Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (10): 2754-2763.doi: 10.13229/j.cnki.jdxbgxb.20221624

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Topology optimization design of multiphase porous structures considering geometric nonlinearity

Huan-lin ZHOU1(),Xin GUO1,Xuan WANG1,2(),Li-xue FANG1,Kai LONG3   

  1. 1.College of Civil Engineering，Hefei University of Technology，Hefei 230009，China
    2.School of Mechanical Engineering，Tianjin University，Tianjin 300072，China
    3.State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources，North China Electric Power University，Beijing 102206，China
  • Received:2022-12-25 Online:2024-10-01 Published:2024-11-22
  • Contact: Xuan WANG E-mail:zhouhl@hfut.edu.cn;xuanwang@hfut.edu.cn

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Abstract:

A topology optimization method of multiphase porous structures considering geometric nonlinearity effects is proposed based on SIMP interpolation model. The multi-phase porous structure is formed by controlling the local volume fraction of different material phases. To reduce the number of constraints in the optimization problem， the p-norm is used to aggregate multiple local volume constraints into a global constraint function. The additional hyperelastic technique is used to avoid mesh distortion under large geometric deformation. Finally， two optimization examples are presented to verify the effectiveness of the proposed method. The optimization results show that the proposed method can achieve reasonable distribution among different material phases， and the displacement and stress of the porous structures considering the nonlinear effect are smaller. Compared with the single material structure， the porous structures composed of multi-materials has better mechanical properties.

Key words: mechanical engineering, porous structure, geometric nonlinearity, topology optimization, local volume constraint, multiphase materials

CLC Number: 

  • O342

Fig.1

Design domain of cantilever beam"

Fig.2

Topology optimization results of porous structures of two-phase materials based on linear elastic theory"

Fig.3

Topology optimization results of porous structures of two-phase materials considering nonlinear"

Fig.4

Iterative histories of objective function and volume fraction considering nonlinear theory"

Fig.5

Displacement cloud diagram of nonlinear porous structure"

Fig.6

Displacement cloud diagram of linear poroustruture"

Fig.7

Stress cloud diagram of nonlinear porous structure"

Fig.8

Stress cloud diagram of linear porous structure"

Fig.9

Topology optimization results of porous structures of two-phase materials under different local volume filter radii"

Table 1

Objective function and volume fraction underdifferent local volume filter radius"

Casesre柔度实体体积分数材料2体积分数
Case 159.8320.4280.1993
Case 268.8420.4350.1973
Case 378.3570.4440.1986
Case 488.0860.4500.1999

Fig.10

Design domain of two point fixed structure"

Fig.11

Topology optimization results of porous structures of two-phase materials based on linear elastic theory"

Fig.12

Topology optimization results of porous structures of two-phase materials considering geometric nonlinear"

Fig.13

Topology optimization results of porous structures of three-phase materials based on linear elastic theory"

Fig.14

Topology optimization results of porous structures of three-phase materials considering geometric nonlinear theory"

Fig.15

Iterative histories of objective function and volume fraction considering geometric nonlinear theory"

Table 2

Compliance function and maximum displacement for different material phases"

材料相数柔度实体体积分数最大位移/mm
单相1.0230.4004.100
两相0.8500.4003.405
三相0.7640.4003.055
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