Analysis Of Topology Optimization Algorithms For Thermo-mechanical Coupling Problems

In this paper,using the solid isotropic material penalty method,the sensitivity analysis method and the homogenization method,the topology optimization of the thermo-mechanical coupling problem and the thermo-mechanical coupling problem of the periodic composite material is studied,and the topology optimization algorithm of the thermo-mechanical coupling problem and the thermo-mechanical coupling problem of the periodic composite material is given.Research and analysis.Under a certain regularity assumption,a reasonable asymptotic expansion is given to eliminate the coupling between the micro and macro,and the uniform solution and equivalent heat transfer coefficient under the coupling of temperature field and displacement field are obtained.,and the existence of a uniform solution to the structural optimization problem is proved.In addition,based on the Free FEM++ software,the topology optimization structure simulation algorithm for the thermo-mechanical coupling problem and the composite material thermo-mechanical coupling problem is realized,and based on the homogenization theory,the homogenization of the thermo-mechanical coupling structure optimization problem of periodic composite materials is realized,and the corresponding numerical calculation is given.For example,the calculation results show the effectiveness of the homogenization method.Chapter 1 introduces the research background and significance of this paper,the research status of thermo-mechanical coupled topology optimization problems at home and abroad,and the related definitions and symbols in this paper.Chapter 2 introduces the topology optimization method for thermo-mechanical coupling problems,constructs and analyzes the topology optimization model of thermomechanical coupling problems,and gives the corresponding numerical algorithm and numerical simulation using Free FEM++ software.Chapter 3 introduces the topology optimization method for the thermal-mechanical coupling problem of periodic composite materials,constructs and analyzes the topology optimization model for the thermal-mechanical coupling problem of periodic composite materials,and gives the corresponding numerical algorithm and uses Free FEM++software for numerical simulation.Chapter 4 summarizes the research results obtained in this paper and gives an outlook for research work infuture.