Local analytical design sensitivity analysis of the forging problem using FEM Original Research Article

The present paper concerns the development of a new Local Analytical Sensitivity Analysis (LASA) for calculating the design sensitivities of the forging problem response. The proposed approach is based on the differentiation with respect to the design parameters of each local equation of the highly nonlinear mechanical problem. Thus, the desired design sensitivities are solutions to the finite element resolution of the sensitivity problem corresponding to this differentiation. The justification of the mathematical formalism of the proposed local analytical sensitivity analysis (LASA) has been developed by considering an open flat die forging of an incompressible cylinder. The numerical implementation has been achieved with finite element Local Sensitivity Analysis Software (LSAS). The first part concerns only the first-step forging operation. For this case, the sensitivity results obtained with LSAS are very satisfactory compared to the analytical solutions or/and to the centered finite differences (CFD) computations. The second part consists of associating the incremental character of the forging problem resolution with the proposed LASA approach. The gradient computation of the dissipated strain energy with respect to the design parameter is presented by considering the previous problem with frictionless sliding contact. The numerical gradients obtained by using the LASA approach or/and the CFD computations are compared to the ones calculated from the analytical sensitivities. Comparing to the CFD method calculation (three highly nonlinear computations), the LASA associated with the incremental character of the forging problem results (one linear computation) achieves to best accuracy along with significant improvements in the required sensitivity computing time.