Open Access

ARTICLE

A Parameter-Free Approach to Determine the Lagrange Multiplier in the Level Set Method by Using the BESO

Zihao Zong, Tielin Shi, Qi Xia^*
The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China
* Corresponding Author: Qi Xia. Email:
(This article belongs to this Special Issue: Novel Methods of Topology Optimization and Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 128(1), 283-295. https://doi.org/10.32604/cmes.2021.015975

Received 28 January 2021; Accepted 31 March 2021; Issue published 28 June 2021

Abstract

A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method. It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method. It first computes the difference between the volume of current design and the upper bound of volume. Then, the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material. Numerical examples proved that this approach is effective to constrain the volume. More importantly, there is no parameter in the proposed approach, which makes it convenient to use. In addition, the convergence is stable, and there is no big oscillation.

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Keywords

Lagrange multiplier; threshold of sensitivity; BESO method; level set method; topology optimization

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