Topology Optimization with Selective Problem Setups

Topology optimization has demonstrated its power in structural design under a variety of physical disciplines. Generally, a topology optimization problem is formulated with clearly-defined problem setup. Both design domain shape and boundary condition are clearly-defined during pre-processing. Optimization with multiple choices of design domains or boundary conditions have to be performed with multiple runs of the algorithm to make the best choice among the selective problem setups. The computational cost is proportional to the number of problem setup choices which can be inefficient if a large number of choices are involved. Therefore, to save the computational cost, a novel topology optimization method is developed to solve the design problem with selective problem setups. This method employs a novel meshing strategy and material interpolation model to unify the multiple problem setups into a single optimization problem. Therefore, the optimization algorithm only runs once to concurrently derive the optimal structural shape and the best problem setup choice in a very efficient manner. In addition, the problem formulation is simple. Only N more design variables are added to realize the interpolation among N+1 problem setup choices, other than the density variables for structural topology description. A few numerical examples will be demonstrated to show the effectiveness of the proposed method.