Topology optimization of heat transfer and elastic problems based on element differential method

Zhang，Si Qi1; Xu，Bing Bing1; Gao，Zhong Hao1; Jiang，Geng Hui2; Zheng，Yong Tong3; Liu，Hua Yu1; Jiang，Wen Wei1; Yang，Kai1; Gao，Xiao Wei1

2023-04-01

10.1016/j.enganabound.2023.01.026

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS   Impact Factor & Quartile

0955-7997

1873-197X

The element differential method (EDM) is a robust and efficient strong-form numerical method, which has attracted a lot of attention of the researchers about the numerical methods since proposed. EDM has higher stability than some other strong-form methods and is more efficient than conventional Galerkin FEM. In this paper, the EDM is combined with Solid Isotropic Material with Penalization (SIMP) method to solve 2–3D topological optimization problems under different conditions. The key of the paper is to derive the objective function of second-order EDM element, which is suitable for the SIMP-based topology optimization process. And the sensitivity is solved by Optimality Criteria (OC) method. In the article, topology optimization examples are considered in different mechanics or thermal loads. In the topology optimization of the elastic problem of 3D cantilever beam, the EDM-based SIMP method can reduce the structural compliance by 17∼27% compared with SIMP method based on FEM. And in the heat transfer problems of the 3D plate, the EDM-based SIMP method reduced the compliance by 3.4%. The results show that the present method has good accuracy, efficiency and robustness in topology optimization of 2D and 3D minimum compatibility problems.

Elastic problem Element differential method Heat transfer problem Solid isotropic material with penalization Topology optimization

SCI

English

Others

National Natural Science Foundation of China["12072060","12072064"]

Engineering ; Mathematics

Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications

WOS:000930511000001

ELSEVIER SCI LTD

ENGINEERING

2-s2.0-85147194960

Scopus

1.State Key Laboratory of Structural Analysis for Industrial Equipment,Key Laboratory of Advanced Technology for Aerospace Vehicles,Liaoning Province,Dalian University of Technology,Dalian,116024,China
2.Key Laboratory of Power Machinery and Engineering,School of Mechanical and Power Engineering,Shanghai Jiao Tong University,Shanghai,200240,China
3.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Zhang，Si Qi,Xu，Bing Bing,Gao，Zhong Hao,et al. Topology optimization of heat transfer and elastic problems based on element differential method[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS,2023,149:190-202.

Zhang，Si Qi.,Xu，Bing Bing.,Gao，Zhong Hao.,Jiang，Geng Hui.,Zheng，Yong Tong.,...&Gao，Xiao Wei.(2023).Topology optimization of heat transfer and elastic problems based on element differential method.ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS,149,190-202.

Zhang，Si Qi,et al."Topology optimization of heat transfer and elastic problems based on element differential method".ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 149(2023):190-202.