Topology Optimization Design For Thermo-mechanical Coupling Physical Problems

Topology optimization is a mathematical method and tool to optimize the distribution of materials in a given design area according to some established design requirements and constraints.It changes the traditional design method based on experience and intuition,and has a broad application prospect in the fields of aerospace,automobile and industrial equipment.In practical production,many devices are often faced with the impact of external load and high temperature environment.Thermo-mechanical coupling topology optimization concept has received more and more attention and research.But traditional thermo-mechanical coupling topology optimization to stay on the macro level,and the topology optimization design of the homogeneous material is more and more difficult to adapt to the modern industrial demand for quality of high quality light products,how to give full play to the application of material microstructure in product performance,improve the structure of the stiffness and thermal performance of the potential to become a new research hotspot.In this paper,the SIMP optimization method combined with the energy homogenization theory is used to optimize the performance of the microstructure,and the thermo-mechanical coupling oriented multiscale structure/material design is studied.The main work is as follows:First of all,the macro equivalent material properties is derived with energy equalization method combined with the topology optimization method respectively to extreme heat conduction performance and multifunctional(extreme elastic properties and thermal properties weighted)topology optimization design of microstructure,for 2D and 3D situation,eventually optimized structure can conform to the principle of material,the optimal allocation,has certain guiding significance to the optimization design of microstructure.Then,on the basis of the above optimization design of microstructure performance,the traditional thermo-mechanical coupling topology optimization design theory based on homogeneous materials is introduced,and a multiscale single objective optimization design method for thermo-mechanical coupling structure/material is proposed,and the sensitivity of the constraint equation and the objective function is derived.By comparing with the traditional single-scale topological optimization,it is verified that the multiscale integrated topological structure can significantly improve the stiffness performance of the structure.Then,on the basis of 2D case,the 3D multiscale single objective topology optimization design for thermo-mechanical coupling is realized,which proves the effectiveness and expansibility of the theoretical model.Secondly,on the basis of single-objective topological optimization,a multi-objective thermo-mechanical coupling concurrent topology optimization design model with structural stiffness and heat dissipation performance as optimization objectives is established and the sensitivity of constraint equation and objective function is derived.Through a numerical example shows the objective function under different weight coefficient,macrostructure and microstructure evolution process and structure under different weight coefficient of displacement and temperature change,the results of numerical examples verify the effectiveness of the proposed multi-objective parallel topology optimization method and the significant improvement of the stiffness and heat dissipation performance of the macrostructure.Finally,at the end of this paper,the research results are summarized and the future research work is forecasted.