Multi-material proportional topology optimization using hybrid threshold interpolation - Vu, Cuong (Vietnam Journal of Science and Technology, 2025)
Proportional Topology Optimization (PTO) is a non-gradient topology optimization method that is characterized by its simplicity, ease of implementation, and concurrent efficiency and accuracy. While relatively recent, this approach has already demonstrated notable achievements when compared to others. In this paper, PTO is used to solve the multi-material topology optimization problems. We consider the minimum compliance problems satisfying the mass constraint and cost constraints. The elastic modulus is interpolated as threshold functions and cost is linear functions. The functions with scaling and translation coefficients are introduced to interpolate the elastic modulus and the cost properties for multiple materials with respect to the normalized density variables. Density filtering is used to remove checkerboard patterns. A threshold projection is applied for multi-material density in order to reduce the presence of intermediate ones. The numerical examples are conducted from multiple perspectives to illustrate the proposed method. Within each perspective, various cases are compared to find the optimal solution.