Thermal constraints

The casting system of a cast part is designed so that it drives the shrinkage porosity due to solidification in the risers. In order for the solidification system to have an acceptable cost, thick parts shall be avoided. This can be done either by imposing a maximum thickness constraint, or by imposing a thermal constraint such that the cast part solidifies in a prescribed time interval. The solidification is simulated using a non-linear transient heat equation with phase-change, which is very costly to be used during the optimization process. We examine the possibility of using much simpler thermal models as a first step (see Chapter 5 in my Ph.D Thesis: "Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method").

2d cantilever: volume minimization under a compliance constraint.
Boundary conditions. Optimized shape under a thermal constraint, using a Poisson equation model. Initialization. Optimized shape under a thermal constraint, using a linear transient heat equation model. Optimized shape under a maximum thickness constraint of 0.50. Optimized shape under a thermal constraint, using an eigenvalue approximation model.