A constant strain triangle element oriented multi-material topology optimization with a moved and regularized Heaviside function

Abstract

This study presents an optimal topology material distribution method in the framework of minimum compliance with a constraint on the total amount of multi-material using constant strain triangle (CST) elements and Moved and Regularized Heaviside Function (MRHF) filters. The sensitivity formulations for objective function and sensitivity for structures are derived in terms of multiphase design variables through triangle elements. Mathematical formulations of topology optimization problem solving the minimum compliance by using multiple materials are an alternating active-phase algorithm with a Gauss-Seidel version as an optimization model of optimality criteria. Moreover, MRHF that has the role of a filter in multiple materials is considered to produce obvious material distributions and improve the convergence of objective values. Some optimal topology results under the influence of rmin and filter are also investigated and verify the CST element-based multi-material topology optimization is appropriate to the use of MRHF and produces reasonable optimal results.