Hierarchical optimization for topology design of multi-material compliant mechanisms

Wang, N. F.; Hu, Kai; Zhang, X. M.

doi:10.1080/0305215x.2016.1277062

Cited by 13 publications

(11 citation statements)

References 45 publications

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“…Additionally, from Figure , it can be found that a localized strong material area appears on the compliant member, even though it is enclosed entirely by the weak material. This agrees well with the designs in the works about multi‐material topology optimization of compliant mechanisms …”

Section: Numerical Examplessupporting

confidence: 90%

“…Additionally, from Figure , it can be found that some localized strong material areas appear on the compliant members. This agrees well with the designs in the works about multi‐material topology optimization of compliant mechanisms . It is worth noting that a localized strong material area is enclosed entirely by the weak material and does not appear on the compliant member.…”

Section: Numerical Examplessupporting

confidence: 89%

“…The topology design of multi‐material compliant mechanisms by the multiple Sequential Element Rejection and Admission (SERA) method is presented in the work by Alonso et al The optimization is conducted to maximize the mutual potential energy subject to M constraints on the target volume fraction of the M materials. A bi‐level hierarchical optimization method is introduced to address the multi‐material design of compliant mechanisms in the work by Wang et al The hierarchical optimization develops decomposition approaches allowing the original complex multi‐material optimization problem to be reduced to a set of low‐order single‐material optimization sub‐problems. For each single‐material sub‐problem, the maximization of the Mutual Potential Energy (MPE) is treated as the objective function, subject to the corresponding volume fraction constraint of each material.…”

Section: Introductionmentioning

confidence: 99%

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Stress‐based multi‐material topology optimization of compliant mechanisms

Chu

Gao

Xiao

et al. 2017

Numerical Meth Engineering

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In this paper, a level-set-based method is presented to deal with the multi-material topology optimization of compliant mechanisms with stress constraints. A novel stress-based multi-material topology optimization model of compliant mechanisms is proposed. In this model, the multi-material level set topology description model and the separable stress interpolation scheme are adopted.The weighted sum method is used to deal with the multi-objective optimization of the output displacement and compliance of compliant mechanisms. The penalty of stresses is also considered in the objective function to control the local stress level in different materials. To solve the optimization problem, the parametric level set method is employed, and the sensitivity analysis is conducted. Application of the method is demonstrated by 2 numerical examples. Results show that the multi-material structures without undesirable de facto hinges can be obtained. The output displacement and compliance of the compliant mechanisms are optimized, and stress constraints in different materials are simultaneously satisfied. KEYWORDS compliant mechanisms, level set method, multi-material topology optimization, stress constraint 1 | INTRODUCTION Compliant mechanisms are defined as those which utilize the deformation of the flexible pieces to transfer motion, force, and energy. 1 In the last 20 years, topology optimization of compliant mechanisms is always attracting great attention. 2-4 There are 2 kinds of compliant mechanisms: lumped compliant mechanisms and distributed compliant mechanisms.The flexibility of the lumped compliant mechanisms is mainly derived from the localized areas (ie, hinge areas), 5 while the flexibility of the distributed compliant mechanisms is provided by the whole mechanism. 6 Whether lumped or distributed compliant mechanisms are optimal is a long standing and still open question in the field. 7 One issue is certain; however, there are 2 main difficulties in the topology design of the compliant mechanisms, namely the combination of the stiffness and flexibility, and the control of the stress level. 8 Compliant mechanisms should be stiff enough to support the applied loads and flexible enough to meet the kinematic requirements at the same time. The methods of dealing with the topology optimization of compliant mechanisms can be classified into 2 categories. The first one is to maximize some kinds of mechanical measurements, including mechanical advantage, 9 geometrical advantage, 10,11 mechanical efficiency, 12 and output displacement. 7,13 A comparative study of the above formulations for the topology optimization of compliant mechanisms is given in the work by Deepak et al. 14 The second handling method is considering a multi-objective topology optimization based on both the stiffness

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Section: Numerical Examplessupporting

confidence: 90%

Section: Numerical Examplessupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stress‐based multi‐material topology optimization of compliant mechanisms

Chu

Gao

Xiao

et al. 2017

Numerical Meth Engineering

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“…In the context of multi-material structures, there are some examples of structures topologically optimized using multiple materials to emulate an actuated structure [6], and create compliant mechanisms [7,8]. A thorough review of these approaches can be found in [9].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Generatively Encoded Multi-Material Lattice Structures for Desired Deformation Behavior

Ćurković

2021

Symmetry

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Natural systems achieve favorable mechanical properties through coupling significantly different elastic moduli within a single tissue. However, when it comes to man-made materials and structures, there are a lack of methods which enable production of artifacts inspired by these phenomena. In this study, a method for design automation based on alternate deposition of soft and stiff struts within a multi-material 3D lattice structure with desired deformation behavior is proposed. These structures, once external forces are applied, conform to the geometry given in advance. For that purpose, a population-based algorithm was proposed and integrated with a multi-material physics simulator. To reduce the amount of data processed during optimization, a generative encoding method based on discrete cosine transform (DCT) was proposed. This enabled a compressed topological description and promoted symmetry in material distribution. The simulation results showed different three-dimensional lattice structures designed with proposed algorithm to meet a set of desired deformation behaviors. The relation between residual deformation error, targeted deformation geometry, and material distribution is discussed.

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“…Kang et al present a novel topology optimization method for the design of structures with multiphase embedded components under the minimum distance constraints in the level set framework. Wang et al develop a bilevel hierarchical optimization method to address the multimaterial design of compliant mechanisms, which allows to convert the original complex multimaterial optimization problem into a set of low‐order single‐material optimization problems using some decomposition approaches.…”

Section: Introductionmentioning

confidence: 99%

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

Chu

Xiao

Gao

et al. 2018

Numerical Meth Engineering

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Summary In multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress‐constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty‐based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress‐constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.

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Hierarchical optimization for topology design of multi-material compliant mechanisms

Cited by 13 publications

References 45 publications

Stress‐based multi‐material topology optimization of compliant mechanisms

Stress‐based multi‐material topology optimization of compliant mechanisms

Optimization of Generatively Encoded Multi-Material Lattice Structures for Desired Deformation Behavior

A level set–based method for stress‐constrained multimaterial topology optimization of minimizing a global measure of stress

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