Research Article

A multi-discretization scheme for topology optimization based on the parameterized level set method

¹ School of Civil Engineering and Transportation, State Key Laboratory of Subtropical Building Science, South China University of Technology, 381 Wushan Rd, Tianhe, Guangzhou, PR China
² State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 2 Linggong Rd, Ganjingzi, Dalian, PR China
³ Architecture and Civil Engineering Institute, Guangdong University of Petrochemical Technology, 139 Guandu 2nd Rd, Maoming, PR China

^* e-mail: ctpwei@scut.edu.cn

Received: 17 May 2019
Accepted: 21 October 2019

Abstract

In the framework of the parameterized level set method, the structural analysis and topology representation can be implemented in a decoupling way. A parameterized level set function, typically, using radial basis functions (RBFs), is a linear combination of a set of prescribed RBFs and coefficients. Once the coefficients are determined, the theoretical level set function is determined. Exploiting this inherent property, we propose a multi-discretization method based on the parameterized level set method. In this approach, a coarse discretization is applied to do the structural analysis whereas another dense discretization is employed to represent the structure topology. As a result, both efficient analysis and high-resolution topological design are available. Note that the dense discretization only accounts for a more precise and smooth description of the theoretical level set function rather than introduce extra design freedom or incur interference to structural analysis or the optimization process. In other words, this decoupling way will not add to the computational burden of structural analysis or result in non-uniqueness of converged results for a particular analysis setting. Numerical examples in both two-dimension and three-dimension show effectiveness and applicability of the proposed method.