Development of a Material Mixing Method for Topology Optimization of a Structure with Multiple Thermal Criteria

Abstract

A material mixing method to obtain an optimal topology for a structure in a thermal environment is suggested in this paper. This method is based on Evolutionary Structural Optimization (ESO), which has been used to optimize topology of only one material structure. The proposed material mixing method extends the ESO method to a mixing several materials for a structure in the multicriteria optimization of thermal flux and thermal stress. To do this, the multiobjective design optimization technique is implemented. The overall efficiency of material usage is measured in terms of the combination of thermal stress levels and heat flux densities by using a combination strategy with weighting factors. Therefore, the optimal topologies having the maximum thermal stress levels and the maximum heat flux densities were obtained under the various constraints. The suggested method couples an evolutionary iterative process of a finite element heat conduction solution and a finite element themoelastic solution. Also it implements material transformation line and element removal line for mixing several materials in a structure. By means of the transformation line and the removal line, the critical efficiency level of material usage is identified, below which the elements are to be transformed or removed. As the first step, the elements having lower efficiency than the transformation line are transformed into a other material. In the second step, the elements having a lower efficiency than the removal line, which is established as the lower efficiency than the transformation line, are removed. An optimal topology can be obtained by repetition of this procedure at each iteration In this paper, some practical design examples of a printed circuit board (PCB) substrate are presented to illustrate validity of the suggested material mixing method for thermal design optimization in multiple load environments. It is found that the suggested method works very well for topology optimization of a structure in the multicriteria optimization of thermal flux and thermal stress.