Shape optimization and preform design in metal forming processes
نویسندگان
چکیده
A continuum sensitivity analysis is presented for the computation of the shape sensitivity of ®nite hyperelastic±viscoplastic deformations involving contact with friction using a direct dierentiation method. Weak shape sensitivity equations are developed that are consistent with the kinematic analysis, constitutive sub-problem as well as the analysis of the contact/friction sub-problem used in the solution of the direct deformation problem. The shape sensitivities are de®ned in a rigorous sense and the linear sensitivity analysis is performed in an in®nite-dimensional continuum framework. The direct deformation and the sensitivity deformation problems are implemented using the ®nite element method. The shape sensitivity analysis is validated by a comparison of the results with those obtained from the solution of the perturbed direct deformation problem (i.e. using ®nite dierences). Finite-dimensional gradients of objective functions are then computed using the results of the shape sensitivity analysis for the purpose of preform design and shape optimization in metal forming. The eectiveness of the proposed methodology is demonstrated by solving practical shape optimal design problems in forging processing. Ó 2000 Elsevier Science B.V. All rights reserved.
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