TY - JOUR
T1 - A study on basis functions of the parameterized level set method for topology optimization of continuums
AU - Wei, Peng
AU - Yang, Yang
AU - Chen, Shikui
AU - Wang, Michael Yu
N1 - Funding Information:
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (11372004), State Key Laboratory of Structural Analysis for Industrial Equipment (GZ18109), the grant from the Ford University Research Program (URP) (Award No.2017-9198R), and the start-up funds from the State University of New York at Stony Brook.
Publisher Copyright:
© 2020 by ASME.
PY - 2021/4
Y1 - 2021/4
N2 - In recent years, the parameterized level set method (PLSM), which rests on radial basis functions in most early work, has gained growing attention in structural optimization. However, little work has been carried out to investigate the effect of the basis functions in the parameterized level set method. This paper examines the basis functions of the parameterized level set method, including radial basis functions, B-spline functions, and shape functions in the finite element method (FEM) for topology optimization of continuums. The effects of different basis functions in the PLSM are examined by analyzing and comparing the required storage, convergence speed, computational efficiency, and optimization results, with the benchmark minimum compliance problems subject to a volume constraint. The linear basis functions show relatively satisfactory overall performance. Besides, several schemes to boost computational efficiency are proposed. The study on examples with unstructured 2D and 3D meshes can also be considered as a tentative investigation of prospective possible commercial applications of this method.
AB - In recent years, the parameterized level set method (PLSM), which rests on radial basis functions in most early work, has gained growing attention in structural optimization. However, little work has been carried out to investigate the effect of the basis functions in the parameterized level set method. This paper examines the basis functions of the parameterized level set method, including radial basis functions, B-spline functions, and shape functions in the finite element method (FEM) for topology optimization of continuums. The effects of different basis functions in the PLSM are examined by analyzing and comparing the required storage, convergence speed, computational efficiency, and optimization results, with the benchmark minimum compliance problems subject to a volume constraint. The linear basis functions show relatively satisfactory overall performance. Besides, several schemes to boost computational efficiency are proposed. The study on examples with unstructured 2D and 3D meshes can also be considered as a tentative investigation of prospective possible commercial applications of this method.
KW - basis functions
KW - computer-aided design
KW - design methodology
KW - multidisciplinary design and optimization
KW - parameterized level set method
KW - simulation-based design
KW - Topology optimization
UR - http://www.scopus.com/inward/record.url?scp=85100339095&partnerID=8YFLogxK
U2 - 10.1115/1.4047900
DO - 10.1115/1.4047900
M3 - Article
AN - SCOPUS:85100339095
SN - 1050-0472
VL - 143
JO - Journal of Mechanical Design, Transactions of the ASME
JF - Journal of Mechanical Design, Transactions of the ASME
IS - 4
M1 - 041701
ER -