Level set band method: A combination of density-based and level set methods for the topology optimization of continuums
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RESEARCH ARTICLE
Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG
Level set band method: A combination of density-based and level set methods for the topology optimization of continuums
© The Author(s) 2020. This article is published with open access at link.springer.com and journal.hep.com.cn
Abstract The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.
Received October 19, 2019; accepted January 29, 2020
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Peng WEI ( ), Wenwen WANG, Yang YANG School of Civil Engineering and Transportation, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510641, China E-mail: [email protected] Peng WEI State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China Michael Yu WANG Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Hong Kong, China
Keywords level set method, topology optimization, density-based method, level set band\
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Introduction
The successful topology optimization of continuums inspired from the study of the optimal thickness distribution of elastic plates [1] has led to the successive development of several topology optimization models, such as the homogenization method [2], solid isotropic material/microstructure with penalization (SIMP) method [3–5], rational approximation of material property method [6], evolutionary structural optimization (ESO)/bidirectional ESO (BESO) [7–9], level set method (LSM) [10– 14], independent-continuous mapping method [15], moving isosurface threshold method [16], stiffness spreading method [17,18], and moving morphable component/void method [19,20]. The most mature method is SIMP, which has been successfully implemented in commercial software systems, such as OptiStruct, Tosca, and ANSYS. SIMP has
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