Sensitivity analysis and optimization of thermo-elasto-plastic processes with applications to welding side heater design

A computational scheme is presented to optimize quasi-static weakly coupled thermo-elasto-plastic processes in three dimensional Lagrangian reference frames. Sensitivity formulations are developed from the radial return algorithm based thermo-elasto-plastic finite element equations using the direct differentiation method. These formulations are exemplified in the optimization of the side heaters in the transient thermal tensioning welding process for minimum residual stress. The results of the direct differentiation sensitivity analysis are validated by comparing with finite difference sensitivity calculations. Optimization is performed using the BFGS line search method.