The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient PDE and space-time state dependent pointwise constraints. An elegant bi-level reformulation of the optimization problem is introduced which makes it possible to manage the infinite number of design parameters and state-constraints efficiently. The computational cost of this method is independent of the number of design parameters and constraints. The validity and efficiency of the presented method are supported by several examples, from simple benchmarks to complex industrial castings. According to numerical results, the presented approach makes a complete solution to the problem of automatic optimal rider design in the shape casting process.
R. Tavakoli, Minimum weight Topology optimization subject to unsteady heat equation and space-time pointwise constraints -- toward automatic optimal riser design in the shape casting process, preprint 2020.