Topological Optimization Of Heat Radiation Structures

Topology optimization has been widely used in continuum structures, MEMS and heat radiation structures design. Topology optimization is one of the most challenging tasks in structural design. In this thesis, a modified density penalization method has been proposed. Numerical study has been carried out to investigate the efficiency of this method.First, a fundamental theory of SIMP method is introduced in this thesis. Moreover, the material model and finite element method (FEM) in density penalization method are discussed. Key steps of 2-dimenation and 3-dimenation element matrix formulation, including interpolating function selection and determination of the coefficients of shape function are implemented. The SIMP method and the heat conduction analyze model are integrated to formulate topology optimization model of heat radiation structures. Then numerical instability in topology optimization methods such as checkerboards, mesh-dependence and local minima are discussed and corresponding methods to avoid those problems are listed in the study.A modified density penalization model is also proposed and the issue of anisotropic material in heat conduction structure topology optimization is studied. Besides, a criteria method based on temperature gradient for the optimization of material orientation is proposed.Finally, a computer program for topological optimization of heat conduction structures is developed using SIMP. Furthermore, numerical experiments for a series of representative examples are implemented, which shows that this method is feasible and effective.