SUMMARYAn Eulerian ÿnite element formulation for quasi-state one way coupled thermo-elasto-plastic systems is presented. The formulation is suitable for modeling material processes such as welding and laser surfacing. In an Eulerian frame, the solution ÿeld of a quasi-state process becomes steady state for the heat transfer problem and static for the stress problem. A mixed small deformation displacement elastoplastic formulation is proposed. The formulation accounts for temperature dependent material properties and exhibits a robust convergence. Streamline upwind Petrov-Galerkin (SUPG) is used to remove spurious oscillations. Smoothing functions are introduced to relax the non-di erentiable evolution equations and allow for the use of gradient (sti ness) solution scheme via the Newton-Raphson method. A 3-dimensional simulation of a laser surfacing process is presented to exemplify the formulation. Results from the Eulerian formulation are in good agreement with results from the conventional Lagrangian formulation. However, the Eulerian formulation is approximately 15 times faster than the Lagrangian.
E. Adams Dr.; Columbus; OH 43221; U.S.A.
SUMMARYA 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 ÿnite 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.