Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation

doi:10.3901/JME.2022.13.240

Abstract

Abstract: With the framework for topology optimization via Solid Isotropic Material with Penalization method (SIMP), a novel and simple method for topology optimization based on Helmholtz equation is constructed to solve the problem of cavity connectivity in the topology optimization design for additive manufacturing. First, the structure continuity is defined as a new equivalent description of structural connectivity according to the characteristics of enclosed void in order to encapsulate connectivity constraints into the framework of topology optimization. Then, the anisotropic Helmholtz equation is used to ensure the continuity of the entity structure in a specific direction by setting different parameters, and the topology optimization model considering the cavity connectivity constraint is constructed. Finally, the MMA algorithm is used to solve the topology optimization model, and the limit of cavity connectivity is realized. Several optimization examples prove the performance of the proposed method for topology optimization of continuum structure with connectivity constraints for additive manufacturing without adding new constraints and intermediate variables compared with conventional methods. This method can also be easily extended to the topology optimization of continuum structure with conventional manufacturing methods to avoid enclosed void.

Key words: topology optimization, additive manufacturing, connectivity constraints, structural continuity, anisotropic Helmholtz equation

CLC Number:

TH122

WANG Tianci, LIU Long, LI Zhizhong, XIANG Jifang, YI Bing. Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation[J]. Journal of Mechanical Engineering, 2022, 58(13): 240-250.

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