Optimization of thermal processes using an Eulerian formulation and application in laser surface hardening

A systematic design approach has been developed for thermal processes combining the nite element method, design sensitivity analysis and optimization. Conductive heat transfer is solved in an Eulerian formulation, where the heat ux is xed in space and the material ows through a control volume. For constant velocity and heat ux distribution, the Eulerian formulation reduces to a steady-state problem, whereas the Lagrangian formulation remains transient. The reduction to a steady-state problem drastically improves the computational e ciency. Streamline Upwinding Petrov–Galerkin stabilization is employed to suppress the spurious oscillations. Design sensitivities of the temperature eld are computed using both the direct di erentiation and the adjoint methods. The systematic approach is applied in optimizing the laser surfacing process, where a moving laser beam heats the surface of a plate, and hardening is achieved by rapid cooling due to the heat transfer below the surface. The optimization objective is to maximize the rate of surface hardening. Constraints are introduced on the computed temperature and temperature rate elds to ensure that phase transformations are activated and that melting does not occur. Copyright ? 2000 John Wiley & Sons, Ltd.