FEA model representing a RSW setup is defined and received in a computer system. The FEA model contains multiple solid elements representing a pair of electrodes and two workpieces. Numerically-calculated heat-power distributions and structural behaviors of the workpieces are obtained by conducting a time-marching simulation using FEA model with a set of time-dependent electrode forces and corresponding set of time-dependent electrical current. An overlapped contact area and corresponding contact center between first and second element contact faces of each of the solid element pairs in contact are determined. Respective elemental coordinates of the contact center in the first and second element contact faces are calculated. Augmented terms for Joule heating effects are added to the overall stiffness matrix for obtaining Joule heat rate power at each contact center, which is then distributed to respective corner nodes of the first and second element contact faces according to respective elemental coordinates.