Optimization of thermo-elasto-plastic processes using Eulerian sensitivity analysis

A computational scheme for the analysis and optimization of quasi-static thermo-mechanical processes is presented in this paper. In order to obtain desirable mechanical transformations in a workpiece using a thermal treatment process, the optimal control parameters need to be determined. The problem is addressed by posing the process as a decoupled thermo-mechanical nite element problem and performing an optimization using gradient methods. The forward problem is solved using the Eulerian formulation since it is computationally more e cient compared to an equivalent Lagrangian formulation. The design sensitivities required for the optimization are developed analytically using direct di erentiation. This systematic design approach is applied to optimize a laser forming process. The objective is to maximize the angular distortion of a specimen subject to the constraint that the phase transition temperature is not exceeded at any point in the model