LOCAL ANALYTICAL DESIGN SENSITIVITY ANALYSIS OF THE FORGING PROBLEM USING FEM

The present paper concerns the development of a new Local Analytical S ensitivity Analysis (LASA) for calculating the design sensitivities of the forging problem response. The proposed approach is based on the d ifferentiation with respect to the design parameters of each local equ ation of the highly nonlinear mechanical problem. Thus, the desired de sign sensitivities are solutions to the finite element resolution of t he sensitivity problem corresponding to this differentiation. The just ification of the mathematical formalism of the proposed local analytic al sensitivity analysis (LASA) has been developed by considering an op en flat die forging of an incompressible cylinder. The numerical imple mentation has been achieved with finite element Local Sensitivity Anal ysis Software (LSAS). The first part concerns only the first-step forg ing operation. For this case, the sensitivity results obtained with LS AS are very satisfactory compared to the analytical solutions or/and t o the centered finite differences (CFD) computations. The second part consists of associating the incremental character of the forging probl em resolution with the proposed LASA approach. The gradient computatio n of the dissipated strain energy with respect to the design parameter is presented by considering the previous problem with frictionless sl iding contact. The numerical gradients obtained by using the LASA appr oach or/and the CFD computations are compared to the ones calculated f rom the analytical sensitivities. Comparing to the CFD method calculat ion (three highly nonlinear computations), the LASA associated with th e incremental character of the forging problem results (one linear com putation) achieves to best accuracy along with significant improvement s in the required sensitivity computing time. (C) 1998 Elsevier Scienc e S.A. All rights reserved.