structural principle from the natural form, and summarizes as the morphological operation rules. The morphological manipulation rules provide a geometric feedback-based design process of both the building structural performance and its space with the manipulation rule of Graphic static. While extracting building structural principle, the Layout Optimization method is applied to obtain the force flow inside the nature biological form boundary under a certain load, and the force flow is presented with strut and tie model, summarizing the structural characteristic of human femur. The combinatorial and transformation methods of graphic statics are employed in the morphological operation stage to transform the form diagram while maintaining equilibrium, which facilitates designers to explore the structural form from both performance and space perspectives. Finally, the design process of a stadium inspired by the human femur is taken as an example to demonstrate how the introduced workflow can be used in the conceptual design stage and optimization of buildings.
... Several notable topology optimisation methods have been widely developed in topology optimisation field, e.g. the homogenisation method (Bendsoe 1989;Bendsoe and Kikuchi 1988), the solid isotropic material with penalisation (SIMP) method (Bendsoe and Sigmund 1999;Bendsoe and Sigmund 2004), the evolutionary structural optimisation (ESO) (Xie and Steven 1993;Xie and Steven 1994), the bi-directional evolutionary structural optimisation (BESO) ) (see figure 3) and the level-set method (LSM) (Wang et al. 2003;Allaire et al. 2004). Among others, BESO method has been proved to be a reliable optimisation technique, which has been successfully applied in many engineering and architectural design (Zhao et al. 2018;Yan et al. 2019;Burry et al. 2005). Although most topology optimisation techniques aim at achieving the most optimised solution, the structural layout with the highest performance may contradict the functional requirements and aesthetic designing concepts in real problematic practices. ...
Conference Paper
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This paper posits a design approach that integrates multi-agent generative algorithms and structural topology optimisation to design intricate, structurally efficient forms. The research proposes a connection between two dichotomous principles: architectural complexity and structural efficiency. Both multi-agent algorithms and Bi-directional evolutionary structural optimisation (BESO) (Huang and Xie 2010), are emerging techniques that have significant potential in the design of form and structure.This research proposes a structural behaviour feedback loop through encoding BESO structural rules within the logic of multi-agent algorithms. This hybridisation of topology optimisation and swarm intelligence, described here as SwarmBESO, is demonstrated through two simple structural models. The paper concludes by speculating on the potential of this approach for the design of intricate, complex structures and their potential realisation through additive manufacturing.
... The second substrategy characterizes the optimization problem, and considers constant relative stiffness between roof and columns. This method was previously demonstrated by [30], with constant relative stiffness being enforced during optimization to ensure that the algorithm was solving the equivalent structural system in every iteration. In this study, implementing constant relative stiffness can effectively improve the optimization result, as the columns' axial stiffness can vary throughout optimization to give different structural systems. ...
Article
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The roof–column structural system is utilized for many engineering and architectural applications due to its structural efficiency. However, it typically requires column locations to be predetermined, and involves a tedious trial-and-error adjusting process to fulfil both engineering and architectural requirements. Finding efficient column distributions with the aid of computational methods, such as structural optimization, is an ongoing challenge. Existing methods are limited, with continuum methods involving the generation of undesired complex shapes, and discrete methods involving a time-consuming process for optimizing columns’ spatial order. This paper presents a new optimization method to design the distribution of a given number of vertical supporting columns under a roof structure. A computational algorithm was developed on the basis of the optimality-criterion (OC) method to preserve and removed candidate columns pre-embedded with design requirements. Three substrategies are presented to improve optimizer performance. The effectiveness of the new method was validated with a range of roof–column structural models. Treating column locations as design variables provides opportunities to significantly improve structural performance.
... The topology optimization method [27][28][29][30] has widely been evoked to design the microstructures of materials [31]. In particular, concurrent topology optimization schemes have been developed for designing both the first-and second-level structures consisting of different unit blocks [32][33][34]. ...
Article
Design of fractal microstructures holds promise for developing advanced materials with improved mechanical properties and multiple functions. In this paper, a concurrent topology optimization method is proposed to design both two-and three-dimensional, fractal or hierarchical microstructures. The Boolean subtraction operator (BSO) is introduced to guarantee the self-similarity among a hierarchical structure at different levels. This method allows us to generate a diversity of fractal structures which have, for instance, the geometric feature of either clockwise or counterclockwise chirality. By evoking the fractal Menger sponge as the non-designed domain, we have obtained fractal structures in which all internal transversal sections have hybrid fractal morphologies. Though our attention is here focused only on the mechanical properties of materials, the proposed method can also be applied to design fractal structures with optimal optical, acoustic, and electromagnetic properties.
... As a kind of follow-up, Zhao, Liu and Feng have investigated the aeroelastic behavior of Typha (an emergent aquatic macrophyte) blades in wind (Zhao et al. 2016). The biomechanical morphogenesis of the leaves and stalks of representative emergent plants, which can stand upright and survive in harsh water environments, has been considered in Zhao et al. (2018). In Zhao et al. (2020), it has been demonstrated that the leaves and stalks of several species of emergent plants exhibit morphologies of twisting and gradient chirality. ...
Article
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The static properties of leaves with parallel venation from terrestrial orchids of the genus Epipactis were modelled as coupled elastic rods using the geometrically exact Cosserat theory and the resulting boundary-value problem was solved numerically using a method from Shampine, Muir and Xu. The response of the leaf structure to the applied force was obtained from preliminary measurements. These measurements allowed the Young's modulus of the Epipactis leaves to be determined. The appearance of wrinkles and undulation characteristics for some leaves has been attributed to the small torsional stiffness of the leaf edges.
... Successful applications of topology optimization include the creation of bio-scaffolds for hip implants [25,26], the design of aerospace structures [27], and elucidating the structure-property relationship in plants [28]. In the field of turbomachinery, however, most topology optimization research have focused on improving the contour of the blades [29,30]. ...
Article
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Gas turbine blades are subjected to unusually harsh operating conditions—rotating at high velocities in gas streams whose temperature can exceed the melting temperature of the blade. In order to survive these conditions, the blade must efficiently transfer heat to an internal cooling flow while effectively managing mechanical stresses. This work describes a new design strategy for the internal structure of turbine blades that makes use of architected materials tailored to reduce stresses and temperatures throughout the blade. A full 3D characterization was first performed to determine the thermomechanical properties of generalized honeycomb materials with different design parameters: honeycomb angle and wall thickness. A turbine blade cross section was then divided into multiple discrete domains so that different generalized honeycomb materials could be assigned to each of the domains. Optimization of the material assignments was performed in order to minimize the stress ratio—ratio of the maximum Mises' stress and the temperature dependent yield stress—in the entire model. The optimized design showed substantial improvement with respect to a baseline model; the factor of safety was increased by 171%, while the maximum Mises' stress and temperature decreased by 42% and 72% respectively. The use of generalized honeycomb materials allows for local control of the material properties to tune the performance of the turbine blade. The results of the optimization clearly indicate that auxetic honeycombs outperform conventional designs; since their lower in plane stiffness helps to reduce stresses caused by thermal gradients. Our results demonstrated the feasibility of using 3D printing compatible architected materials in turbine blades to increase their factor of safety and potentially increase operating temperatures to improve thermal efficiency.
... Later researchers proposed several methods for topology optimization of continuum structures, e.g., the solid isotropic material with penalization (SIMP) method [2], the bi-directional evolutionary structural optimization (BESO) method [3], [4] and the level set method (LSM) [5], [6], etc. By changing the prescribed objective, these techniques can be applied to various disciplines, including biomechanics [7], thermodynamics [8], [9] acoustics [10] and optics [11], [12]. ...
Article
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Background: As an advanced design technique, topology optimization has received much attention over the past three decades. Topology optimization aims at finding an optimal material distribution in order to maximize the structural performance while satisfying certain constraints. It is a useful tool for the conceptional design. At the same time, additive manufacturing technologies have provided unprecedented opportunities to fabricate intricate shapes generated by topology optimization. Objective: To design a highly efficient structure using topology optimization and to fabricate it using additive manufactur-ing. Method: The bi-directional evolutionary structural optimization (BESO) technique provides the conceptional design, and the topology-optimized result is post-processed to obtain smooth structural boundaries. Results: We have achieved a highly efficient and elegant structural design which won the first prize in a national competition in China on design optimization and additive manufacturing. Conclusion: In this paper, we present an effective topology optimization approach to maximizing the structural load-bearing capacity and establish a procedure to achieve efficient and elegant structural designs. In the loading test of the final competition, our design carried the highest loading and won the first prize of the competition, which clearly demonstrates the capability of BESO in engineering applications.
... As surprising as it is to develop topological optimization methods in engineering, it is even more exciting to see scholars achieve success with this methodology in botanical research [28]. Vein-inspired patterns have been applied in heat conduction systems, based on a design idea originating from the self-adaptive growth of veins such that the flow resistance through the whole network is minimized [29]. ...
Article
The stiffness and heat dissipation of thin planar structures in industrial engineering are taken as the background for this research. Plant leaves with various vein patterns, such as tobacco (Nicotiana tabacum L.) and chili (Capsicum annuum L.) leaves, are treated as the research objects. Through a combination of morphological and mechanical analysis, the distribution patterns and properties of leaf veins are mathematically characterized. A topological optimization algorithm is employed to simulate the vein growth process, thus revealing the effects of the mechanical and biological properties of different leaves on their vein morphologies. Additionally, the angles between the main and secondary veins are controlled to satisfy biological constraints. This comprehensive exploration of vein morphological formation can serve as a reference for the design of bionic thin planar structures in engineering.
... The ESO and BESO methods have been used for solving topology optimization problems in many areas of structural engineering. These problems include structural frequency optimization (Xie and Steven 1994), minimizing structural volume with a displacement or compliance constraint (Liang et al. 2000), structural complexity control in topology optimization (Zhao et al. 2020a;Xiong et al. 2020), topology optimization for energy absorption structures (Huang et al. 2007), design of periodic structures (Huang and Xie 2008), geometrical and material nonlinearity problems (Huang and Xie 2007a), stiffness optimization of structures with multiple materials (Huang and Xie 2009), maximizing the fracture resistance of quasi-brittle composites (Xia et al. 2018a), stress minimization designs (Xia et al. 2018b), biomechanical morphogenesis (Zhao et al. 2018(Zhao et al. , 2020b, stiffness maximization of structures with von Mises constraints (Fan et al. 2019), and diverse and competitive designs (Xie et al. 2019;Yang et al. 2019;He et al. 2020). ...
Article
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Previous studies on topology optimization subject to stress constraints usually considered von Mises or Drucker–Prager criterion. In some engineering applications, e.g., the design of concrete structures, the maximum first principal stress (FPS) must be controlled in order to prevent concrete from cracking under tensile stress. This paper presents an effective approach to dealing with this issue. The approach is integrated with the bi-directional evolutionary structural optimization (BESO) technique. The p-norm function is adopted to relax the local stress constraint into a global one. Numerical examples of compliance minimization problems are used to demonstrate the effectiveness of the proposed algorithm. The results show that the optimized design obtained by the method has slightly higher compliance but significantly lower stress level than the solution without considering the FPS constraint. The present methodology will be useful for designing concrete structures.
... Different topology optimization methods, such as the homogenization method [1,2], the solid isotropic material with penalization (SIMP) method [2,3], the level set method [4,5] and the bi-directional evolutionary structural optimization (BESO) method [6][7][8] have been used widely in multiple disciplines [9][10][11][12]. The structural design in many architectural and engineering projects was based on the BESO method [13][14][15]. According to the structural contribution of each element, the BESO method gradually removes inefficient elements from the structure and adds elements to the most needed areas. ...
Conference Paper
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Topology optimization techniques are widely used to maximize the performance or minimize the weight of a structure through optimally distributing its material within a prescribed design domain. However, existing optimization techniques usually produce a single optimal solution for a given set of loading and boundary conditions. In architectural design, it is highly desirable to obtain multiple design options which possess not only high structural performance, but also distinctly different shapes and forms. Here we propose three simple and effective strategies for achieving diverse and competitive structural designs, including: (i) penalizing precedent designs, (ii) using constraints as design drivers, and (iii) introducing randomness into structural models. These strategies are successfully applied in the computational morphogenesis of a variety of structures. The results demonstrate that the developed methodology is capable of providing the designer with structurally efficient and topologically different solutions. The structural performance of alternative designs is only slightly lower than that of the optimal design. This methodology holds great potential for practical applications in architecture and engineering. The proposed strategies are applicable to commonly used topology optimization techniques, although examples shown in this study are based on the bi-directional evolutionary structural optimization (BESO) technique.
... Another way to indirectly influence the BESO result is to set the material properties and evolutionary parameters. With the different relative material Young's modulus, the distribution density of BESO structures between the two materials can be designed purposefully [5]. For example, Figure 2 ...
Conference Paper
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This research explores innovations in structural design and construction through the generative design technique BESO (Bi-directional Evolutionary Structural Optimization)[1]and the application of robotic fabrication to produce efficient and elegant spatial structures. The innovative pavilion discussed in this paper demonstrates a design and fabrication process and thecollaborationbetween architecture and engineering research groups through a series of small-scale test models and a full-scale model of topologically optimized spatial structures. The focus of this work is the use of a modified BESO technique to optimize the structure which features branches of various sizes, inspired by Gaudi’s Sagrada Familia Bacilica, and the introduction of large-scalerobotic 3D printing developed at RMIT University.The advantages of the new design and construction process are efficient material usage and elegant structural forms.
... Several optimization techniques have attracted much attention, including the homogenization method [1,2], the solid isotropic material with penalization (SIMP) method [2,3], the level-set method [4,5], and the bi-directional evolutionary structural optimization (BESO) method [6][7][8]. Among others, the BESO method has been proved to be a reliable optimization technique, which has been successfully applied in many engineering designs [9][10][11][12]. BESO is a gradient-based method. ...
Article
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Topology optimization techniques have been widely used in structural design. Conventional optimization techniques usually are aimed at achieving the globally optimal solution which maximizes the structural performance. In practical applications, however, designers usually desire to have multiple design options, as the single optimal design often limits their artistic intuitions and sometimes violates the functional requirements of building structures. Here we propose three stochastic approaches to generating diverse and competitive designs. These approaches include (1) penalizing elemental sensitivities, (2) changing initial designs, and (3) integrating the genetic algorithm into the bi-directional evolutionary structural optimization (BESO) technique. Numerical results demonstrate that the proposed approaches are capable of producing a series of random designs, which possess not only high structural performance, but also distinctly different topologies. These approaches can be easily implemented in different topology optimization techniques. This work is of significant practical importance in architectural engineering where multiple design options of high structural performance are required.
... Liu et al also employed the BESO method to realize the sound insulation of the pyramidal lattice sandwich structure [49], which can be effectively utilized for designing light-weight load bearing structures for ranging from ground to aerospace vehicles. Zhao et al [50] addressed the internal architecture of emergent plants using the BESO method, who provided a comprehensive discussion about the main reason of the organs in plants living in the same natural environment and evolving into a wide variety of geometric architecture. Huang, Radman and etc [51][52][53] also used the ESO/BESO method to discuss the topology optimization of material microstructures with the extreme material properties, like the maximal bulk modulus and maximal shear modulus. ...
Thesis
It is known that topology optimization is located at the conceptual design phase, which can effectively determine the numbers, connectivity and existence of holes in the structural design domain and evolve design elements to improve the concerned performance. General speaking, topology optimization works as an important tool to seek for the optimal material distribution, which has been identified as one of the most promising sub-field of structural optimization due to its superior features occurring in the conceptual design stage without prior knowledge of the design domain. In the current work, the main intention is to propose a novel numerical method for the topology optimization with more effectiveness and efficiency for the single-material structures and structures with multiple materials. Meanwhile, the proposed topology optimization method is also applied to implement the rational design of auxetic metamaterials and auxetic composites. In Chapter 1, we provide a brief description for the main intention of the current work. In Chapter 2, the comprehensive review about the developments of topology optimization, isogeometric topology optimization and the rational design of auxetic materials is provided. In Chapter 3, a more effective and efficient topology optimization method using isogeometric analysis is proposed for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF mainly involves two steps: (1) the smoothness of nodal densities is improved by the Shepard function; (2) the higher-order NURBS basis functions are combined with the smoothed nodal densities to construct the DDF with the continuity. A topology optimization formulation to minimize the structural mean compliance is developed using the DDF and isogeometric analysis (IGA) is applied to solve structural responses. An integration of the geometry parametrization and numerical analysis offer several benefits for the optimization. The Chapter 4 intends to develop a Multi-material Isogeometric Topology Optimization (M-ITO) method. Firstly, a new Multi-material Interpolation model is established with the use of NURBS (Non-uniform Rational B-splines), termed by the “N-MMI” model, which mainly involves three components: (1) Multiple Fields of Design Variables (DVFs); (2) Multiple Fields of Topology Variables (TVFs); (3) Multi-material interpolation. Two different M-ITO formulations are developed using the N-MMI model to address the problems with multiple volume constraints and the total mass constraint, respectively. The decoupled expression and serial evolving of the DVFs and TVFs can effectively eliminate numerical difficulties in the multi-material problems. In Chapter 5, the proposed ITO method is applied for the systematic design of both 2D and 3D auxetic metamaterials. An energy-based homogenization method (EBHM) to evaluate the macroscopic effective properties is numerically implemented by IGA, with the imposing of periodic boundary formulation on material microstructure. An ITO formulation for 2D and 3D auxetic metamaterials is developed using the DDF, where the objective function is defined as a combination of the homogenized elastic tensor. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. In Chapter 6, the proposed M-ITO method is applied for the systematic design of both 2D and 3D auxetic composites. The homogenization, that evaluates macroscopic effective properties of auxetic composites, is numerically implemented by IGA, with the imposing of the periodic boundary formulation on composite microstructures. The developed N-MMI model is applied to describe the multi-material topology and evaluate the multi-material properties. A topology optimization formulation for the design of both two-dimensional (2D) and three-dimensional (3D) auxetic composites is developed. Finite element simulations of auxetic composites are discussed using the ANSYS to show different deformation mechanisms. Finally, conclusions and prospects are given in Chapter 7.
... Compared with the transverse ribs of traditional box girder, the bionic design of bamboo can correspondingly reduce the number of transverse ribs, which could meet the stability requirements, as well as the lightweight requirements, while also meeting the strength and toughness requirements. Zhao et al. [134] explored the biomechanical morphology of the leaves and stems of representative emergent plants by combining experimental and numerical methods, and they developed an interdisciplinary topological optimization method that combines mechanical properties and dual ecological constraints. In the two-way evolutionary structure optimization technique, the proposed biophysical insights are expected to be used to design efficient and advanced structures (aircraft wings and turbine blades). ...
Article
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In the field of mechanical equipment manufacturing, the focus of research and development is not on weight reduction, but on how to choose between the rigidity and performance of components (such as strength or flexibility). For this contradiction, lightweight is one of the best solutions. The problems associated with lightweight were initially considered and systematically studied in aircraft manufacturing in engineering. Therefore, lightweight has been greatly developed in aviation research and has played an increasingly important role in construction machinery. This paper presents a brief description of the current status of lightweight in machinery by reviewing some significant progress made in the last decades. Potential research topics are also discussed from the four aspects of material, structure, bionics, and manufacturing, and they forecast the development trend of lightweight in the future construction machinery. The entire body of literature about the field is not covered due to the limitation of the length of paper. The scope of this review is limited and closely related to the development of lightweight technology in engineering applications.
... Through a long history of natural selection, many biological tissues and organs have evolved into elegant architecture with superior mechanical properties [1,2]. Natural materials take a wide diversity of morphologies, such as hierarchies, arrays, spirals, and fractals, which have attracted much attention from the viewpoint of mechanics and materials science [3,4]. Among others, twisting chirality exists in the slender organs of various plants, for examples, the leaves of Typha orientalis (Fig. 1A), Sparganium stoloniferum, Acorus calamus, Pancratium maritimum, and Narcissus poeticus, the stalks of Scirpus rosthorni and Sagittaria trifolia, the petals of Paphiopedilum dianthum, and the roots of Arabidopsis [5][6][7][8][9][10]. ...
Article
The mechanical properties and biological functions of tissues and organs in plants are closely related to their structural forms. In this study, we have performed systematic measurements and found that the leaves and stalks of several species of emergent plants exhibit morphologies of twisting and gradient chirality. Inspired by the experimental findings, we investigate, both theoretically and numerically, the static bending and vibrational properties of these plant organs. By modeling the leaves and stalks as pre-twisted cantilever beams, the effects of the cross-sectional geometry, loading condition, handedness perversion, twisting configuration, and morphological gradient, on their mechanical behavior are evaluated. Our analysis reveals that both static and dynamic responses of the beams can be easily tuned by changing their structural parameters. For any part of the beams, its chiral morphology has more significant influences on the overall structural performance (e.g., bending stiffness and natural frequencies) if it is closer to the clamped end. This work not only deepens our understanding of the structure–property–function interrelations of chiral plants, but also holds potential applications in the bio-inspired design of innovative devices and structures.
... Several optimization techniques have been developed in the past three decades, including the solid isotropic material with penalization (SIMP) [1][2][3], the level set [4][5][6], and the bi-directional evolutionary structural optimization (BESO) [7][8][9][10][11]. These techniques have made significant contributions to the areas of, e.g., advanced structures and materials, mechanical and civil engineering, architecture industry, and aerospace and automotive industry [12][13][14][15][16]. The techniques have also provided an excellent platform for the biomechanical morphogenesis of living systems with hierarchical structures [17] and the design of micro and nano systems such as photonic crystals, waveguides, resonators, filters, and plasmonics [18][19][20]. Although a number of remarkable achievements have been made in the field of structural topology optimization, technologically challenging and practically important issues still exist. ...
Article
Structural shape and topology optimization has undergone tremendous developments in recent years due to its important applications in many fields. However, effectively controlling the structural complexity of the optimization result remains a challenging issue. The structural complexity is usually characterized by the distribution and geometries of interior holes. In this work, a new approach is developed based on the graph theory and the set theory to control the number and size of interior holes of the optimized structures. The minimum distance between the edges of any two neighboring holes can also be constrained. The structural performance and the effect of the structural complexity control are well balanced by using this approach. We use three typical numerical examples to verify the effectiveness of the developed approach. The optimized structures with and without constraints on the structural complexity are quantitatively compared and analyzed. The present methodology not only enables the designer to have a direct control over the topology of the optimized structures, but also provides diverse and competitive solutions.
... Topology optimization ( Bendsoe & Sigmund, 2003;Huang & Xie, 2010;Wang, Wang, & Guo, 2003 ) recasts a structural design problem into a mathematical programming problem. It has been used in design of aerospace vehicles ( Aage, Andreassen, Lazarov, & Sigmund, 2017;Zhu, Zhang, & Xia, 2016 ), additive manufactured products Wang & Kang, 2017 ), optical and acoustic metasurfaces ( Callewaert, Velev, Kumar, Sahakian, & Aydin, 2018;He & Kang, 2018;Lin et al., 2018 ) and biomechanical structures ( Zhao, Zhou, Feng, & Xie, 2018 ). In particular, in conjunction with the inverse homogenization method ( Sigmund, 1994;Sigmund & Torquato, 1997 ), topology optimization has been used to design microstructures with various target properties, e.g. ...
Article
Mechanical properties of hierarchical lattice structures depend not only on their overall shapes and topologies, but also on their microstructural configurations. This paper proposes a new method for concurrent topology optimization of structures composed of layer-wise graded lattice microstructures. Both macroscale design variables representing the distribution of different lattice materials and microscale design variables defining the topologies of the microstructural unit cells are to be simultaneously optimized. This formulation thus integrates the microstructure design into the structural design, instead of pursuing a grey macroscale design and then interpreting the intermediate densities into certain microstructures. The proposed method also enlarges the design space by allowing for graded microstructures. Two new design constraints, namely the structural coverage constraint and the average porosity constraint, are introduced into the proposed optimization formulation to reduce the complexity of the constraints in the layer-wise graded design. The macroscale and microscale designs are linked by using the Asymptotic homogenization method to compute the effective elastic properties of the microstructured materials. Numerical examples show validity of the proposed method. It is also found that layer-wise graded lattice structures outperform those with uniform lattice microstructures in terms of structural stiffness. Finite element simulations of constructed models of the optimized designs suggest that graded lattice structures exhibit higher buckling resistance and ultimate load bearing capacity than single-scale solid material structures or uniform lattice structures under the same material usage.
... In this fields, one of the most extensive attention is the layout design of functionally graded structures over the last few years. However, most existing researches mainly focus on the design of structures whose material properties are graded in whole design domain [26][27][28][29][30][31][32][33][34][35][36], and there exists very little researches on topology optimization of FG structures that simultaneously includes uniform and graded parts. From the perspective of material distribution description, design of structure with graded surface is much more challenging than design of pure uniform or graded structure. ...
Article
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Ribbed slabs are widely used in the building industry. Designing ribbed slabs through conventional engineering techniques leads to limited structural forms, low structural performance and high material waste. Topology optimization is a powerful tool for generating free-form and highly efficient structures. In this research, we develop a mapping constraint optimization approach to designing ribbed slabs and shells. Compared with conventional ones, the presented approach is able to produce designs with higher performance and without isolated ribs. The approach is integrated into three optimization methods and used to design both flat slabs and curved shells. Several numerical examples are used to demonstrate the effectiveness of the new approach. The findings of this study have potential applications in the design of aesthetically pleasing and structurally efficient ribbed slabs and shells.
Article
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This paper presents a study of the morphogenesis of brain corals based on an experimental investigation and a topological optimization method. The resistance to matter interchange was employed to allocate the optimal space for the growth of polyp colonies from the perspective of topological optimization, where the optimized structures are those of natural brain corals. Computational fluid dynamics simulations revealed that these complicated structures can provide shelter to protect polyps from ocean currents. A reverse mold was prepared from silica gel and used to cast models from mixtures of cement and calcium carbonate, where the mixture ratio was determined based on compressive strength and biocompatibility. Based on an acid corrosion experiment, the matter interchange capability was verifi�ed. This study also proved that the many folds in the structure of brain corals contribute to the circulation of seawater, thus maintaining the concentration of nutrients and hindering the deposition of harmful substances. This paper establishes an innovative methodology for the creation of artificial brain corals, which is important for environmental restoration. Keywords: Brain corals, Topological optimization, Turbulent hydrodynamics, Matter interchange
Article
In this paper, the length scale control (LSC) methods, including the maximum length scale control (MaxLSC) and the minimum length scale control (MinLSC) for both the solid and void phase, are proposed for density-based multi-material topology optimization. The three-field approach is extended to multi-material topology optimization problems. The local constraints are built by introducing porosity and material rate to achieve MaxLSC for the solid and void phases, respectively. A p-mean function is utilized to aggregate the MaxLSC constraints into a single global one. The MinLSC is proposed based on geometric constraints and the indicator functions with a normalization gradient norm. The optimization formulations and the sensitivity analysis of the related optimization responses are subsequently derived. Four numerical tests demonstrate that the proposed LSC methods are effective to control the feature length scales and contribute to improving the manufacturability of the optimized structures. The length scales of the joints between different materials can be effectively controlled by the proposed LSC constraints for the entire solid phases. Besides, the LSC constraints are found to achieve diverse topology designs and achieving structural redundancy.
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A topology optimization approach for designing the layout of plate structures is proposed in this article. In this approach, structural mechanical behavior is analyzed under the framework of Kirchhoff plate theory, and structural topology is described explicitly by a set of moving morphable components. Compared to the existing treatments where structural topology is generally described in an implicit manner, the adopted explicit geometry/layout description has demonstrated its advantages on several aspects. Firstly, the number of design variables is reduced substantially. Secondly, the obtained optimized designs are pure black-and-white and contain no gray regions. Besides, numerical experiments show that the use of Kirchhoff plate element helps save 95–99% computational time, compared with traditional treatments where solid elements are used for finite element analysis. Moreover the accuracy of the proposed method is also validated through a comparison with the corresponding theoretical solutions. Several numerical examples are also provided to demonstrate the effectiveness of the proposed approach.
Thesis
Topology optimization has been regarded as a scientific and efficient tool to search the optimal material distribution with the best structural performance, subject to the prescribed constraints. It has been accepted a wide array of applications in many fields, like the biology, the mechanical, the medical and etc. However, the conventional works, where the topology optimization is performed on the basis of the homogenized materials, cannot maintain the high requirements of the ultra-lightweight, the specific properties and the integration of the functionals in the modern industrial products. How to explore the performance of material microstructures in improving the functional becomes more and more popular in the research field of the topology optimization, where material layouts and material properties are both considered in the multiscale design of structure-material. In the current work, the parametric level set method (PLSM) combined with the homogenization theory is firstly applied to study the design of mechanical metamaterials and optimize material microstructures. The topology optimization formulation for the multiscale design of structure-material is studied, which is later applied to discuss the single material microstructure, multiple microstructures and the dynamic, respectively. Firstly, the topology optimization formulation for the rational design of mechanical metamterials is proposed based on the parmetric level set. An energy-based homogenization method (EBHM) is developed to evaluate the macroscopic effective properties of material microstructures, which can effectively remove several numerical difficulties of numerical homogenization method, such as the complexity of the theoretical derivations. We adopt the PLSM and the EBHM to develop the topology optimization formulation for the systematic design of mechanical metamaterials. Several numerical examples in 2D and 3D for the maximal bulk modulus, the maximal shear modulus and the negative Poisson’s ratio are studied to demonstrate the effectiveness. Secondly, the topology optimization formulation for the multiscale design of structure-material with a kind of microstructures to maximize the stiffness performance is proposed. In the formulation for mechanical metamaterials, we introduce the conventional topology optimization considering the homogenized materials. In terms of the single kind of material microstructures, we employ the PLSM and the EBHM to develop the multiscale topology optimization formulation. The PLSM can ensure the smooth structural boundary and distinct material interface to improve the manufacturability, and the EBHM is beneficial to reduce the computational cost of the finite element analysis. The topologies at the macro and micro are concurrently optimized to improve the stiffness performance. Then, the topology optimization formulation for the multiscale design of structure-material with multiple kinds of microstructures to maximize the stiffness performance is proposed. The macrostructural topology, the topologies of multiple kinds of microstructures and their overall distribution in the macrostructure should be simultaneously considered. A multiscale topology optimization formulation with two stages are proposed, where the first stage employes the variable thickness sheet method to construct the material distribution optimization model for seeking the optimal layout of material microstructures. In the second stage, the topologies of the macrostructure and multiple kinds of material microstructures are concurrently optimized based on the PLSM and the EBHM. Later, the topology optimization formulation for the multiscale design of structure-material with multiple kinds of microstructures for the minimization of frequency responses is proposed, which should consider the macrostructural topology, the topologies of multiple kinds of microstructures and their overall distribution in the macrostructure. Based on the proposed multiscale topology optimization formulation for the stiffness, we propose the multiscale topology optimization formulation with two stages for the frequency responses. The quasi-static Ritz vector is applied to approximate the displacement responses to reduce the computational cost, and the kinematical connectors are pre-defined in microstructures to ensure the connectivity between adjacent microstructures, so that the macrostructure can have a reasonable loading transmission path. Subsequently, we employ the ANSYS engineering software to simulate the mechanical metamaterials and present the auxetic behavior. The proposed materials design formulation and the multiscale topology optimization formulation are applied to the discussions of lattice materials in the aerospace and the main-bearing structures in the satellite, respectively. The effectiveness and the engineering practicability can be presented in the final designs. Finally, the concluded remarks of the current work and the key contributions are both outlined in the final section, and we also provide some prospects for the future works.
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Nature provides inspirations for solving many challenging scientific and technological problems. In this study, a computational methodology is developed for the morphological optimization of three-dimensional, multi-component biological organs. The structural optimization of scorpion telson, which consists of a curved stinger and a venom container, is considered as an example by using this method. Both experimental and numerical results indicate that, through a long history of natural selection, the load-bearing capacity of the venom apparatus of a scorpion has been optimized together with its flexible segmented tail, important biological functions (e.g., venom storage and transportation), and superb sting strategy. The optimal range of the sting direction of a scorpion is theoretically determined and verified by finite element analysis. The curved scorpion stinger makes the venom container a robust design that is insensitive to the loading direction. The biomechanical mechanisms underlying the robust design are deciphered by comparing the venom apparatuses of scorpions and honey bees. This work deepens our understanding of the structure–property–function interrelations of the venomous sharp weapons of both scorpions and honey bees, and the presented methodology can also be extended to design engineering structures with optimal morphologies (e.g., curved hypodermic needles and segmented robotic arms) and explore other biological tissues and organs.
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The Typha leaf has a structure of lightweight cantilever beam, exhibiting excellent mechanical properties with low density. Especially, the leaf blade evolved high strength and low density with high porosity. In this paper, the structure of Typha leaf was characterized by microcomputed tomography (Micro-CT) and scanning electron microscopy (SEM), and the relationship with flexural properties was analyzed. The three-point bending test was performed on leaves to examine flexural properties, which indicated that the flexural properties vary from the base to the apex in gradient. The cross-sectional geometry shape of the leaf blade presented a strong influence on the optimized flexural stiffness. The load carrying capacity of the leaf depended on the development level of the epidermal tissue, the vascular bundle, the mechanical tissue, and the geometric properties. The investigation can be the basis for lightweight structure design and the application in the bionic engineering field.
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In the design of industrial products ranging from hearing aids to automobiles and aeroplanes, material is distributed so as to maximize the performance and minimize the cost. Historically, human intuition and insight have driven the evolution of mechanical design, recently assisted by computer-aided design approaches. The computer-aided approach known as topology optimization enables unrestricted design freedom and shows great promise with regard to weight savings, but its applicability has so far been limited to the design of single components or simple structures, owing to the resolution limits of current optimization methods1,2. Here we report a computational morphogenesis tool, implemented on a supercomputer, that produces designs with giga-voxel resolution- more than two orders of magnitude higher than previously reported. Such resolution provides insights into the optimal distribution of material within a structure that were hitherto unachievable owing to the challenges of scaling up existing modelling and optimization frameworks. As an example, we apply the tool to the design of the internal structure of a full-scale aeroplane wing. The optimized full-wing design has unprecedented structural detail at length scales ranging from tens of metres to millimetres and, intriguingly, shows remarkable similarity to naturally occurring bone structures in, for example, bird beaks. We estimate that our optimized design corresponds to a reduction in mass of 2-5 per cent compared to currently used aeroplane wing designs, which translates into a reduction in fuel consumption of about 40-200 tonnes per year per aeroplane. Our morphogenesis process is generally applicable, not only to mechanical design, but also to flow systems3, antennas4, nano-optics5 and micro-systems. © 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
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Significance Oscillatory morphodynamics of collective cells is of fundamental importance for concerting cellular events and tissue-level developments in many living systems. We demonstrate that the collective cell oscillations in an epithelium-like monolayer are attributed to a chemomechanical Hopf bifurcation tailored by external forces and boundary physics and geometry. Our findings not only offer mechanistic insights into the synchronization and activation of supracellular oscillations in Drosophila embryogenesis but also help uncover collective events in other scenarios, including wound healing and cancer invasion.
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We seek to understand the effect of chirality on the reconfiguration and the self-buckling strength of chiral plants subjected to wind and gravity by experimental and theoretical modeling of their large deformation. Chiral rod and ribbon specimens are made of polyurethane foam reinforced with nylon fibers and ABS plastic. Wind tunnel tests are performed to evaluate the effect of chirality on flow-induced reconfiguration. A theoretical model is developed by coupling the Kirchhoff rod theory with a semi-empirical formulation for aerodynamic loading evaluation. A range of geometrical, material and flow parameters are studied in the experimental and theoretical model. It is shown that for rods, chirality decreases the maximum root bending moment. For ribbons, chirality leads to a trade-off with higher self-buckling strength but also higher root bending moment. Moreover, chirality reduces the effect of the loading direction on deformation. Chirality plays an important structural role in the interaction of slender structures with fluid flow and gravity loading.
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The evolutionary structural optimization (ESO) method developed by Xie and Steven (1993, [162]), an important branch of topology optimization, has undergone tremendous development over the past decades. Among all its variants , the convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) method developed by Huang and Xie (2007, [48]) allowing both material removal and addition, has become a widely adopted design methodology for both academic research and engineering applications because of its efficiency and robustness. This paper intends to present a comprehensive review on the development of ESO-type methods, in particular the latest con-vergent and mesh-independent BESO method is highlighted. Recent applications of the BESO method to the design of advanced structures and materials are summarized. Compact Malab codes using the BESO method for benchmark structural and material microstructural designs are also provided.
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Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable. Domains of high density then define the shape of the mechanical element. For intermediate densities, material parameters given by an artificial material law can be used. Alternatively, the density can arise naturally through the introduction of periodically distributed, microscopic voids, so that effective material parameters for intermediate density values can be computed through homogenization. Several examples in two-dimensional elasticity illustrate that these methods allow a determination of the topology of a mechanical element, as required for a boundary variations shape optimization technique.
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In this paper we seek to summarize the current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method. The checkerboard problem refers to the formation of regions of alternating solid and void elements ordered in a checkerboard-like fashion. The mesh-dependence problem refers to obtaining qualitatively different solutions for different mesh-sizes or discretizations. Local minima refers to the problem of obtaining different solutions to the same discretized problem when choosing different algorithmic parameters. We review the current knowledge on why and when these problems appear, and we list the methods with which they can be avoided and discuss their advantages and disadvantages.
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A well-developed aerenchyma is a major characteristic of aquatic plants. However, because such tissues are also found in wetland and terrestrial plants, it is not always possible to use their presence or absence to distinguish aquatic species. Whereas patterns of aerenchyma in roots have been studied in detail, those of the shoots have not. We collected and tested 110 species of various aquatic and wetland plants, including ferns (5), basal angiosperms (5), monocots (65), and eudicots (35). Three common and two rare types of aerenchyma were observed in their roots (three schizogeny and two lysigeny), plus five types of schizogeny in their shoots. We re-confirmed that, although a well-developed aerenchyma is more common in most organs of aquatic plants than in wetland plants, this presence cannot be used as strict evidence for the aquatic quality of vascular plants. Here, aerenchyma patterns were stable at the genus level, and the consistency of pattern was stronger in the roots than in the shoots. Furthermore, significant trends were verified in several higher taxa, and those consistencies of patterns partially coincided with their phylogeny.
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This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.
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The Typha leaf, with special multi-level structure, low density and excellent mechanical properties, is an ideal bionic prototype utilized for lightweight design. In order to further study the relationship between the structure and mechanical properties, the three-dimensional macroscopic morphology of Typha leaves was characterized by micro computed tomography (Micro-CT) and its internal microstructure was observed by scanning electron microscopy (SEM). The combination of experimental and computational research was carried out in this paper, to reveal and verify the effect of multi-level structure on the mechanical properties. A universal testing machine and a self-developed mechanical testing apparatus with high precision and low load were used to measure the mechanical properties of the axial compression and lateral bending of the leaves, respectively. Three models with different internal structures were established based on the above-mentioned three-dimensional morphologies. The result demonstrated that the structure of partitions and diaphragms within the Typha leaf could form a reinforcement ribs structure which could provide multiple load paths and make the process of compression and bending difficult. The further nonlinear finite element analysis through LS-DYNA proved that internal structure could improve the ability of the models to resist compression and deformation. The investigation can be the reference for lightweight thin-walled structure design and inspire the application of the bionic structural materials.
Book
Contents: Preface.- Introduction.- Basic Evolutionary Structural Optimization.- ESO for Multiple Load Cases and Multiple Support Environments.- Structures with Stiffness or Desplacement Contraints.- Frequency Optimization.- Optimization Against Buckling.- ESO for Pin- and Rigid-Jointed Frames.- ESO for Shape Optimization and the Reduction of Stress Concentrations.- ESO Computer Program Evolve97.- Author Index.- Subject Index.
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Cattail or Typha, an emergent aquatic macrophyte widely distributed in lakes and other shallow water areas, has slender blades with a chiral morphology. The wind-resilient Typha blades can produce distinct hydraulic resistance for ecosystem functions. However, their stem may rupture and dislodge in excessive wind drag. In this paper, we combine fluid dynamics simulations and experimental measurements to investigate the aeroelastic behavior of Typha blades in wind. It is found that the chirality-dependent flutter, including wind-induced rotation and torsion, is a crucial strategy for Typha blades to accommodate wind forces. Flow visualization demonstrates that the twisting morphology of blades provides advantages over the flat one in the context of two integrated functions: improving wind resistance and mitigating vortex-induced vibration. The unusual dynamic responses and superior mechanical properties of Typha blades are closely related to their biological/ecosystem functions and macro/micro structures. This work decodes the physical mechanisms of chirality-dependent flutter in Typha blades and holds potential applications in vortex-induced vibration suppression and the design of, e.g., bioinspired flight vehicles.
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One of the critical issues in orthopaedic regenerative medicine is the design of bone scaffolds and implants that replicate the biomechanical properties of the host bones. Porous metals have found themselves to be suitable candidates for repairing or replacing the damaged bones since their stiffness and porosity can be adjusted on demands. Another advantage of porous metals lies in their open space for the in-growth of bone tissue, hence accelerating the osseointegration process. The fabrication of porous metals has been extensively explored over decades, however only limited controls over the internal architecture can be achieved by the conventional processes. Recent advances in additive manufacturing have provided unprecedented opportunities for producing complex structures to meet the increasing demands for implants with customized mechanical performance. At the same time, topology optimization techniques have been developed to enable the internal architecture of porous metals to be designed to achieve specified mechanical properties at will. Thus implants designed via the topology optimization approach and produced by additive manufacturing are of great interest. This paper reviews the state-of-the-art of topological design and manufacturing processes of various types of porous metals, in particular for titanium alloys, biodegradable metals and shape memory alloys. This review also identifies the limitations of current techniques and addresses the directions for future investigations.
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Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease.
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Cattail, a type of herbaceous emergent aquatic macrophyte, has upright-standing leaves with a large slenderness ratio and a chiral morphology. With the aim of understanding the effect of chiral morphology on their mechanical behavior, we investigated, both experimentally and theoretically, the twisting chiral morphologies and wind-adaptive reconfigurations of cattail leaves. Their multiscale structures were observed by using optical microscope and scanning electron microscopy. Their mechanical properties were measured by uniaxial tension and three-point bending tests. By modeling a chiral leaf as a pre-twisted cantilever-free beam, fluid dynamics simulations were performed to elucidate the synergistic effects of the leaf's chiral morphology and reconfiguration in wind. It was observed that the leaves have evolved multiscale structures and superior mechanical properties, both of which feature functionally gradient variations in the height direction, to improve their ability to resist lodging failure by reducing the maximal stress. The synergistic effect of chiral morphology and reconfiguration can greatly improve the survivability of cattail plants in wind.
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Through natural selection, many plant organs have evolved optimal morphologies at different length scales. However, the biomechanical strategies for different plant species to optimize their organ structures remain unclear. Here, we investigate several species of aquatic macrophytes living in the same natural environment but adopting distinctly different twisting chiral morphologies. To reveal the principle of chiral growth in these plants, we performed systematic observations and measurements of morphologies, multiscale structures, and mechanical properties of their slender emergent stalks or leaves. Theoretical modeling of pre-twisted beams in bending and buckling indicates that the different growth tactics of the plants can be strongly correlated with their biomechanical functions. It is shown that the twisting chirality of aquatic macrophytes can significantly improve their survivability against failure under both internal and external loads. The theoretical predictions for different chiral configurations are in excellent agreement with experimental measurements.
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Porous solids are important as membranes, adsorbents, catalysts, and in other chemical applications. But for these materials to find greater use at an industrial scale, it is necessary to optimize multiple functions in addition to pore structure and surface area, such as stability, sorption kinetics, processability, mechanical properties, and thermal properties. Several different classes of porous solids exist, and there is no one-size-fits-all solution; it can therefore be challenging to choose the right type of porous material for a given job. Computational prediction of structure and properties has growing potential to complement experiment to identify the best porous materials for specific applications. Copyright © 2015, American Association for the Advancement of Science.
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Through natural selection, many animal organs with similar functions have evolved different macroscopic morphologies and microscopic structures. Here, we comparatively investigate the structures, properties, and functions of honey bee stings and paper wasp stings. Their elegant structures were systematically observed. To examine their behaviors of penetrating into different materials, we performed penetration-extraction tests and slow motion analyses of their insertion process. In comparison, the barbed stings of honey bees are relatively difficult to be withdrawn from fibrous tissues (e.g., skin), while the removal of paper wasp stings is easier due to their different structures and insertion skills. The similarities and differences of the two kinds of stings are summarized on the basis of the experiments and observations. © 2015. Published by The Company of Biologists Ltd.
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Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
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Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elastic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self-weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.
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Biological materials are typically multifunctional but many have evolved to optimize a chief mechanical function. These functions include impact or fracture resistance, armor and protection, sharp and cutting components, light weight for flight, or special nanome-chanical/chemical extremities for reversible adhesive purposes. We illustrate these principles through examples from our own research as well as selected literature sources. We conduct this analysis connecting the structure (nano, micro, meso, and macro) to the mechanical properties important for a specific function. In particular, we address how biological systems respond and adapt to external mechanical stimuli. Biological materials can essentially be divided into mineralized and non-mineralized. In mineralized biological materials, the ceramics impart compressive strength, sharpness (cutting edges), and stiffness while the organic components impart tensile strength, toughness and ductility. Non-mineralized biological materials in general have higher tensile than compressive strength, since they are fibrous. Thus, the mineralized components operate optimally in compression and the organic components in tension. There is a trade-off between strength and toughness and the stiffness and density, with optimization. Mineralization provides load bearing capability (strength and stiffness) whereas the biopolymer constituents provide viscoelastic damping and toughness. The most important component of the nascent field of Biological Materials Science is the development of bioinspired materials and structures and understanding of the structure-property relationships across various length scales, from the macro-down to the molecular level. The most successful efforts at developing bioinspired materials that attempt to duplicate some of the outstanding properties are presented. (c) 2012 Elsevier Ltd. All rights reserved.
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In this paper, we constructed a new honeycomb by replacing the three-edge joint of the conventional regular hexagonal honeycomb with a hollow-cylindrical joint, and developed a corresponding theory to study its mechanical properties, i.e., Young’s modulus, Poisson’s ratio, fracture strength and stress intensity factor. Interestingly, with respect to the conventional regular hexagonal honeycomb, its Young’s modulus and fracture strength are improved by 76% and 303%, respectively; whereas, for its stress intensity factor, two possibilities exist for the maximal improvements which are dependent of its relative density, and the two improvements are 366% for low-density case and 195% for high-density case, respectively. Moreover, a minimal Poisson’s ratio exists. The present structure and theory could be used to design new honeycomb materials.
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We develop and evaluate a novel 3D computational bone framework, which is capable of enabling quantitative assessment of bone micro-architecture, bone mineral density and fracture risks. Our model for bone mineral is developed and its parameters are estimated from imaging data obtained with dual energy x-ray absorptiometry and x-ray imaging methods. Using these parameters, we propose a proper 3D microstructure bone model. The research starts by developing a spatio-temporal 3D microstructure bone model using Voronoi tessellation. Then, we simulate and analyze the architecture of human normal bone network and osteoporotic bone network with edge pruning process in an appropriate ratio. Finally, we design several measurements to analyze Bone Mineral Density (BMD) and bone strength based on our model. The validation results clearly demonstrate our 3D Microstructure Bone Model is robust to reflect the properties of bone in the real world.