Topology optimization of a PCB substrate considering mechanical constraints and heat conductivity

A material mixing method was suggested to obtain an optimal topology for a multiple material structure with multiple thermal criteria, based on Evolutionary Structural Optimization (ESO). To examine the validity of the method, it was applied to a printed circuit board (PCB) substrate. The overall efficiency of material usage in a PCB substrate was measured in terms of the combination of thermal stress and heat flux density by using a combination strategy with weighting factors. A Pareto optimal topology solution having multiple thermal criteria was obtained. The effects of weighting factors for multiple thermal criteria as well as mechanical boundary conditions on optimal topologies were investigated. It was found that as the weighting factor for heat flux density becomes larger, the sizes of holes at the center portion become larger in order to dissipate thermal energy much more efficiently. It was also found that as the magnitudes of the heat conduction are getting larger, a similar tendency of the optimal topologies is obtained to the above. The thermal stress on the clamped four sides is larger than that on the two sides clamped. It is verified that the suggested material mixing method works very well for topology optimization of a PCB substrate for various mechanical boundary conditions with multiple thermal criteria.