Optimal riser design in sand casting process by topology optimization with SIMP method I: Poisson approximation of nonlinear heat transfer equation

The optimal design of a casting feeding system is considered. The problem is formulated as the volume constrained topology optimization and is solved with the finite element analysis, explicit design sensitivity, and numerical optimization. In contrast to the traditional topology optimization where the objective function is defined on the design space, in the presented method, the design space is a subset of the complement of the objective function space. To accelerate optimization procedure, the nonlinear unsteady heat transfer equation is approximated with a Poisson-like equation. The feasibility of the presented method is supported with illustrative examples.