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

Abstract

SUMMARYA systematic design approach has been developed for thermal processes combining the ÿnite element method, design sensitivity analysis and optimization. Conductive heat transfer is solved in an Eulerian formulation, where the heat ux is ÿxed 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 ÿeld 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 ÿelds to ensure that phase transformations are activated and that melting does not occur.

Adaptive sparse grid based HOPGD: Toward a nonintrusive strategy for constructing space‐time welding computational vademecum

“…Note that this steady‐state description is suitable for problems with a stationary regime reached throughout the process, like welding (eg, other work). In addition, the solutions are solved in , where BCs are not defined and should be chosen in an appropriate way to well approximate original solutions in the fixed frame.…”

Elasto-visco-plastic analysis of welding residual stress

“…For a quasi-steady state problem, the transient heat transfer analysis of equation (1) reduces to a boundary value problem in an Eulerian frame [37][38][39][40] …”

Simulation on the thermal cycle of a welding process by space–time convection–diffusion finite element analysis

“…Its nodal values on a particular element at time t are given by a 3 × m matrix (10) In this study, the nodal velocities…”

“…Rajadhyaksha and Michaleris [10] proposed an Eulerian finite element formulation, to optimize a quasi-static thermal process using a SUPG formulation. They concluded that an Eulerian formulation can drastically reduce the computational run-time, and then can be applied to the optimization of quasistate processes.…”

“…Although a steady state Eulerian method [7,10,11] may be more effective for an infinitely long weld with constant crosssection, it cannot deal with the starting and ending transients of starting and stopping a weld. The proposed space-time method can deal gracefully and naturally with the starting and ending transients of starting and stopping a weld.…”