Superposition Methods for Topology Optimization for Non-Concurrent Loads

Problems with non-concurrent loads with variable load directions are often encountered in engineering. While dynamic topology optimization more realistically solves such problems, it is also much more computationally expensive and requires complex mathematical formulations and solvers. Hence, in this paper, we compared the performances of three superposition methods for fusing topologies obtained for various load directions. The top88 algorithm was used to generate 91 initial topologies using MATLAB, which were then joined via the superimposition method, weighted-density parameter, and the revolutionary superposition layout method. The performances of superposed topologies were then analysed by calculating their compliances for various load conditions via the finite element method also using MATLAB. The results have shown that the superimposition method and the weighted-density parameter method yield rather similar results. Both methods provided structures with lower total compliances compared to the revolutionary superposition layout method, making them more suitable for problems where stiffness is paramount.