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Volume 38, Issue 3
Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions

Fang Feng, Hui Yang & Shengfeng Zhu

DOI: 10.4208/cicp.OA-2024-0111

Commun. Comput. Phys., 38 (2025), pp. 850-886.

Published online: 2025-08

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  • Abstract

This paper focuses on modelling and numerical shape and topology optimization for a nonlinear hemivariational inequality in a Stokes flow with contact and frictional conditions. For the energy functional to be minimized subject to geometric volume constraint, we present shape sensitivity analysis and propose a volume preserving gradient-type method for shape optimization. Moreover, we build a relaxed topology optimization model for the hemivariational inequality in a Stokes fluid and solve it by a level set method. Numerical examples are presented to verify effectiveness of the shape and topology optimization algorithms.

  • Keywords

Shape optimization, topology optimization, Stokes flow, hemivariational inequality, level set method.

  • AMS Subject Headings

52B10, 65D18, 68U05, 68U07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-38-850, author = {Feng , FangYang , Hui and Zhu , Shengfeng}, title = {Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2025}, volume = {38}, number = {3}, pages = {850--886}, abstract = {

This paper focuses on modelling and numerical shape and topology optimization for a nonlinear hemivariational inequality in a Stokes flow with contact and frictional conditions. For the energy functional to be minimized subject to geometric volume constraint, we present shape sensitivity analysis and propose a volume preserving gradient-type method for shape optimization. Moreover, we build a relaxed topology optimization model for the hemivariational inequality in a Stokes fluid and solve it by a level set method. Numerical examples are presented to verify effectiveness of the shape and topology optimization algorithms.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0111}, url = {http://global-sci.org/intro/article_detail/cicp/24317.html} }
TY - JOUR T1 - Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions AU - Feng , Fang AU - Yang , Hui AU - Zhu , Shengfeng JO - Communications in Computational Physics VL - 3 SP - 850 EP - 886 PY - 2025 DA - 2025/08 SN - 38 DO - http://doi.org/10.4208/cicp.OA-2024-0111 UR - https://global-sci.org/intro/article_detail/cicp/24317.html KW - Shape optimization, topology optimization, Stokes flow, hemivariational inequality, level set method. AB -

This paper focuses on modelling and numerical shape and topology optimization for a nonlinear hemivariational inequality in a Stokes flow with contact and frictional conditions. For the energy functional to be minimized subject to geometric volume constraint, we present shape sensitivity analysis and propose a volume preserving gradient-type method for shape optimization. Moreover, we build a relaxed topology optimization model for the hemivariational inequality in a Stokes fluid and solve it by a level set method. Numerical examples are presented to verify effectiveness of the shape and topology optimization algorithms.

Feng , FangYang , Hui and Zhu , Shengfeng. (2025). Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions. Communications in Computational Physics. 38 (3). 850-886. doi:10.4208/cicp.OA-2024-0111
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