Inverse methods in design of industrial forging processes

An approach to optimal shape design in forging is presented. The design problem is formulated as an inverse problem incorporating a finite element 3D analysis model and an optimisation technique conducted on the basis of design sensitivities. The mechanical analysis provides information to predict deformation, stresses and strains necessary to the shape optimisation problem. The objective is to minimise a function describing die underfill and excessive material waste. Analytical sensitivities of the objective function are required and the calculation of discrete derivatives based on the differentiation of the discrete problem equations is considered. Due to the time-dependent deformation process the direct differentiation method has been implemented. The capability of the proposed inverse approach to deal with optimal forging of industrial parts is demonstrated.