An efficient isogeometric-based framework is presented to integrate optimum design and formability analysis of sheet metal forming processes. To assess the quality of the formed parts, several objective functions such as fracture, wrinkling, thickness variation, and stretching are studied. In this framework, geometric parameters of addendum surfaces and middle tools are considered as design variables, the objective functions are calculated using the recently developed one-step and multi-step inverse isogeometric methods, and the optimum design variables are obtained using the genetic global optimization algorithm. The major advantage of employing the inverse methods is to analyze the formability of the parts with a low computation time. In this research, the effects of altering addendum surfaces and/or middle tools on the quality of the formed parts are simultaneously observed since modeling, formability analysis, and optimization stages of sheet metal forming simulation are integrated using the NURBS functions. To evaluate the performance of the inverse isogeometric models in calculation of the studied objective functions, the results obtained by these models are compared to those of experiment and forward FEM. Comparisons of the results indicate that these models predict the objective functions with acceptable accuracy at a low computation time. For instance, in sheet metal forming analysis of a rectangular box with three different addendum surfaces, the maximum error in prediction of minimum thickness using the one-step inverse model is approximately 4.65% more than forward FEM, while the solution time of forward FEM is around 40 times greater. Finally, the presented optimization procedure is applied to design addendum surfaces in forming of a rectangular box and the middle tools in a two-stage drawing of a square box. The results of these problems confirm the credibility of the present approach in rapid optimum design of addendum surfaces and intermediate tools with acceptable accuracy.
Contact Modelling in Isogeometric Analysis: Application to Sheet Metal Forming Processes
