Volume 30, Issue 5
A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method

Zhengfang Zhang, Yanqiang Dong & Weifeng Chen

Commun. Comput. Phys., 30 (2021), pp. 1370-1389.

Published online: 2021-10

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  • Abstract

The topology optimization of a linearized elasticity system with the area (volume) constraint is investigated. A non-ersatz material approach is proposed. By introducing a fixed background domain, the linearized elasticity system is extended into the background domain by a characteristic function. The piecewise constant level set (PCLS) method is applied to represent the original material region and the void region. A quadratic function of PCLS function is proposed to replace the characteristic function. The functional derivative of the objective functional with respect to PCLS function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of 2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.

  • Keywords

Non-ersatz material approach, piecewise constant level set method, linearized elasticity system, sensitivity analysis, penalty gradient algorithm.

  • AMS Subject Headings

49R05, 47A75, 65F18, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cwf818@zufe.edu.cn (Weifeng Chen)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-30-1370, author = {Zhang , Zhengfang and Dong , Yanqiang and Chen , Weifeng}, title = {A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1370--1389}, abstract = {

The topology optimization of a linearized elasticity system with the area (volume) constraint is investigated. A non-ersatz material approach is proposed. By introducing a fixed background domain, the linearized elasticity system is extended into the background domain by a characteristic function. The piecewise constant level set (PCLS) method is applied to represent the original material region and the void region. A quadratic function of PCLS function is proposed to replace the characteristic function. The functional derivative of the objective functional with respect to PCLS function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of 2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0231}, url = {http://global-sci.org/intro/article_detail/cicp/19933.html} }
TY - JOUR T1 - A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method AU - Zhang , Zhengfang AU - Dong , Yanqiang AU - Chen , Weifeng JO - Communications in Computational Physics VL - 5 SP - 1370 EP - 1389 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0231 UR - https://global-sci.org/intro/article_detail/cicp/19933.html KW - Non-ersatz material approach, piecewise constant level set method, linearized elasticity system, sensitivity analysis, penalty gradient algorithm. AB -

The topology optimization of a linearized elasticity system with the area (volume) constraint is investigated. A non-ersatz material approach is proposed. By introducing a fixed background domain, the linearized elasticity system is extended into the background domain by a characteristic function. The piecewise constant level set (PCLS) method is applied to represent the original material region and the void region. A quadratic function of PCLS function is proposed to replace the characteristic function. The functional derivative of the objective functional with respect to PCLS function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of 2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.

Zhengfang Zhang, Yanqiang Dong & Weifeng Chen. (2021). A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method. Communications in Computational Physics. 30 (5). 1370-1389. doi:10.4208/cicp.OA-2020-0231
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