Optimal design of nonlinear parabolic systems. Part 2: Variable spatial domain with applications to casting optimization
In Part 1, design sensitivity expressions for nonlinear parabolic systems were derived and then specialized for the analysis for thermal systems which govern many processing operations. However, that presentation did not account for shape variations. Here we present the shape sensitivity analysis for the thermal system. The sensitivities are derived via the domain parameterization method and computed with the finite element method. Various means for parameterizing the shape are also discussed. Finally, the sensitivity analysis is coupled with nonlinear programming to optimize the design of a sand casting.