Multi-objective topology optimization design of thermal-mechanical coupling structure based on FPTO method

The coupling problem between the structural field and temperature field is widely encountered in engineering applications and holds significant research importance. In the context of thermo-mechanical coupling topology optimization, the thermal stress resulting from the temperature field can cause structural deformation, consequently impacting the structural performance. Therefore, it is crucial to conduct rational optimization designs to ensure favorable mechanical behavior and heat dissipation. This study utilizes thermo-mechanical coupling theory to perform multi-objective topology optimization, aiming to minimize compliance and heat dissipation weakness concurrently, thereby obtaining a more comprehensive design scheme with enhanced overall performance. Initially, a topological optimization model for the coupled thermo-mechanical problem is established. Subsequently, the objective functions of structural compliance and heat dissipation weakness are normalized, and their sensitivities are derived. Next, a multi-load case and multi-objective optimization algorithm based on Floating Projection Topological Optimization (FPTO) is proposed to minimize both structural compliance and heat dissipation weakness. By comparing the topological configuration and objective function values obtained using the Solid Isotropic Material with Penalization (SIMP) method, it is evident that the FPTO method achieves clear and smooth boundaries in the topological configuration, while yielding smaller objective function values. Additionally, under appropriate trade-off factors, the FPTO method achieves a more balanced topological structure and optimizes material distribution without increasing the structural volume, thus enabling lightweight structures, providing novel ideas and methods for engineering applications.