Topology optimization of structures under thermo-mechanical coupling by the improved parameterized level set method

This article proposes an efficient parameterized level set method (PLSM) to achieve topology optimization of structures under thermo-mechanical coupling, with minimum compliance as the objective function and volume fraction as the constraint condition. By using the compactly-supported radial basis functions (CS-RBFs) to interpolate the level set function (LSF), it is more convenient and efficient to evolve the LSF while ensuring the smoothness of the boundary of the topology optimization results. Specifically, the thermo-mechanical coupling analysis is conducted on the structure and combined with the proposed PLSM to establish a topology optimization model. The method of moving asymptotes (MMA) is adopted to solve the topology optimization model, while incorporating the shape sensitivity constraint factor to enhance the computational efficiency. Furthermore, the approximate re-initialization scheme is adopted to prevent the gradient of the LSF boundary from being too large or too small, and to improve the numerical stability and convergence speed of the structural topology optimization process. The effectiveness and feasibility of this method have been demonstrated through several typical numerical examples.