Multi-objective Topology Optimization of the Temperature Field Considering the Material Nonlinearities

Abstract

This paper presents a multi-objective topology optimization method for the temperature field considering the material nonlinearities. Although a large number of papers have studied the topology optimizations of the heat transfer problems, none of them considered the influence of the material nonlinearity properties. In this paper, the material nonlinearity is considered. Based on the nonlinear assumption, the mathematical model of the corresponding topology optimization is presented first. Then, the sensitivities of the objectives and the constraints respect to the design variables are derived. And the optimization routines are discussed. After establishing the theories and solving scheme, a software is developed by MATLAB for the topology design of the nonlinear heat transfer. Several nonlinear numerical examples are presented. And the corresponding optimal results generated under the linear assuming are also collected for comparisons. Furthermore, this paper also simply discusses the preventing approaches of instabilities and the implementation methods of some other unusual engineering constraints. These true engineering considerations are very helpful for the real industry design experiences.