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Simple and effective strategies for achieving diverse and competitive structural designs

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Abstract

Shape and topology optimization techniques are widely used to maximize the performance or minimize the weight of a structure through optimally distributing its material within a prescribed design domain. However, existing optimization techniques usually produce a single optimal solution for a given problem. In practice, it is highly desirable to obtain multiple design options which not only possess high structural performance but have distinctly different shapes and forms. Here we present five simple and effective strategies for achieving such diverse and competitive structural designs. These strategies have been successfully applied in the computational morphogenesis of various structures of practical relevance and importance. The results demonstrate that the developed methodology is capable of providing the designer with structurally efficient and topologically different solutions. The structural performance of alternative designs is only slightly lower than that of the optimal design. This work establishes a general approach to achieving diverse and competitive structural forms, which holds great potential for practical applications in architecture and engineering.

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... Wang et al. [16] presented three graphic diversity measures, cross-correlation, modified cross-correlation and the sum of squared differences to set the desired diversity to find diverse competitive designs for topology optimization problems. Xie et al. [17] and Yang et al. [18] presented some simple and effective strategies for achieving diverse and competitive structural designs which are successfully applied in the computational morphogenesis of various structures. Cai et al. [19] explored two strategies, namely, the penalizing length method and the modifying ground structure method, for generating diverse truss structures while maintaining structural performance. ...
... Once a threshold distance is exceeded, the spacecraft subsystem may not work normally. Therefore, this distance constraint is defined as the safety and feasibility constraint, which can be represented by the minimum distance constraint (18) or the maximum distance constraint ...
... A method using a graphic diversity measure was proposed to generate diverse solutions for topology optimization based on the solid isotropic material with penalization (SIMP) method [3,33]. Some simple and effective strategies for achieving diverse and competitive structure designs were proposed based on the bidirectional evolutionary structural optimization (BESO) method [17,16,34]. ...
... This result is similar to the result obtained by Yang [34] using the BESO method [17] in continuum topology optimization. ...
Article
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Structural topology optimization plays an important role in obtaining conceptual designs in the preliminary design stage. However, traditional structural optimization methods can only generate one optimized design for the material distribution under certain constraints. The optimized structure could have some disadvantages, such as an unattractive appearance, difficulty in manufacturing, or high construction cost. Therefore, it is more practical to produce multiple designs that not only have high structural performance but also have substantially different forms from which the designer can choose. Two strategies were explored in this study for generating diverse truss structures, namely, the penalizing length method (PLM) and the modifying ground structure method (MGSM). Using the proposed PLM, it is possible to delete unneeded bars in the optimized structure, such as very slender bars, and the cross-sectional areas of the remaining bars will be automatically redistributed to ensure structural nodal stability. In addition, by generating overlapping potential bars in the ground structure, the structural instability problem caused by pin joints can be overcome. Two-dimensional and three-dimensional numerical examples were provided to indicate the effectiveness of the proposed methods. The numerical results showed that the proposed methodologies can generate diverse structures while maintaining structural performance.
... For instance, the level-set method uses higherdimensional implicit functions [22][23][24][25][26], and the moving morphable components method controls the shapes and layout of a set of structural components. 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]. ...
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Ribbed slabs are widely used in the building industry. Designing ribbed slabs through conventional engineering techniques leads to limited structural forms, low structural performance and high material waste. Topology optimization is a powerful tool for generating free-form and highly efficient structures. In this research, we develop a mapping constraint optimization approach to designing ribbed slabs and shells. Compared with conventional ones, the presented approach is able to produce designs with higher performance and without isolated ribs. The approach is integrated into three optimization methods and used to design both flat slabs and curved shells. Several numerical examples are used to demonstrate the effectiveness of the new approach. The findings of this study have potential applications in the design of aesthetically pleasing and structurally efficient ribbed slabs and shells.
... However, the traditional BESO technique is computationally expensive in the FEA and filtering process. To help engineers and designers obtain high-resolution designs in a timely manner [34,35], the computational efficiency of the BESO technique needs to be further improved. ...
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The bi-directional evolutionary structural optimisation (BESO) has attracted much interest in recent decades. However, the high computational cost of the topology optimisation method hinders its applications in large-scale industrial designs. In this study, a parallel BESO method is developed to solve high-resolution topology optimisation problems. An open-source computing platform, FEniCS, is used to parallelise the finite element analysis (FEA) and optimisation steps. Significant improvements in efficiency have been made to the FEA and the filtering process. An iterative solver, a reanalysis approach and a hard-kill option in BESO have been developed to reduce the computational cost of the FEA. An isotropic filter scheme is used to eliminate the time-consuming elemental adjacency search process. The efficiency and effectiveness of the developed method are demonstrated by a series of numerical examples in both 2D and 3D. It is shown that the parallel BESO can efficiently solve problems with more than 100 million tetrahedron elements on a 14-core CPU server. This work holds great potential for high-resolution design problems in engineering and architecture. Keywords: Topology optimisation, Bi-directional evolutionary structural optimisation, FEniCS, Parallel computing, High-resolution
... Theoretically, if the supporting and loading conditions remain unchanged in the process of design evolution, the less artificial interference, the higher the strength of the final optimized structure. However, adding non-design domains is a very simple but effective way to direct the topology optimization process to achieve desired designs [35][36][37]. ...
Article
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This paper proposes a novel bridge design approach based on multi-material topology optimization, which realizes the process from conceptual design to detailed design, and an innovative bridge form is obtained with the proposed approach. In the present study, the multi-material bi-directional evolutionary structural optimization (MBESO) method, which is developed from the bi-directional evolutionary structural optimization (BESO) method, is used as the algorithm which can effectively handle topology optimization problems involving multiple materials. Since the method assigns two different materials to the tension and compression members in a structure, it is particularly suitable for designing bridge structures composed of steel and concrete. A three-span bridge with a main span of 350 m is used as an example to apply the MBESO method for the topology optimization design, and a set of techniques are introduced, such as the variation of the design domain, the utilization of symmetry, the selection of the non-design domain and the consideration of multiple load cases, to obtain multiple optimization results. By 2 comprehensively studying the functionality, ease of construction, and aesthetic properties, a competitive result is selected as the proposed conceptual design for the bridge, and then a detailed design, including an implementable construction process, is achieved and verified by finite element analysis. The comparison between the proposed bridge and other typical bridge types based on technical and economic indicators clearly shows the obvious advantages of the new type of bridge design. This research work realizes the whole process to obtain the detailed design of a new bridge type from the form-finding with the MBESO method, revealing the considerable value of applying multi-material topology optimization to the design of practical long-span bridges.
... To overcome this bottleneck, we have developed a series of techniques capable of producing multiple designs that have distinctly different configurations but possess similar structural performance to that of the optimal solution (He et al., 2020;Yang et al., 2019). We show that vastly different designs could be obtained by sacrificing a small amount (e.g., 3%) of the structural performance. ...
Article
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In recent years, topology optimization has become a popular strategy for creating elegant and innovative forms for architectural design. However, the use of existing topology optimization techniques in practical applications, especially for large-scale projects, is rare because the generated forms often cannot satisfy all the design requirements of architects and engineers. This paper identifies the limitations of commonly used assumptions in topology optimization and highlights the importance of having multiple solutions. We show how these limitations could be removed and present various techniques for generating diverse and competitive structural designs that are more useful for architects. Unlike conventional topology optimization, we may include load and support conditions as additional design variables to enhance the structural performance substantially. Furthermore, we show that varying the design domain provides a plethora of opportunities to achieve more-desirable design outcomes.
... This approach allows the designer to directly control the topological feature of both 2D and 3D structures. Numerical results demonstrate that the developed methodology is capable of providing the designer with structurally efficient and topologically different designs [50][51][52]. This work provides a useful tool for engineers and architects to control the topology directly in structural optimization. ...
Article
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Shape and topology optimization techniques aim to maximize structural performance through material redistribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. Structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two- and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Numerical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations.
... 1 From the aspect of designers, it is also a practical methodology to break the limitations of experience and produces innovative designs. 2,3 Bi-disc systems are used in the environment with different physical requirements in the inner and outer sides. In the process of lightweight design, it is necessary to guarantee that the optimized design not only satisfies the stiffness but also meets the strength from the view of usage and safety. ...
Article
Aiming at solving the lightweight design problems for bi‐disc systems with consideration of the stiffness and strength simultaneously, a two stage topology optimization framework based on independent continuous and mapping (ICM) method is developed. Firstly, topology optimization formulations are established to guarantee the optimized design satisfying the key nodal displacement and stress constraints. Secondly, an information function is introduced to realize the transformation of the material properties between elements and components. Composite exponential filter functions are selected to establish the relationship between the properties of elements and corresponding topology design variables. Thirdly, approximate explicit quadratic programming model is obtained by the sensitivity analysis and Taylor expansion. In the process of solving, the duality theory is used to establish the approximate dual model with less design variables. Finally, a series of topology optimization design problems for bi‐disc systems are presented and discussed to illustrate the robustness and feasibility of the method. This study finds some new torsional bi‐disc designs and can also provide some theoretical references for the lightweight topology optimization of a multi‐component system.
... It is worth mentioning that the existing optimization techniques usually aim to produce a single optimal solution for a given set of loading and boundary conditions. In practice, it is highly desirable to obtain multiple design options which not only possess high structural performance but also have distinctly different shapes and forms [40,41]. By imposing different constraints on the evolution of the design space (e.g., setting a non-design region), or using different termination criteria for the form-finding process, the ADD method is capable of providing the designer with diverse and competitive structural designs. ...
Article
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Topology optimization has rapidly developed as a powerful tool of structural design in multiple disciplines. Conventional topology optimization techniques usually optimize the material layout within a predefined, fixed design domain. Here, we propose a subdomain-based method that performs topology optimization in an adaptive design domain (ADD). A subdomain-based parallel processing strategy that can vastly improve the computational efficiency is implemented. In the ADD method, the loading and boundary conditions can be easily changed in concert with the evolution of the design space. Through the automatic, flexible, and intelligent adaptation of the design space, this method is capable of generating diverse high-performance designs with distinctly different topologies. Five representative examples are provided to demonstrate the effectiveness of this method. The results show that, compared with conventional approaches, the ADD method can improve the structural performance substantially by simultaneously optimizing the layout of material and the extent of the design space. This work might help broaden the applications of structural topology optimization.
... Based on the SIMP method, multiple designs are achieved by introducing geometric diversity constraints (Wang et al., 2018), and a surrogate model is proposed to solve a 3D, multiscale compliance design problem (Gao et al., 2019). With BESO, some modifications are presented to generate geometrically different designs with similar structural performance (Yang et al., 2019;He et al., 2020), eliminate enclosed voids in topology optimization for additive manufacturing (Xiong et al., 2020), and obtain self-supporting optimized models (Bi et al., 2020). However, the above methods are developed for a certain objective on the basis of a specific conventional topology optimization method and are perplexing to architects or designers who are not familiar with the relevant algorithm. ...
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With the ability to generate forms with high efficiency and elegant geometry, to-pology optimization has been increasingly used in architectural and structural designs. However , the conventional topology optimization techniques aim at achieving the structurally most efficient solution without any potential for architects or designers to control the design details. This paper introduces three strategies based on Bi-directional Evolutionary Structural Optimization (BESO) method to artificially pre-design the topological optimized structures. These strategies have been successfully applied in the computational morphogenesis of various structures for solving practical design problems. The results demonstrate that the developed methodology can provide the designer with structurally efficient and topologically different solutions according to their proposed designs with multi-filter radii, multi-volume fractions, and multi-weighting coefficients. This work establishes a general approach to integrating objective topology optimization methods with subjective human design preferences, which has great potential for practical applications in architecture and engineering industry.
... 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). ...
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Purpose-Furniture plays a significant role in daily life. Advanced computational and manufacturing technologies provide new opportunities to create novel, high-performance and customized furniture. This paper aims to enhance furniture design and production by developing a new workflow in which computer graphics, topology optimization and advanced manufacturing are integrated to achieve innovative outcomes. Design/methodology/approach-Workflow development is conducted by exploring state-of-the-art computational and manufacturing technologies to improve furniture design and production. Structural design and fabrication using the workflow are implemented. Findings-An efficient transdisciplinary workflow is developed, in which computer graphics, topology optimization and advanced manufacturing are combined. The workflow consists of the initial design, the optimization of the initial design, the postprocessing of the optimized results and the manufacturing and surface treatment of the physical prototypes. Novel chairs and tables, including flat pack designs, are produced using this workflow. The design and fabrication processes are simple, efficient and low-cost. Both additive manufacturing and subtractive manufacturing are used. Practical implications-The research outcomes are directly applicable to the creation of novel furniture, as well as many other structures and devices. Originality/value-A new workflow is developed by taking advantage of the latest topology optimization methods and advanced manufacturing techniques for furniture design and fabrication. Several pieces of innovative furniture are designed and fabricated as examples of the presented workflow.
... 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 Xiong 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). ...
Article
Full-text available
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.
... Wang et al [46] achieve diverse and competitive designs by incorporating graphic diversity constraints, which is in the framework of SIMP method. Based on different penalty method, Yang et al [47] presents five simple and effective strategies to achieve multiple solutions, where these strategies are demonstrated to provide the designer with structurally efficient and topologically different solutions. Recently, He and Xie et al [48] proposed three stochastic approaches to generate diverse and competitive designs in the framework of bi-directional evolutionary structural optimization (BESO), where a series of random designs are produced with distinctly different topologies. ...
Preprint
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This paper proposes a new parametric level set method for topology optimization based on Deep Neural Network (DNN). In this method, the fully connected deep neural network is incorporated into the conventional level set methods to construct an effective approach for structural topology optimization. The implicit function of level set is described by fully connected deep neural networks. A DNN-based level set optimization method is proposed, where the Hamilton-Jacobi partial differential equations (PDEs) are transformed into parametrized ordinary differential equations (ODEs). The zero-level set of implicit function is updated through updating the weights and biases of networks. The parametrized reinitialization is applied periodically to prevent the implicit function from being too steep or too flat in the vicinity of its zero-level set. The proposed method is implemented in the framework of minimum compliance, which is a well-known benchmark for topology optimization. In practice, designers desire to have multiple design options, where they can choose a better conceptual design base on their design experience. One of the major advantages of DNN-based level set method is its ability to generate diverse and competitive designs with different network architectures. Several numerical examples are presented to verify the effectiveness of the proposed DNN-based level set method.
... The search for minimum material consumption is evident in drawing inspiration from solutions found in Nature. The availability of algorithmic tools for optimization combines aesthetic expression with structural logic [56,57]. Arboreal divisions can be an infinite set of topologies of structures with an attractive geometric form to obtain. ...
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Sustainable Development Goals have become a key factor in the design in the twenty-first century. The relationship between the architectural and structural systems is becoming a matter of relevance for sustainable design. The search for minimum material consumption can be seen by drawing inspiration from the solutions found in Nature. The high efficiency of natural forms, has become a contribution to research on tree-like structures. The purpose of the research was to identify the main aspects of arboreal supporting structures shaping and optimization at the early state of design. The methodology is to optimize the geometry of dendriforms, based on optimizing the shape of the bending moment diagram and adjusting it to the shape of the final bar structure. The primary conclusion of the studies indicates that the structural and architectural optimization, implemented in an early stage of designing might significantly improve material consumption without substantial changes in architectural appearance.
... The optimized results from BESO technique contain zig-zag boundaries, which may lead to the reduction of structural performance and difficulty to manufacture. In order to obtain accurate structural boundaries, a smoothing technique is proposed for reconstructing the element-based model [35][36]. ...
Article
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Background: As an advanced design technique, topology optimization has received much attention over the past three decades. Topology optimization aims at finding an optimal material distribution in order to maximize the structural performance while satisfying certain constraints. It is a useful tool for the conceptional design. At the same time, additive manufacturing technologies have provided unprecedented opportunities to fabricate intricate shapes generated by topology optimization. Objective: To design a highly efficient structure using topology optimization and to fabricate it using additive manufactur-ing. Method: The bi-directional evolutionary structural optimization (BESO) technique provides the conceptional design, and the topology-optimized result is post-processed to obtain smooth structural boundaries. Results: We have achieved a highly efficient and elegant structural design which won the first prize in a national competition in China on design optimization and additive manufacturing. Conclusion: In this paper, we present an effective topology optimization approach to maximizing the structural load-bearing capacity and establish a procedure to achieve efficient and elegant structural designs. In the loading test of the final competition, our design carried the highest loading and won the first prize of the competition, which clearly demonstrates the capability of BESO in engineering applications.
... 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). ...
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Previous studies on topology optimization subject to stress constraints usually considered von Mises or Drucker–Prager criterion. In some engineering applications, e.g., the design of concrete structures, the maximum first principal stress (FPS) must be controlled in order to prevent concrete from cracking under tensile stress. This paper presents an effective approach to dealing with this issue. The approach is integrated with the bi-directional evolutionary structural optimization (BESO) technique. The p-norm function is adopted to relax the local stress constraint into a global one. Numerical examples of compliance minimization problems are used to demonstrate the effectiveness of the proposed algorithm. The results show that the optimized design obtained by the method has slightly higher compliance but significantly lower stress level than the solution without considering the FPS constraint. The present methodology will be useful for designing concrete structures.
... For example, the original design domain showed in Figure 1(a) without any modification generates the form in Figure 1(c). However, with setting the functional cavity and nondesign domain into the model before calculation, the final design can be partly manipulated by designers intently Figure 1(b) [4]. ...
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This research explores innovations in structural design and construction through the generative design technique BESO (Bi-directional Evolutionary Structural Optimization)[1]and the application of robotic fabrication to produce efficient and elegant spatial structures. The innovative pavilion discussed in this paper demonstrates a design and fabrication process and thecollaborationbetween architecture and engineering research groups through a series of small-scale test models and a full-scale model of topologically optimized spatial structures. The focus of this work is the use of a modified BESO technique to optimize the structure which features branches of various sizes, inspired by Gaudi’s Sagrada Familia Bacilica, and the introduction of large-scalerobotic 3D printing developed at RMIT University.The advantages of the new design and construction process are efficient material usage and elegant structural forms.
... The results also show that there exist multiple similar performance porous structural designs with different geometric features. From the point of view of design, this can contribute to the diversity of the designs (Wang et al. 2018;Yang et al. 2019). ...
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Porous structures are of valuable importance in additive manufacturing. They can also be exploited to improve damage tolerance and fail-safe behavior. This paper presents a projection approach to design optimized porous structures in the framework of density-based topology optimization. In contrast to conventional constraint approach, the maximum local volume limitation is integrated into the material interpolation model through a filtering and projection process. This paper also presents two extensions of the basic approach, including a robust formulation for improving weak structural features and mesh/design refinement for enhancing computational stability and efficiency. The applicability of the proposed methodology is demonstrated by a set of numerical minimum compliance problems. This approach can be used in a wider range of applications concerning porous structures.
... Wang et al. firstly proposed a method to obtain multiple diverse competitive designs for stiffness problems using density-based topology optimization method. Then, Yang et al. (Yang et al. 2019) provided five simple and effective strategies that can be easily implemented and used to achieve diverse and competitive solutions for practical applications in architecture and engineering based on bi-directional evolutionary structural optimization method. In this paper, we extend the concept of diverse design into diverse discrete material optimization (DDMO) of multi-patch hybrid laminates under the vibration environment. ...
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In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle.
... Based on the SIMP method, Wang et al. achieved multiple designs by introducing graphic diversity constraints and the technique was applied to several 2D optimization problems [33]. Based on different penalty methods, Yang et al. proposed five simple strategies to obtain diverse and competitive designs, which can be easily integrated into commonly used topology optimization techniques [34]. Zhao et al. developed an approach to control the number and size of the interior holes of structures [35]. ...
Article
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Topology optimization techniques have been widely used in structural design. Conventional optimization techniques usually are aimed at achieving the globally optimal solution which maximizes the structural performance. In practical applications, however, designers usually desire to have multiple design options, as the single optimal design often limits their artistic intuitions and sometimes violates the functional requirements of building structures. Here we propose three stochastic approaches to generating diverse and competitive designs. These approaches include (1) penalizing elemental sensitivities, (2) changing initial designs, and (3) integrating the genetic algorithm into the bi-directional evolutionary structural optimization (BESO) technique. Numerical results demonstrate that the proposed approaches are capable of producing a series of random designs, which possess not only high structural performance, but also distinctly different topologies. These approaches can be easily implemented in different topology optimization techniques. This work is of significant practical importance in architectural engineering where multiple design options of high structural performance are required.
... There are two main challenges interrupting the integration process in the design phase; computing power and design variation. These obstacles are addressed by current research, including the GPU based tool by Bialkowski [4] and the diverse structural designs by Yang [5]. However, architects would require more than fast processing and a variation of design options. ...
Conference Paper
The research conducted on the applications of Topology Optimization (TO) in the architectural field is limited. This paper investigates the significance of assigning the right design and non-design domain and support conditions in the TO process and its effects on the optimization results. The existing approach of TO relies on defining the design domains in areas that are part of the structural elements. This research challenges the norm of where the structure is allocated to evaluate the results against the criteria of minimizing material. The study investigates the idea of interpreting the design domains in a more rational perspective, using anthropometric criteria to create efficient spaces with minimum material use. The methodology involves modelling a spatial structure that evaluates scenarios with different design domains, using the SIMP method. The research is part of the Material Balance Research group projects in Politecnico di Milano, where a case study is conducted on a roof canopy in an attraction park to investigate the results on a practical project. The study illustrates the impact of assigning the right design domain on the optimization process, not only on the performative and material distribution but in terms of meeting design criteria and creating usable spaces. It also reexamines the idea of optimization and highlights the concept of an optimized design not necessarily being the best design.
... The structural performance and the effect of the SCC can be well balanced by using this approach. The present methodology can effectively enhance the manufacturability of the optimized designs generated by structural optimization and provide the designer with diverse and competitive solutions [43]. This work holds great promise in advanced manufacturing and computational morphogenesis. ...
Article
Structural shape and topology optimization has undergone tremendous developments in recent years due to its important applications in many fields. However, effectively controlling the structural complexity of the optimization result remains a challenging issue. The structural complexity is usually characterized by the distribution and geometries of interior holes. In this work, a new approach is developed based on the graph theory and the set theory to control the number and size of interior holes of the optimized structures. The minimum distance between the edges of any two neighboring holes can also be constrained. The structural performance and the effect of the structural complexity control are well balanced by using this approach. We use three typical numerical examples to verify the effectiveness of the developed approach. The optimized structures with and without constraints on the structural complexity are quantitatively compared and analyzed. The present methodology not only enables the designer to have a direct control over the topology of the optimized structures, but also provides diverse and competitive solutions.
... We emphasize that the choice of the parameters is dependent on the specific example and it is very difficult to give a set of universally applicable optimal parameters. From another point of view, using different parameters may also provide the engineers with diverse designs [43,44] in the conceptual design phase. More discussion on the aggregation parameters µ σ and µ κ can be found in [27,45]. ...
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Topology optimization considering material strength, structural stiffness and stability has great potential in engineering applications. In this paper, a topology optimization model considering the three vital performance indices is formulated by taking stress and buckling constrained continuum structures for compliance minimization. An effective optimization algorithm is developed for dealing with various issues and difficulties involved in the solution. The Kreisselmeier–Steinhauser (K–S) aggregation function is introduced to approximate the maximum von Mises stress together with a stability transformation method (STM) based correction scheme to reduce the approximation error. A smooth buckling aggregation function is constructed with a number of low-order buckling load factors to replace the original possibly non-smooth buckling constraints. To improve the robustness of the algorithm and achieve better designs, a continuation strategy for several optimization parameters is employed. With all these techniques, stable convergence of the iterative solution process is achieved. Three numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
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近年来,越来越多的设计师使用拓扑优化技术来寻找优美且新颖的建筑设计。然而由于无法直接满足建筑师与工程师提出的诸多设计需求,现有方法生成的拓扑优化设计往往很少在实际案例(特别是大型项目)中出现。本文指出了拓扑优化中惯用假设的局限性,并揭示了寻找设计多解的重要性。为了生成多样化、高性能且满足使用需求的设计,我们突破了这些限制并提出了面向建筑领域的拓扑优化新方法。与传统的拓扑优化不同,我们可以将荷载和边界条件作为额外的设计变量,以显著提高最终设计的结构性能。此外,改变设计域能带来更多的可能性,使设计者可以从诸多设计方案中的获得满意的结果。
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This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.
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Evolutionary Structural Optimization (ESO) method is one of the powerful and promising techniques for pursuing the optimal structural form. Although it is easy to carry out the calculation of ESO, there have been remained some weak points in its evolutionary process, by which inefficiency of calculation is caused or unreasonable solutions are generated. The authors have already proposed a new method through the usage of the contour lines, which is named Extended ESO method, in order to remove such defects of the original ESO as well as to enable the structures to not only be scraped off but also grow up toward the final optimal structures. In this paper, extension for 3-dimensional structures of the Extended ESO method is proposed and the effectiveness of the proposed scheme is shown through some numerical examples as well as the application to the actual structural design project.
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The evolutionary structural optimization (ESO) and basic ESO (BESO) processes and given various illustrative examples are described. Such processes are based on the concept of slowly removing inefficient materials from a structures so that the residual structure evolves towards the optimum. It is shown that the simple ESO and BESO algorithms are capable of solving a wide range of shape and topology optimization problems.
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This paper presents a method for optimal design of compliant mechanism topologies. The method is based on continuum-type topology optimization techniques and finds the optimal compliant mechanism topology within a given design domain and a given position and direction of input and output forces. By constraining the allowed displacement at the input port, it is possible to control the maximum stress level in the compliant mechanism. The ability of the design method to find a mechanism with complex output behavior is demonstrated by several examples. Some of the optimal mechanism topologies have been manufactured, both in macroscale (hand-size) made in Nylon, and in microscale (<.5mm)) made of micromachined glass.
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This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.
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In this article, a modified (‘filtered’) version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ‘filtering’ technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs. Copyright © 2001 John Wiley & Sons, Ltd.
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Material based models for topology optimization of linear elastic solids with a low volume constraint generate very slender structures composed mainly of bars and beam elements. For this type of structure the value of the buckling critical load becomes one of the most important design criteria and so its control is very important for meaningful practical designs. This paper tries to address this problem, presenting an approach to introduce the possibility of critical load control into the topology optimization model.Using the material based formulation for topology design of structures, the problem of optimal structural reinforcement for a critical load criterion is formulated. The stability problem is conveniently reduced to a linearized eigenvalue problem assuming only material effective properties and macroscopic instability modes. The respective optimality criteria are presented by introducing the Lagrangian associated with the optimization problem. Based on this Lagrangian a first-order method is used as a basis for the numerical update scheme. Two numerical examples to validate the developments are presented and analysed.
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A serlous difficulty in topology optimization with only stress andlocal buckling constraints was pointed out recently by Zhou (1996a). Possibilities for avoiding this pitfall are (i) inclusion of system stability constraints and (ii) application of imperfections in the ground structure. However, it is shown in this study that the above modified procedures may also lead to erroneous solutions which cannot be avoided without changing the ground structure.
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Many engineering structures consist of specially-fabricated identical components, thus their topology optimizations with multiobjectives are of particular importance. This paper presents a unified optimization algorithm for multifunctional 3D finite periodic structures, in which the topological sensitivities at the corresponding locations of different components are regulated to maintain the structural periodicity. To simultaneously address the stiffness and conductivity criteria, a weighted average method is employed to derive Pareto front. The examples show that the optimal objective functions could be compromised when the total number of periodic components increases. The influence of thermoelastic coupling on optimal topologies and objectives is also investigated.
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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.
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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.
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Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, isotropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.
  • J D Deaton
  • R V Grandhi
J.D. Deaton, R.V. Grandhi, A survey of structural and multidisciplinary continuum topology optimization: post 2000, Struct. Multidiscip. Optim. 49 (1) (2014) 1-38.
  • L Xia
  • Q Xia
  • X Huang
  • Y M Xie
L. Xia, Q. Xia, X. Huang, Y.M. Xie, Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review, Arch. Comput. Methods Eng. 25 (2) (2018) 437-478.
  • G Cheng
  • Z Jiang
G. Cheng, Z. Jiang, Study on topology optimization with stress constraints, Eng. Optim. 20 (2) (1992) 129-148.
  • G D Cheng
  • X Guo
G.D. Cheng, X. Guo, ε-Relaxed approach in structural topology optimization, Struct. Optim. 13 (4) (1997) 258-266.