Topology optimization method for the design of bioinspired self-similar hierarchical microstructures

Zhang, Hui-Kai; Wu, Wenjun; Kang, Zhan; Feng, Xi‐Qiao

doi:10.1016/j.cma.2020.113399

Cited by 27 publications

(8 citation statements)

References 44 publications

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“…Optimization problems can be solved by using different approaches such as the optimality criteria (OC) method [33,36], the sequential linear/integer programming method [33,39], the method of moving asymptotes [40], and the non-gradient method [41][42][43]. These methods have been used in diverse fields of, for example, additive manufacturing [44,45], metamaterials [46][47][48][49], bionics [32,48,50,51], medical devices [52], flexible electronics [53], soft robotics [54,55] and aerospace [22,27,56].…”

Section: Methodsmentioning

confidence: 99%

Multi-functional topology optimization ofVictoria cruzianaveins

Zhang

Zhou

Fang

et al. 2022

J. R. Soc. Interface.

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The growth and development of biological tissues and organs strongly depend on the requirements of their multiple functions. Plant veins yield efficient nutrient transport and withstand various external loads. Victoria cruziana , a tropical species of the Nymphaeaceae family of water lilies, has evolved a network of three-dimensional and rugged veins, which yields a superior load-bearing capacity. However, it remains elusive how biological and mechanical factors affect their unique vein layout. In this paper, we propose a multi-functional and large-scale topology optimization method to investigate the morphomechanics of Victoria cruziana veins, which optimizes both the structural stiffness and nutrient transport efficiency. Our results suggest that increasing the branching order of radial veins improves the efficiency of nutrient delivery, and the gradient variation of circumferential vein sizes significantly contributes to the stiffness of the leaf. In the present method, we also consider the optimization of the wall thickness and the maximum layout distance of circumferential veins. Furthermore, biomimetic leaves are fabricated by using the three-dimensional printing technique to verify our theoretical findings. This work not only gains insights into the morphomechanics of Victoria cruziana veins, but also helps the design of, for example, rib-reinforced shells, slabs and dome skeletons.

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Section: Methodsmentioning

confidence: 99%

Multi-functional topology optimization ofVictoria cruzianaveins

Zhang

Zhou

Fang

et al. 2022

J. R. Soc. Interface.

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“…Lattice microstructures are increasingly used in wide industrial domains taking full advantage of constituent materials, providing the chance to design novel geometries to satisfy the specified demands corresponding to macroscale physical performances [ 53 ]. For the sake of putting into use lattice microstructures for CM design, homogenization theory is introduced to compute the effective elastic properties of lattice microstructures [ 54 , 55 ]. The perturbation theory is utilized to asymptotically expand the elastic governing equation; then, the relationship between the effective elastic tensor and local strain is achieved as follows:

where

denotes the effective elastic tensor;

and

represent the volume of the periodic microstructure and local displacement field, respectively;

denotes the elastic tensor of constitutive material; and

represents the local microscopic variable.…”

Section: Effective Elastic Properties Of Multiple Lattice Microstruct...mentioning

confidence: 99%

Topology Optimization for Hybrid Lattice Compliant Mechanisms with Multiple Microstructures

Wei

Wang

et al. 2022

Materials

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Hybrid lattice compliant mechanisms (HLCMs) composed of multiple microstructures have attracted widespread interest due to their superior compliant performance compared to the traditional solid compliant mechanisms. A novel optimization scheme for HLCMs is presented using the independent continuous mapping (ICM) method. Firstly, the effective properties of multiple orthogonal and anisotropic lattice microstructures are obtained by taking advantage of homogenization theory, which are used to bridge the relationship between the macrostructure layout and microstructure recognition. Then, a new parallel topology optimization model for optimizing HLCMs is built via a generalized multi-material, recognizing interpolation scheme with filter functions. In addition, the characterization relationship between independent continuous variables and performance of different elements is established. Sensitivity analysis and linear programming are utilized to solve the optimal model. Lastly, numerical examples with a displacement inverter mechanism and compliant gripper mechanism demonstrate the effectiveness of the proposed method for designing HLCMs with various lattice microstructures. Anisotropic lattice microstructures (ALMs) significantly facilitate the efficient use of constitutive properties of materials. Hence, HLCMs consisting of various ALMs achieve superior compliant performance than counterparts comprising different orthogonal lattice microstructures (OLMs). The presented method offers a reference to optimize HLCMs, as well as promotes the theoretical development and application of the ICM method.

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“…In the HMs, the size of the second-level members can be several orders lower than that of the HM unit cell [29]. Moreover, the second-level microstructures could either have similar geometries as the first-level configurations [30] or include spatially-varying configurations. Compared to the multiscale microstructures in which the microstructures in the smaller length scale behave as a homogeneous material for the members in the larger length scale [12], the hierarchical members in HMs perform as structures.…”

Section: Introductionmentioning

confidence: 99%