Minimum Weight Topology Optimization Subject to Unsteady Heat Equation and Space-time Pointwise Constraints – toward Automatic Optimal Riser Design in the Shape Casting Process

The automatic optimal design of feeding system in the shape casting process is considered, i.e., to find the optimal position, size, shape and topology of risers, and riser-necks. It is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient PDE and an infinite number of space-time pointwise constraints. In addition to regularization and relaxation of the original model, an elegant bilevel 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 asymptotically independent from 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 our numerical results, the presented approach makes a relatively complete solution to the problem of automatic optimal rider design in the shape casting process.