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Morphological optimization of scorpion telson
Abstract
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.
... In recent years, several optimization methods, e.g., the homogenization method [1,2], the solid isotropic material with penalization (SIMP) method [2,3], the bi-directional evolutionary structural optimization (BESO) method [4][5][6][7], and the level-set method [8,9] have undergone tremendous development. These methods have been successfully extended to a wide range of engineering applications, including advanced manufacturing [10][11][12][13][14][15][16], architectural design [17][18][19][20][21][22][23][24], biomechanical morphogenesis [25][26][27][28][29], civil engineering [30][31][32][33][34][35], and metamaterials [36,37]. Although remarkable progress has been made in topology optimization, it remains a challenging issue to directly control the structural complexity in three-dimensional optimization problems. ...
... The distance transform algorithm can turn a binary mesh model with featured voxels and non-featured voxels into another digital image in which the value of each non-featured voxel is its distance to the nearest featured voxels (Fig. 6). In discrete spaces, the distance between voxels can be calculated by several distance metrics, including the city block (denoted as d 6 ), chessboard (denoted as d 26 ), and Euclidean distance (denoted as d E ) metrics. For example, the city block and chessboard distances are calculated by the lengths of the shortest 6-path and 26-path between two voxels, respectively. ...
... Conduct shape optimization according to Eqs. (24a) and (24b). In each iteration, update the new structural skeleton M sk and thin sheet components M sheet , and apply minimum length scale control according to Eqs. (25) and (26). ...
Shape and topology optimization problems are usually associated with geometrical restrictions. Effective control of structural complexity during the optimization process is important for various considerations, e.g., functionality, manufacturability, and aesthetics. Most existing approaches characterize structural complexity as the number of cavities. However, for three-dimensional structures, the genus (i.e., the number of tunnels) should also be considered as an additional topological constraint. In this paper, a hole-filling method is integrated into the bi-directional evolutionary structural optimization (BESO) computational framework to control the number and size of existing cavities and tunnels during the form-finding process. In the hole-filling method, excess cavities are filled with solid material and excess tunnels are covered by building sheet-like patches. The minimum size of the truss-like components and the minimum thickness of the sheet-like components can be controlled separately. Several two-and three-dimensional compliance minimization problems are presented to demonstrate the effectiveness and potential applications of the proposed approach. The structural performances of the optimized structures with and without complexity control are compared and analyzed. The results show that the developed methodology can produce structurally efficient designs with controllable topologies. It is also demonstrated that the generation of sheet-like components can considerably increase the stiffness of the optimized structure. The proposed approach is capable of generating diverse and competitive designs for architects and engineers to achieve a fine balance between architectural novelty and structural efficiency.
... In recent years, several optimization methods, e.g., the homogenization method [1,2], the solid isotropic material with penalization (SIMP) method [2,3], the bi-directional evolutionary structural optimization (BESO) method [4][5][6][7], and the level-set method [8,9] have undergone tremendous development. These methods have been successfully extended to a wide range of engineering applications, including advanced manufacturing [10][11][12][13][14][15][16], architectural design [17][18][19][20][21][22][23][24], biomechanical morphogenesis [25][26][27][28][29], civil engineering [30][31][32][33][34][35], and metamaterials [36,37]. Although remarkable progress has been made in topology optimization, it remains a challenging issue to directly control the structural complexity in three-dimensional optimization problems. ...
... The distance transform algorithm can turn a binary mesh model with featured voxels and non-featured voxels into another digital image in which the value of each non-featured voxel is its distance to the nearest featured voxels (Fig. 6). In discrete spaces, the distance between voxels can be calculated by several distance metrics, including the city block (denoted as d 6 ), chessboard (denoted as d 26 ), and Euclidean distance (denoted as d E ) metrics. For example, the city block and chessboard distances are calculated by the lengths of the shortest 6-path and 26-path between two voxels, respectively. ...
... Conduct shape optimization according to Eqs. (24a) and (24b). In each iteration, update the new structural skeleton M sk and thin sheet components M sheet , and apply minimum length scale control according to Eqs. (25) and (26). ...
... Nowadays, topology optimization techniques have been increasingly adopted in a wide range of engineering applications, including advanced manufacturing [1][2][3][4][5][6], architectural design [7][8][9][10][11][12], biomechanical morphogenesis [13][14][15][16][17], and civil engineering [18][19][20][21][22][23][24]. Despite their growing popularity, the optimized designs from conventional optimization techniques often feature complex geometries that pose significant manufacturing challenges [1]. ...
... , set the target volume V (n) using Eq. (16). Otherwise, maintain the previous volume as V (n− 1) . ...
In recent years, topology optimization of periodic structures has become an effective approach to generating efficient designs that meet a variety of practical considerations, including manufacturability, transportability, replaceability, and ease of assembly. Traditional periodic structural optimization typically restricts designs to a uniform assembly configuration utilizing only one type of unit cell. This study proposed a novel clustering-based approach for periodic structural optimization, which allows variable orientations of individual unit cells. A dynamic k-means clustering strategy is introduced to categorize all unit cells into distinct groups and gradually eliminate less efficient unit cells from the optimized design. Meanwhile, a novel technique is introduced to identify and select more efficient orientations of unit cells during the optimization process. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. The results show that periodic structures with clustered oriented unit cells can significantly outperform their traditional periodic counterparts. This study not only incorporates assembly flexibility into periodic topology optimization but also utilizes multiple types of unit cells in a design, thereby further enhancing its structural performance.
... Several continuum topology optimization techniques have been developed in the past decades, e.g., the solid isotropic microstructures with penalization method [27], the bi-directional evolutionary structural optimization (BESO) method [28,29], the level set-based method [30][31][32], and the moving morphable component method [33]. These techniques have been used extensively in dynamic properties where uncertainty is considered [34], multidisciplinary research [35][36][37][38][39][40], and novel structure designs [41][42][43][44]. Liang et al. [20,21] applied the BESO technique to establish an STM for classical deep beams in civil engineering. ...
... cos 2θ + τ xy sin 2θ. (34) Considering the steel bar orientations shown in Fig. 1, directional angles of 0°, 45°, 90°, and 135° were adopted for truss bars I, II, III, and IV, respectively, to calculate the stress in the host concrete. ...
Owing to advancement in advanced manufacturing technology, the reinforcement design of concrete structures has become an important topic in structural engineering. Based on bi-directional evolutionary structural optimization (BESO), a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete (SRC) structures. This approach combines a minimum compliance objective function with a hybrid truss-continuum model. Furthermore, a modified bi-directional evolutionary structural optimization (M-BESO) method is proposed to control the level of tensile stress in concrete. To fully utilize the tensile strength of steel and the compressive strength of concrete, the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete. To demonstrate the effectiveness of the proposed procedures, reinforcement layout optimizations of a simply supported beam, a corbel, and a wall with a window are conducted. Clear steel trajectories of SRC structures can be obtained using both methods. The area of critical tensile stress in concrete yielded by the M-BESO is more than 40% lower than that yielded by the uniform design and BESO. Hence, the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.
... 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]. ...
... In the following, we use Eq. (22) to calculate the elemental sensitivities. ...
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 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. ...
... It can produce 0-1 results where there is no transitional materials in the final design (Xia et al., 2018;. Recently, complex constraints on, e.g. the structural complexity/connectivity and the maximum principal stress have been successfully integrated into the BESO-based topology optimization (Zhao et al., 2020a(Zhao et al., , 2020bXiong et al., 2020;Chen et al., 2021). Novel approaches have developed based on the BESO method for generating diverse and competitive designs (He et al., 2020;Yang et al., 2019;Xie et al., 2019). ...
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.
... ESO removes excess material to achieve an optimal configuration, while BESO allows for the simultaneous removal of inefficient materials and the addition of efficient ones [9]. The BESO enhances the solution process compared to the conventional ESO and is widely used in architecture, aerospace, medicine, and biomechanics [10]. ...
This research presents a novel algorithm designed to reduce computational time in the meso-scale analysis of masonry buildings. The algorithm employs nonlinear topology optimization in conjunction with the Drucker-Prager yield criterion to identify critical zones within a structure. These critical zones are modeled at the meso-scale, while less critical regions are represented at the macro-scale. To evaluate the efficacy and accuracy of the proposed method, three masonry wall samples were analyzed, comparing computational time and accuracy across three modeling strategies: full meso-scale, full macro-scale, and optimized meso-macro scale. The results indicate that while macro-scale models provided faster analyses, they exhibited lower accuracy compared to meso-scale models and demonstrated greater initial stiffness and maximum force due to their elastic-perfectly plastic behavior. In contrast, the optimized meso-scale models reduced the computational time by 32.5%, 46%, and 30% compared to full meso-scale models, while maintaining high accuracy in replicating crack patterns and force–displacement responses observed in experimental data. These findings suggest that the developed algorithm offers an efficient and accurate computational approach for analyzing the complex behavior of masonry buildings under various loading conditions.
... The comprehensive mechanical properties of many animal organs are achieved through their optimized structures [56][57][58]. Here, we measured the geometric parameters of a real suture in the elytra of a diabolical ironclad beetle [9,45]. ...
... Their method can automatically dig tunnels that connect the cavity with the boundary of the structures when the volume constraint is satisfied in the optimisation. Zhao et al.[80,81] developed an approach to explicitly control the structural complexity based on the graph theory and set theory. Users can control the geometric topology of optimised structures by prescribing the distribution of cavities in the initial design. ...
Topology optimisation techniques are increasingly used for creating innovative and efficient structures by redistributing given materials to their most needed locations. However, these techniques typically focus purely on structural performance, often neglecting subjective design requirements, such as aesthetic quality. This thesis is aimed at advancing topology optimisation techniques to produce structures that effectively balance creative forms with structural engineering principles. The thesis makes the following contributions. First, a novel smoothing method is proposed to smooth structural designs obtained by element-based topology optimisation, specifically for the widely used bi-directional evolutionary structural optimisation (BESO) method. The proposed method can efficiently smooth the zig-zag boundaries of the optimised structures by using pre-built lookup tables modified from marching geometry algorithms. Additionally, the smoothing method employs a bi-section approach to preserve the structural volume, ensuring that both unsmoothed and smoothed structures are equivalent. The effectiveness of this smoothing method is demonstrated through a series of 2D and 3D examples; the results show that the structural stiffness can be slightly improved after smoothing. Second, the BESO method has been advanced to SP-BESO by integrating designers’ subjective preferences (SP) into optimisation for 2D structural designs. This novel method introduces interactive systems that allow designers to input preferences by explicitly scoring and drawing. Subsequently, the inputs are converted into weights to guide material redistribution to create topologically different and structurally efficient solutions. The proposed smoothing method is used to refine the solutions so that designers can decide their subjective preferences in subsequent design exploration. Additionally, a user-friendly digital design tool, iBESO, has been developed. This tool can simultaneously execute four SP-BESO optimisers to assist designers in 2D structural design. Experiments with iBESO reveal that the combination of parameters used in the scoring and drawing systems can effectively control whether the final solutions are performance-driven or preference-driven designs. Third, a novel design exploration strategy is proposed, which integrates virtual reality (VR) with SP-BESO to create desirable 3D structures through effective human--computer collaboration. This strategy uses VR sculpting to realise immersive visualisation, intuitive design exploration, and real-time feedback, with the sculpted models influencing material redistribution in topology optimisation. The sculpting--optimisation workflow can be repeated in multiple cycles. This iterative process allows for the continuous refinement of subjective preferences until a final design meets all design requirements. A digital design tool, VR-BESO, has been developed to implement and demonstrate the proposed strategy. The results show that this strategy can effectively harness the strengths of human creativity and computational power to enhance the efficiency of design exploration and the quality of optimised structures. Overall, this thesis has significantly advanced structural design and optimisation by integrating subjective preferences into topology optimisation. It has introduced innovative methodologies, developed advanced digital tools, and enhanced human--computer interaction, laying a strong foundation for future research and practical applications. These contributions mark a substantial progression in creating engineering solutions that are more adaptable and responsive to user needs.
... These cutting-edge methods show great promise for advancing the capabilities of 3DCP and optimizing the production of high-performance structures. Nowadays, structural topology optimization has become increasingly popular in various fields, including additive manufacturing 69,86 , architectural design 87,88 , biochemical 89,90 , and aerospace engineering 91,92 . Among them, the high design flexibility of 3DCP makes it compatible with topology optimization to decrease material usage and improve sustainability. ...
The construction sector has experienced remarkable advancements in recent years, driven by the demand for sustainable and efficient building practices. Among these advancements, 3D concrete printing has emerged as a highly promising technology that holds the potential to revolutionize the construction industry. This review paper aims to provide a comprehensive analysis of the latest developments in three vital areas related to 3D concrete printing: sustainable materials, structural optimization, and toolpath design. A systematic literature review approach is employed based on established practices in additive manufacturing for construction to explore the intersections between these areas. The review reveals that material recycling plays a crucial role in achieving sustainable construction practices. Extensive research has been conducted on structural optimization methodologies to enhance the performance and efficiency of 3D printed concrete structures. In the printing process, toolpath design plays a significant role in ensuring the precise and efficient deposition of concrete. This paper discusses various toolpath generation strategies that take factors such as geometric complexity, printing constraints, and material flow control into account. In summary, the insights presented in this paper may serve as guidelines for researchers, engineers, and industry professionals towards sustainable and efficient construction practices using 3D concrete printing technology.
... In addition to the civil and architectural applications, Airbus (Krog et al., 2009) successfully applied topology optimization on its A380, A400, and A350 plane models, including the design of wing ribs, engine mount frames, and floor crossbeams. Apart from the artificial structures, Ma et al. (2021b) and Zhao et al., (2018Zhao et al., ( , 2020 utilized topology optimization to facilitate the analysis of biostructures in plants and animals that have evolved over millions of years. ...
Free-form architectural design has gained significant interest in modern architectural practice. Due to their visually appealing nature and inherent structural efficiency, free-form shells have become increasingly popular in architectural applications. Recently, topology optimization has been extended to shell structures, aiming to generate shell designs with ultimate structural efficiency. However, despite the huge potential of topology optimization to facilitate new design for shells, its architectural applications remain limited due to complexity and lack of clear procedures. This paper presents four design strategies for optimizing free-form shells targeting architectural applications. First, we propose a topology-optimized ribbed shell system to generate free-form rib layouts possessing improved structure performance. A reusable and recyclable formwork system is developed for their effective and sustainable fabrication. Second, we demonstrate that topology optimization can be combined with funicular form-finding techniques to generate a rich variety of elegant designs, offering new design possibilities. Third, we offer cost-effective design solutions using modular components for free-form shells by combining surface planarization and periodic constraint. Finally, we integrate topology optimization with user-defined patterns on free-form shells to facilitate aesthetic expression, exemplified by the Voronoi pattern. The presented strategies can facilitate the usage of topology optimization in shell designs to achieve high-performance and innovative solutions for architectural applications.
... The MMC technique was implemented by a 188-line [34] and a 256-line Matlab code [35], respectively. The BESO technique has been used extensively due to its excellent optimization results [36][37][38][39]. It was implemented through a 100-line Python code, which can solve the compliance minimization problems but features low computational efficiency [40]. ...
Structural topology optimization has undergone tremendous developments in the past three decades. Making the most of high-performance computing resources contributes to broadening the application of topology optimization in large-scale design problems. In this paper, a subdomain-based parallel strategy is proposed for general three-dimensional topology optimization. The optimization process is significantly accelerated through subdomain division, matrix calculation, and hard-kill algorithm. This strategy is integrated into an efficient and compact Python code, which is valid for design space with an arbitrary shape. The complete code, given in Appendix 1, can be easily extended to tackle different kinds of optimization problems. Four compliance minimization problems are taken as examples to demonstrate the efficiency of the proposed strategy. This work has potential applications in areas such as mechanical engineering, advanced manufacturing, and architectural design.
... Several techniques have been developed, including, e.g., the homogenization method (Bendsøe and Kikuchi, 1988), the solid isotropic material with penalization (SIMP) (Bendsøe, 1989;Zhou and Rozvany, 1991;Sigmund and Maute, 2013), the bi-directional evolutionary structural optimization (BESO) (Xie and Steven, 1993;Xie, 2009, 2010), the level set (Allaire et al., 2002;Wang et al., 2003;Otomori et al., 2015), and the moving morphable components (MMC) (Guo et al., 2014;Guo et al., 2016). These techniques have been applied extensively in multiple disciplines, e.g., mechanical engineering, architectural design, additive manufacturing, and biomechanical morphogenesis (Zhu et al., 2009;Meng et al., 2020;Zhao et al., 2020a;Zhao et al., 2020b). ...
The morphogenesis of plant organs and tissues has fascinated scientists for centuries. However, it remains a challenge to quantitatively decipher the biomechanical mechanisms underlying the morphological evolutions of growing plants. In this study, we investigate the formation, optimization, and evolution mechanisms of plant roots through biomechanical morphogenesis. A transdisciplinary computational framework is established based on the adaptive design domain topology optimization method. Two typical kinds of root systems are studied for illustration, including the taproot and the fibrous systems. The effects of coupled biomechanical and environmental factors on the growth and form of the root systems are revealed. It is found that the morphological evolutions of both systems tend to maximize the transport efficiency of water and nutrients. Lateral roots are constantly generated, forming a hierarchically branched layout. The thickness and concentration of roots depend on the growth history, while the growth directions of root caps are regulated by geotropism, hydrotropism, and growth inertia. These results are consistent with experimental observations. This work not only helps understand the topological formation of root systems, but also provides a quantitative tool for exploring the structure–property–function interrelations of living systems.
Keywords: Root growth; Morphogenesis; Adaptive design domain; Transport of water and nutrients; Growth history
... With the development of topology optimization design methods, modular robots are increasingly applying such methods to achieve innovative designs of morphologies [66,67]. Compared with traditional topology optimization design methods (e.g., the level set method [68], the evolutionary structural optimization method [69], and the moving morphable component method [70]), isogeometric topology optimization (ITO) [71] is a modern structural optimization technique that leverages isogeometric Figure 2 The framework of evolutionary synthesis of mechatronic systems [65] analysis. ...
Design automation is a core technology in industrial design software and an important branch of knowledge-worker automation. For example, electronic design automation (EDA) has played an important role in both academia and industry. Design automation for intelligent robots refers to the construction of unified modular graph models for the morphologies (body), controllers (brain), and vision systems (eye) of intelligent robots under digital twin architectures, which effectively supports the automation of the morphology, controller, and vision system design processes of intelligent robots by taking advantage of the powerful capabilities of genetic programming, evolutionary computation, deep learning, reinforcement learning, and causal reasoning in model representation, optimization, perception, decision making, and reasoning. Compared with traditional design methods, MOdular DEsigN Automation (MODENA) methods can significantly improve the design efficiency and performance of robots, effectively avoiding the repetitive trial-and-error processes of traditional design methods, and promoting automatic discovery of innovative designs. Thus, it is of considerable research significance to study MODENA methods for intelligent robots. To this end, this paper provides a systematic and comprehensive overview of applying MODENA in intelligent robots, analyzes the current problems and challenges in the field, and provides an outlook for future research. First, the design automation for the robot morphologies and controllers is reviewed, individually, with automated design of control strategies for swarm robots also discussed, which has emerged as a prominent research focus recently. Next, the integrated design automation of both the morphologies and controllers for robotic systems is presented. Then, the design automation of the vision systems of intelligent robots is summarized when vision systems have become one of the most important modules for intelligent robotic systems. Then, the future research trends of integrated “Body-Brain-Eye” design automation for intelligent robots are discussed. Finally, the common key technologies, research challenges and opportunities in MODENA for intelligent robots are summarized.
... Several constraints, such as volume fraction, passive areas, and practical fabrication, are added in the optimisation to limit the admissible shape. In the last few decades, several techniques like the homogenisation method, SIMP method, ESO method, BESO method, level set method, and phase-field method [37][38][39] have been developed and widely used in aerospace [40,41], biochemical [42,43], mechanical [44,45], and structural engineering [46,47]. Over the years, topology optimisation methods are continuously evolving to improve effectiveness and efficiency. ...
Topology optimisation (TO) has the potential to be widely applied in additive manufacturing (AM) to produce innovative and efficient structures, allowing engineers to optimise the aesthetics and performance in the conceptualisation stage. However, challenges arise in generating smooth boundaries to improve the finite element analysis (FEA) accuracy and achieve structural aesthetics. This demand has demonstrated a vital practicability concern that needs to be addressed before TO results can be used in AM.
The primary aim of this thesis is to introduce a body-fitted triangular/tetrahedral mesh into TO, significantly increasing boundary smoothness and optimisation accuracy. The void elements are excluded from planar/spatial optimisation to save computation time, even though a versatile meshing algorithm based on solving a force equilibrium generates them. Based on the zero-level contour, both the level set (LS) method and the bi-directional evolutionary structural optimisation (BESO) method can be combined with the proposed method, which avoids the grey-scale problem and closely matches elegant solid-void interfaces. Numerical examples in 2D and 3D converge within dozens of iterations and illustrate ultra-smooth boundaries, verifying the effectiveness and robustness of the proposed method.
This project was the first to report the TO methods incorporating reaction-diffusion equation and nonlinear diffusion regularisation using the body-fitted mesh to address the issue of zig-zagging shapes obtained using structural rectangular mesh. The key finding was that the zig-zag interfaces between the void and solid phases in the optimised pattern greatly affect the structural aesthetics and analysis accuracy, especially in fluid, optic, and electromagnetic optimisation problems. The proposed method is computationally complex due to the mesh generation procedure before FEA in each iteration. However, adopting the bi-section method and large element removal ratio (ERR) boosts convergence and reduces the computational cost. The significance of this research is to improve the TO accuracy and efficiency, ensuring elegant configurations that can be directly produced by AM without post-processing.
... Inspired by the flexibility and dexterity of animals' slender (small diameter/length ratio) as well as flexible structures, researchers have successfully designed various bionic robots that could move flexibly and work in complex space and unstructured environments [1][2][3][4][5]. For instance, through the bionic design of the octopus arm, some researchers have developed robots for minimally invasive surgery [6], tapered soft actuators with suckers that can grasp objects of different shapes [7], and continuous soft manipulators [8], etc. ...
Some birds’ necks show excellent flexible bending ability, which can be mimicked to design bionic robot. The main challenge is how to deal with the bird neck’s inherent flexibility and redundant degrees of freedom. In this study, a design method of a class of bionic hyper-redundant robots mimicking the neck of birds is proposed, taking the chicken as an example. In our design, a bionic vertebrae unit (BVU) with the combination of springs and universal joint is first defined to simulate chicken cervical vertebrae, which is further employed to investigate the connection and motion characteristics. Then, three BVUs in parallel driven by three steel wires form a single cervical segment. Finally, connecting four identical cervical segments constitutes the proposed bionic hyper-redundant robot. The kinematics of the driving space, joint space and task space of the proposed bionic hyper-redundant robot are investigated by combing the geometric analysis method and Denavit-Hartemberg (D-H) parameter method. The reachable workspace is further computed by the Monte Carlo method. Furthermore, the maximum position deviation of the single plane motion experiment on the prototype is about 5.8% of the total length of the four cervical segments. A series of displays of space shape, including S-shaped bionic bending configuration and the successful winding and lifting of the object of interest, proves that the proposed robot has excellent flexibility and application potential and that the proposed design method is effective.
... Wu et al. introduced a layout method for optimizing hierarchical lattice shells [24]. By integrating biomechanical mechanisms into the structural form-finding process, Zhao et al. revealed the formation and optimization mechanisms of biological organs and tissues [25,26]. Rian et al. developed a fractal geometry method to design grid-shell structures [27]. ...
Shells are widely used in architectural and engineering design due to their appealing geometry and efficient structural form. However, designing free-form shells with specific geometrical patterns remains a challenging issue as both aesthetical and
mechanical properties need to be considered. Based on structural topology optimization, this paper develops a direct approach to generating high-performance shells with embedded geometrical patterns. In this approach, graph theory and the nonuniform rational basis spline (NURBS) method are combined to produce parametric designs based on polygonal meshes. This approach is capable of optimizing shells with complicated geometry and different thicknesses. The effectiveness of the approach is demonstrated by three representative examples. The techniques developed in this study can be used to design efficient free-form shells for construction.
Keywords: Free-form shells; Geometrical pattern; Topology optimization; Graph
theory; Parametric design.
... Different kinds of new constraints have been imposed during the optimization process in recent years, such that further structural design problems can be addressed effectively and practically [27][28][29][30][31][32][33][34][35][36]. In addition, topology optimization has been applied in transdisciplinary research such as biomechanical morphogenesis [37][38][39] and metamaterial designs [40][41][42][43]. ...
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.
... 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]). ...
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 these methods, the ESO method and its advanced version, the bi-directional evolutionary structural optimization (BESO) method, are popular among many researchers and designers because of their simplicity and the availability of well-developed commercial software such as Ameba [11]. The ESO method and the BESO method have been widely used in various fields such as structure, architecture, aerospace, medicine, and biomechanics [12][13][14]. Besides, some new structural optimization algorithms have been developed, such as YUKI, Jaya, and Cuckoo [15][16][17], which provide new strategies and perspectives for structural optimization and are promising to be applied to future topology optimization to enhance the efficiency of the computation. However, there are still some modifications to be done to combine these novel algorithms with topology optimization algorithms. ...
A novel method is proposed to optimize the topology of composite structures made of more than two materials with different mechanical properties in tension and compression. In this method, the design domain of the structure is divided into tensile and compressive regions according to the first invariant of the stress tensor. Then two groups of materials suitable for tension and compression are arranged in the tensile and compressive regions of the structure, respectively. Using a bridge-type beam with a concentrated force as an example, the study of the four-material topologically optimized structures reveals the effects of the volume fractions and material mechanical properties on the optimization results. Further, the three-material topology optimization method, which is derived from the four-material topology optimization method, is used to design a series of novel sandwich structures. Application examples demonstrate that the proposed method can achieve a balance between enhancing structural stiffness and saving material costs, providing solutions competitive in various aspects and exploiting the performance and potential of different materials better than previous single- or dual-material topology optimization methods.
Keywords: Bi-directional evolutionary structural optimization (BESO), multi-material topology optimization, multiple materials, sandwich structure.
... 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]. ...
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.
... However, structural topology optimization was scarcely used in engineering because of the complicated and cumbersome calculations. In recent years, with the advances in various optimization algorithms and the rapid development of computers, it has been increasingly used in civil engineering [3][4][5][6], astronautics and aeronautics [7], and biomechanics [8]. ...
This work uses the zero-level contour of a parameterized level set function, a linear combination of cubic B-spline basis functions, to express the structural profile in structural topology optimization. Together with mean compliance, diffusion energy is minimized under a volume constraint to control the structural complexity. The design variables, namely the coefficients of cubic B-spline basis functions, are updated by solving the reaction–diffusion equation within a finite element analysis framework. The bisectional algorithm accurately calculates the Lagrangian multiplier of the volume constraint in each iteration. In addition to expressing the optimized structure smoothly, the proposed method is highly efficient. For instance, it only takes 20 iterations to solve the cantilever and MBB beams in 2D. For 3D optimization, we obtain several elegant bridge designs using nearly one million elements, demonstrating the great potential of the proposed method for practical applications.
... Based on the graph theory and set theory, Zhao et al. [41] developed a direct approach to explicitly controlling the structural complexity during the form-finding process. This approach has been successfully applied to the morphological optimization of biological organs [42]. Some of the above approaches are limited to 2-dimensional (2D) optimization. ...
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 ...
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]. ...
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 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. ...
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.
... 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). ...
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]. ...
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.
... However, this method was not used in engineering until the maturity of finite element analysis in the 1980s. In the last few decades, several techniques like the homogenization method [9], the solid isotropic microstructure with penalization (SIMP) method [10,11], the evolutionary structural optimization (ESO) method [2,12], the bidirectional evolutionary structural optimization (BESO) method [13,14], the level set method [15][16][17], and the phase-field method [18][19][20] have been developed and widely used in aerospace [21,22], bio-chemical [23,24], mechanical [25,26], and structural engineering [27,28]. ...
The level set method can express smooth boundaries in structural topology optimization with the level set function's zero-level contour. However, most applications still use rectangular/hexahedral mesh in finite element analysis, which results in zigzag interfaces between the void and solid phases. We propose a reaction diffusion-based level set method using the adaptive triangular/tetrahedral mesh for structural topology optimization in this work. Besides genuinely expressing smooth boundaries, such a body-fitted mesh can increase finite element analysis accuracy. Unlike the traditional upwind algorithm, the proposed method breaks through the constraint of Courant-Friedrichs-Lewy stability condition with an updating scheme based on finite element analysis. Numerical examples for minimum mean compliance and maximum output displacement at specified positions, in both 2D and 3D, converge within dozens of iterations and present elegant structures.
... Although many advances have been made in studying the physics and material properties of the insect cuticle, there is still much that is unknown about the selective pressures acting upon the composite structure of the cuticle [7,[12][13][14][15]. Recent studies on slender structures in arthropods, such as the scorpion stingers [16,17], wasp ovipositors [18], and grasshopper tibiae [19] have highlighted the critical importance of functional material gradients to the performance of exoskeletal structures. Such gradients can be generated by differential sclerotization (or tanning) of the cuticle [19], or by changes in cuticle composite structure [20]. ...
With over 300 species worldwide, the genus Curculio Linnaeus, 1758 is a widespread, morphologically diverse lineage of weevils that mainly parasitize nuts. Females use the rostrum, an elongate cuticular extension of the head, to excavate oviposition sites. This process causes extreme bending and deformation of the rostrum, without apparent harm to the structure. The cuticle of the rostral apex exhibits substantial modifications to its composite structure that enhance the elasticity and resiliency of this structure. Here we develop finite element models of the head and rostrum for three Curculio species representing disparate North American clades and rostral morphotypes. The models were subjected to varying apical loads and to prescribed dislocation of the head capsule, with and without representing the cuticular modifications of the rostral apex. We found that the altered layer thicknesses and macrofiber orientation angles of the rostral apex fully explain the observed elasticity of the rostrum. These modifications have a synergistic effect that greatly enhances the flexibility of the rostral apex. Consequently, the cuticle composite profile of the rostral apex substantially mitigates the risk of fracture in dorso-apical flexion. Removing the cuticular modifications, in turn, causes a negative margin of safety for rostral bending, implying strong risk of catastrophic structural failure. The occipital sulci were identified as an important source of biomechanical constraint upon the elasticity of the rostrum, and exhibit the greatest risk of failure within this structure. The apical cuticle profile greatly reduced the maximum stresses and strain energy accumulated in the rostrum, thereby resulting in a positive margin of safety and reducing the risk of fracture. Our findings imply that the primary selective pressure influencing the evolution of the rostral cuticle was most likely negative selection of structural failure caused by bending.
Statement of significance
Weevils are among the most diverse and evolutionarily successful animal lineages on Earth. Their success is driven in part by a structure called the rostrum, which gives weevil heads a characteristic “snout-like” appearance. Nut weevils in the genus Curculio use the rostrum to drill holes into developing fruits and nuts, into which they deposit their eggs. During oviposition this exceedingly slender structure is bent into a straightened configuration – in some species up to 90∘ – but does not suffer any damage during this process. Using finite element models of the rostra of three morphologically distinct species, we show that the Curculio rostrum is only able to withstand repeated, extreme bending because of modifications to the composite structure of the cuticle in the rostral apex. These modifications were shown previously to enhance the intrinsic toughness of the cuticle; in this study, we demonstrate that modification of the rostral cuticle also results in more evenly distributed bending stresses, further reducing the risk of fracture. This is the first time that the laminate profile, orthotropic behavior, and functional gradation of the cuticle have been incorporated into a three-dimensional finite element model of an insect cuticular structure. Our models highlight the significance of biomechanical constraint – i.e., avoidance of catastrophic structural failure – on the evolution of insect morphology.
... As an important branch of topology optimization, the BESO technique is based on the simple concept of gradually removing inefficient material from a structure and adding material to the most needed locations at the same time [24]. It is widely 3 recognized owing to its high-quality topology solutions [25], ease of understanding and implementation [26], and excellent computational efficiency [27]. ...
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.
... 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). ...
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.
... 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. ...
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.
... Using this approach, the structural performance and the effect of the structural complexity control can be well balanced. This approach has been extended and successfully applied in the morphological optimization of biological organs [50]. However, it remains a challenging issue to eliminate enclosed voids in an optimized design. ...
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.
Since the 21st century, the rapid development of computer technology has brought new inspiration to the long-standing topic of the relationship between architecture, structure, and environment. Performance data have become the driving force for new design and fabrication methods.
Nowadays, in the field of engineering, computer-aided design methodologies, such as finite element analysis and computational fluid dynamics and, have become essential in evaluating architectural and structural designs. However, these engineering analysis techniques have not become widespread for architectural design form-finding. On the other hand, with the development of digital architecture theory, form-finding technology based on biological patterns has gradually moved from avant-garde design to actual practice. As a result, bionic computational design techniques, such as swarm intelligence algorithm and multi-agent system, have become more popular; and architects can assign the behavioural logic in nature to architectural design form-finding so that biological, environmental response strategies can be reproduced in intelligent tectonics. However, this emergent design methodology is often difficult to obtain data feedback from the building itself and its performance, and hardly form the mainstream design strategy in architectural practice. In this context, applying the data of structural performance to multi-agents to realise the research of computational design driven by performance will help break through the above dilemma and provide new ideas to architects and engineers.
Both bi-directional evolutionary structural optimisation (BESO) for topology optimisation method and multi-agent system from swarm intelligence algorithm are emergent technologies developed into new approaches that transform performance-based architectural & structural design. This thesis posits a performance-driven design methodology that establishes a complementary relationship between topological optimisation, behavioural multi-agent algorithms, architectural design, and robotic fabrication.
Firstly, the thesis systematically explores and evaluates the application of topology optimisation and multi-agent algorithms in a form-finding design process and, later, robotic fabrication through literature review, case studies and a series of architectural scale prototypes.
Through a combination of natural inspiration, topology optimisation, multi-agent systems and robotic fabrication, the thesis also establishes a new connection between two dichotomous principles: architectural complexity and structural performance. It demonstrates the process of testing two digital design methods and integrating these two algorithms to establish a real-time structural feedback loop in designing intricate forms.
Finally, the thesis describes a hybrid of architectural and structural performance behaviours by integrating multi-agent generative design algorithms and the BESO method and the closeness of their interaction. This approach creates a negotiation between architectural design concerns and structural optimisation in a simultaneous generative approach. It is an essential shift from the normative sequential workflows that either inform generative approaches with structural analysis or operate sequentially to optimise the complex geometries already created within generative processes structurally.
At the same time, the complexity and intricacy of the geometry generated through this process are demonstrated to be feasible to build through robotic fabrication with large-scale additive manufacturing. A series of installations have been completed to prototype and compare two individual approaches and an integrated method at a small scale, to understand the implications of long-span large spatial structures.
Overall, this thesis has contributed to the research field of performance-driven digital design and fabrication. It offers a new approach that enables creating a complex, expressive architectural form that is highly efficient in material and structural performance. This approach also has the potential to create a closer collaboration between architect and structural engineer in the early stages of design and to avoid the structural rationalisation of unfeasible architectural forms in the architectural, engineering and construction industry The new method also seeks the ornamental complexities in architectural forms and most efficient use of material based on structural performance in the process of generating complex geometry of the building and its various elements, later for the market of mass customisation manufacturing.
Hybrid lattice structures consisting of multiple microstructures have drawn much attention due to their excellent performance and extraordinary designability. This work puts forward a novel design scheme of lightweight hybrid lattice structures based on independent continuous mapping (ICM) method. First, the effective elastic properties of various microstructure configurations serve as a bridge between the macrostructure and the multiple microstructures by the homogenization theory. Second, a concurrent topology optimization model for seeking optimized macroscale topology and the specified microstructures is established and solved by a generalized multi-material interpolation formulation and sensitivity analysis. Third, several numerical examples show that hybrid lattice structures with different anisotropic configurations accomplish a better lightweight effect than those with various orthogonal configurations, which verifies the feasibility of the presented method. Hence, anisotropic configurations are more conducive to the sufficient utilization of constitutive material. The proposed scheme supplies a reference for the design of hybrid lattice structures and extends the application field of the ICM method.
The tail spike of the mantis shrimp is the appendage for counteracting the enemy from behind. Here, we investigate the correlations between the chemical compositions, the microstructures, and the mechanical properties of the spike. We find that the spike is a hollow beam with a varying cross section along the length. The cross section comprises four different layers with distinct features of microstructures and chemical compositions. The local mechanical properties of these layers correlate well with the microstructures and chemical compositions, a combination of which effectively restricts the crack propagation while maximizing the release of strain energy during deformation. Finite element analysis and mechanics modeling demonstrate that the optimized structure of the spike confines the mechanical damage in the region near the tip and prevents catastrophic breakage at the base. Furthermore, we use a 3D printing technique to fabricate multiple hollow cylindrical samples consisting of biomimetic microstructures of the spike and confirm that the combination of the Bouligand structure with radially oriented parallel sheets greatly improves the toughness and strength during compression tests. The multiscale design strategy of the spike revealed here is expected to be of great interest for the development of novel bioinspired materials.
In order to design a painless and mechanically durable micro syringe-needle system for biomedical applications, the study of insect stingers is of interest because of their elegant structures and functionalities. In the present work, the structure, mechanical properties and the mechanical behavior during insertion of wasp and honeybee stingers have been investigated. The non-invasive imaging tool, micro-computed tomography has been employed to reveal the 3D-structures of wasp and honeybee stingers. A quasi-static nanoindentation instrument was used to measure the nanomechanical properties. Both wasp and honeybee stingers have graded mechanical properties, decreasing along their longitudinal direction starting from the base. The computed tomography images and the measured material properties from nanoindentation were fed into a computational framework to determine the mechanical behavior of the stingers during penetration. The computation results predicted the penetration angle of +10o for the wasp stinger and -6o for the honeybee stinger, which mimics the practical insertion mechanism of both stingers. Based on this understanding, a wasp and honeybee stringer inspired micro syringe-needle design has also been proposed.
Over the course of their wildly successful proliferation across the earth, the insects as a taxon have evolved enviable adaptations to their diverse habitats, which include adhesives, locomotor systems, hydrophobic surfaces, and sensors and actuators that transduce mechanical, acoustic, optical, thermal, and chemical signals. Insect-inspired designs currently appear in a range of contexts, including antireflective coatings, optical displays, and computing algorithms. However, as over one million distinct and highly specialized species of insects have colonized nearly all habitable regions on the planet, they still provide a largely untapped pool of unique problem-solving strategies. With the intent of providing materials scientists and engineers with a muse for the next generation of bioinspired materials, here, a selection of some of the most spectacular adaptations that insects have evolved is assembled and organized by function. The insects presented display dazzling optical properties as a result of natural photonic crystals, precise hierarchical patterns that span length scales from nanometers to millimeters, and formidable defense mechanisms that deploy an arsenal of chemical weaponry. Successful mimicry of these adaptations may facilitate technological solutions to as wide a range of problems as they solve in the insects that originated them.
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.
Like many other venomous organisms, scorpions use their venom in defence against predators. Scorpions apply their venomous stinger by extending the caudal part of the body, the metasoma, forward towards the attacker. There are considerable differences in metasoma morphology among scorpion species, and these may afford differences in defensive strike performance.
We investigated the movement trajectory and kinematics of the defensive strike in seven species of scorpions, and how these variables are related to each other, and to morphology.
We recorded defensive strikes using high‐speed video, and reconstructed the trajectory of the telson. From these trajectories, we calculated velocity, acceleration and other kinematic variables. To compare strike trajectory shapes, we used geometric morphometrics.
We have shown that the defensive strike differs in trajectory shape, speed, path length and duration between scorpion species. Body size is also an important factor affecting strike characteristics. Relative metasoma length and girth may also influence strike performance, as well as strike trajectory shape. Strikes with different trajectories have different kinematic properties: those with open trajectory shapes attain higher speeds.
Our results show that performance differences in defensive behaviour between different scorpion species may be partly mediated by morphology, binding together phenotypic, functional and behavioural diversity.
A lay summary is available for this article.
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.
Enhancing quality of food products and reducing volume of waste during mechanical operations of food industry requires a comprehensive knowledge of material response under loadings. While research has focused on mechanical response of food material, the volume of waste after harvesting and during processing stages is still considerably high in both developing and developed countries. This research aims to develop and evaluate a constitutive model of mechanical response of tough skinned vegetables under postharvest and processing operations. The model focuses on both tensile and compressive properties of pumpkin flesh and peel tissues where the behaviours of these tissues vary depending on various factors such as rheological response and cellular structure. Both elastic and plastic response of tissue were considered in the modelling process and finite elasticity combined with pseudo elasticity theory was applied to generate the model. The outcomes were then validated using the published results of experimental work on pumpkin flesh and peel under uniaxial tensile and compression. The constitutive coefficients for peel under tensile test was α = 25.66 and β = -18.48 Mpa and for flesh α = -5.29 and β = 5.27 Mpa. under compression the constitutive coefficients were α = 4.74 and β = -1.71 Mpa for peel and α = 0.76 and β = -1.86 Mpa for flesh samples. Constitutive curves predicted the values of force precisely and close to the experimental values. The curves were fit for whole stress versus strain curve as well as a section of curve up to bio yield point. The modelling outputs had presented good agreement with the empirical values and the constructive curves exhibited a very similar pattern to the experimental curves. The presented constitutive model can be applied next to other agricultural materials under loading in future.
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.
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.
The spider fang is a natural injection needle, hierarchically built from a complex composite material comprising multiscale architectural gradients. Considering its biomechanical function, the spider fang has to sustain significant mechanical loads. Here we apply experiment-based structural modelling of the fang, followed by analytical mechanical description and Finite-Element simulations, the results of which indicate that the naturally evolved fang architecture results in highly adapted effective structural stiffness and damage resilience. The analysis methods and physical insights of this work are potentially important for investigating and understanding the architecture and structural motifs of sharp-edge biological elements such as stingers, teeth, claws and more.
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.
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.
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.
Natural materials such as bone, tooth, and nacre are nanocomposites of proteins and minerals with superior strength. Why is the nanometer scale so important to such materials? Can we learn from this to produce superior nanomaterials in the laboratory? These questions motivate the present study where we show that the nanocomposites in nature exhibit a generic mechanical structure in which the nanometer size of mineral particles is selected to ensure optimum strength and maximum tolerance of flaws (robustness). We further show that the widely used engineering concept of stress concentration at flaws is no longer valid for nanomaterial design.
With natural evolution, honeybee stinger with micro barbs can easily penetrate and trapped in the skin of hostile animals to inject venoum for self-defense. We proposed a novel 3D additive manufacturing method named magnetorheological drawing lithography (MRDL) to efficiently fabricate the bio-inspired microneedle imitating honeybee stinger. Under the assistance of external magnetic field, a parent microneedle was directly drawn on the pillar tip and tilted micro barbs were subsequently formed on the four sides of parent microneedle. Compared with barbless microneedle, the micro-structured barbs enable the bio-inspired microneedle easy skin insertion and difficult removal. The extraction-penetration force ratio of bio-inspired microneedle was triple of the barbless microneedle. The stress concentrations at the barbs helps to reduce the insertion force of bio-inspired microneedle by minimizing the frictional force while increase the adhesion force by interlocking barbs in the tissue during retraction. Such finds may provide an inspiration for the further design of barbed microtip-based microneedle for tissue adhesion, transdermal drug delivery, bio-signal recording, and so on.
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).
Purpose
To tackle the challenge topic of continuum structural layout in presence of random loads, and to develop an efficient robust method.
Design/methodology/approach
An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately via the Taylor expansion technique. The design problem is solved by Bi-directional Evolutionary Structural Optimization (BESO) method utilizing the derived sensitivity numbers.
Findings
The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.
Originality/value
A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.
Microneedles (MNs) are micro-scale needles used for drug delivery and other targets. Micro-scale size endows them with many advantages over hypodermic needles, including painlessness, minimal invasiveness and convenient operation, but it may also lead to risk of mechanical failures, which should be prevented in the clinical applications of MNs. The objective of this review is mainly to introduce studies on the mechanics problems with respect to MNs. Firstly, the basic knowledge of MNs is introduced in brief, so that readers can understand the basic characteristics of MNs. Secondly, researches on inserting behavior and mechanical performances of MNs are discussed. Thirdly, literatures on the drug delivery and the pain resulted from the insertion of MNs are overviewed. Finally, some bio-microneedles and bio-inspired MNs are introduced.
Statement of significance:
Living organisms are adept at resisting contact damage by assembling protective surfaces with spatially varied mechanical properties, i.e., by creating functionally-graded materials. Such gradients, together with multiple length-scale hierarchical structures, represent the prime characteristics of many biological materials. Here, we examine one design motif from a variety of biological tissues where site-specific mechanical properties are generated for enhanced protection by adopting gradients in structural orientation at multiple length-scales, without changes in composition or microstructural dimension. The design strategy of such bioinspired gradients is outlined in terms of the geometry of constituents. This study may offer a feasible approach towards generating functionally-graded mechanical properties in synthetic materials for improved damage resistance.
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.
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.
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.
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.
In classical deterministic topology optimization, the effect of the possible boundary variations on the performance of the structure is not taken into account, which may lead to designs that are very sensitive to manufacturing errors. As a consequence, the performance of the real structure may be far from optimal and even not meet the design requirements. In the present paper, structural topology optimization considering the uncertainty of boundary variations is considered via level set approach. In order to make the optimal designs less sensitive to the possible boundary variations, we choose the compliance and fundamental frequency of structure enduring the worst case perturbation as the objective function for ensuring the robustness of the optimal solution. With use of the Schwarz inequality, the original Bi-level optimization problem is transformed to a single-level optimization problem, which can be solved efficiently. Numerical examples demonstrate the effectiveness of the proposed approach.
Most natural (or biological) materials are complex composites whose mechanical properties are often outstanding, considering the weak constituents from which they are assembled. These complex structures, which have risen from hundreds of million years of evolution, are inspiring Materials Scientists in the design of novel materials.Their defining characteristics, hierarchy, multifunctionality, and self-healing capability, are illustrated. Self-organization is also a fundamental feature of many biological materials and the manner by which the structures are assembled from the molecular level up. The basic building blocks are described, starting with the 20 amino acids and proceeding to polypeptides, polysaccharides, and polypeptides–saccharides. These, on their turn, compose the basic proteins, which are the primary constituents of ‘soft tissues’ and are also present in most biominerals. There are over 1000 proteins, and we describe only the principal ones, with emphasis on collagen, chitin, keratin, and elastin. The ‘hard’ phases are primarily strengthened by minerals, which nucleate and grow in a biomediated environment that determines the size, shape and distribution of individual crystals. The most important mineral phases are discussed: hydroxyapatite, silica, and aragonite.Using the classification of Wegst and Ashby, the principal mechanical characteristics and structures of biological ceramics, polymer composites, elastomers, and cellular materials are presented. Selected systems in each class are described with emphasis on the relationship between their structure and mechanical response. A fifth class is added to this: functional biological materials, which have a structure developed for a specific function: adhesion, optical properties, etc.An outgrowth of this effort is the search for bioinspired materials and structures. Traditional approaches focus on design methodologies of biological materials using conventional synthetic materials. The new frontiers reside in the synthesis of bioinspired materials through processes that are characteristic of biological systems; these involve nanoscale self-assembly of the components and the development of hierarchical structures. Although this approach is still in its infancy, it will eventually lead to a plethora of new materials systems as we elucidate the fundamental mechanisms of growth and the structure of biological systems.
There are several well-established techniques for the generation of solid-void optimal topologies such as solid isotropic
material with penalization (SIMP) method and evolutionary structural optimization (ESO) and its later version bi-directional
ESO (BESO) methods. Utilizing the material interpolation scheme, a new BESO method with a penalization parameter is developed
in this paper. A number of examples are presented to demonstrate the capabilities of the proposed method for achieving convergent
optimal solutions for structures with one or multiple materials. The results show that the optimal designs from the present
BESO method are independent on the degree of penalization. The resulted optimal topologies and values of the objective function
compare well with those of SIMP method.
A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.
A linear elastic response is assumed in most structural topology optimization problems. While this assumption is valid for a wide variety of problems, it is not valid for structures undergoing large displacements. The elastic structural analysis used here accommodates geometric and material non-linearities. The material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities. The filtering scheme is embedded in the structural analysis to resolve the non-existent solution to the solid-void topology problem. In this way, we know precisely what optimization problem is being solved. The structural topology optimization formulation is also used to design compliant mechanisms.
After outlining analytical methods for layout optimization and illustrating them with examples, the COC algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members. The numerical results obtained are shown to be in close agreement (up to twelve significant digits) with analytical results. Finally, the problem of generalized shape optimization (finding the best boundary topology and shape) is discussed.
This paper presents a new approach to structural topology optimization. We represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension. Such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure. Furthermore, a well-founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints. The result is a 3D topology optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation. We have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods. The benefit and the advantages of the proposed method are illustrated with several 2D examples that are widely used in the recent literature of topology optimization, especially in the homogenization based methods.
In the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or nonlinear elasticity. We consider various objective functions with weight and perimeter constraints. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a fixed Eulerian mesh. Although this method is not specifically designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess.
We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh. To cite this article: G. Allaire et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1125–1130.RésuméNous proposons une méthode de lignes de niveaux pour l'optimisation de la forme de structures élastiques. Notre approche combine la méthode des lignes de niveaux d'Osher et Sethian et la dérivée classique de formes. Bien que cette méthode ne soit pas spécifiquement conçue pour faire de l'optimisation topologique, elle permet très facilement les changements de topologie de la forme d'une structure pour des fonctions objectifs très générales. Son coût en temps de calcul est modéré puisqu'il s'agit d'une méthode numérique de capture de formes sur un maillage eulérien fixe. Pour citer cet article : G. Allaire et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1125–1130.
Nonlinear Mechanics of Thin Elastic Rod -Theoretical Basis of Mechanical Models of DNA
- Y Z Liu
- Z Liu
- Z Zhang
- R O Ritchie
Liu, Y.Z., 2006. Nonlinear Mechanics of Thin Elastic Rod -Theoretical Basis of Mechanical Models of DNA. Tsinghua University Press, Beijing.
Liu, Z., Zhang, Z., Ritchie, R.O., 2018b. On the materials science of nature's arms race. Adv. Mater. 30, 1705220.