Shape optimization of castings by using successive response surface methodology

In this paper, an optimization routine for a thermomechanical problem is presented. The optimization routine is based on the successive response surface methodology where the panning and zooming technique presented by Stander and Craig has been implemented and improved. The optimization routine has been applied to an optimization problem of a three-dimensional beam that undergoes a solidification process. The material in the beam is assumed to be low-alloyed gray iron. The thermomechanical solidification analysis is uncoupled where, first, a thermal analysis is performed to determine the thermal history. This thermal history is then used to calculate the residual stresses in the beam. The residual stresses are solved by using classical J2-plasticity with temperature-dependent material properties. The residual stresses from solidification are then carried on to the structural analysis where a mechanical load is applied. These are all linked together via scripts, and the commercial FE software Abaqus is used as the FE solver. The obtained maximum von Mises stress and mass information for every set of parameters are then exported to Matlab where general quadratic response surfaces are fitted by a least square method. Taken together, these response surfaces define a minimum of weight problem, which is solved by using sequential linear programming. To minimize the number of evaluations needed, the parameters are chosen to be D-optimally selected. The numerical results show that the residual stresses from solidification might influence the optimal shape significantly. The residual stress results have been compared with those obtained from casting simulation softwares, and the results are similar. The optimization has been compared with a commercial optimization software and shows very promising results.