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# A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

Changkye Lee1, Sundararajan Natarajan2, Seong-Hoon Kee3, Jurng-Jae Yee3,*

1 University Core Research Center for Disaster-Free & Safe Ocean City Construction, Dong-A University, Busan, 49315, Korea
2 Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India
3 Department of Architectural Engineering, Dong-A University, Busan, 49315, Korea

* Corresponding Author: Jurng-Jae Yee. Email:

(This article belongs to this Special Issue: Recent Advance of the Isogeometric Boundary Element Method and its Applications)

Computer Modeling in Engineering & Sciences 2022, 131(3), 1615-1634. https://doi.org/10.32604/cmes.2022.020377

## Abstract

The aim of this work is to employ a modified cell-based smoothed finite element method (S-FEM) for topology optimization with the domain discretized with arbitrary polygons. In the present work, the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM. This improves the accuracy and yields an optimal convergence rate. The gradients are smoothed over each smoothing domain, then used to compute the stiffness matrix. Within the proposed scheme, an optimum topology procedure is conducted over the smoothing domains. Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain. Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence, efficiency and accuracy.

## Keywords

Lee, C., Natarajan, S., Kee, S., Yee, J. (2022). A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization. CMES-Computer Modeling in Engineering & Sciences, 131(3), 1615–1634.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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