Direct differentiation and adjoint state methods for shape optimization of non-steady forming processes

Lionel Fourment (1) , Daniel Vieilledent (1) , Sh Chung , Jean-Loup Chenot (1) , Pj Spence

1 CEMEF - Centre de Mise en Forme des Matériaux

In this paper, the design of metal forming processes is considered through shape optimization methods. The process is simulated by the FORGE2(R) finite element software. Different objective functions are computed to evaluate the non-quality of the design, and are minimized by a BFGS type algorithm, optimizing the shapes of the intermediate tools. For non-steady problems with remeshings and transfers of variables, the function derivatives must be computed analytically, which is done using the discrete problem equations, either by the direct differentiation method (DDM) or the adjoint state method (ASM). Preliminary results with the ASM are presented for some academic forming problems. Then, using the DDM, the optimization method is applied to industrial problems of axisymmetric forging and sheet reverse superplastic forming.

Domaines: Matériaux

Lionel Fourment, Daniel Vieilledent, Sh Chung, Jean-Loup Chenot, Pj Spence. Direct differentiation and adjoint state methods for shape optimization of non-steady forming processes. 7th International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM 2001), Jun 2001, Toyohashi, Japan. p.133-138. ⟨hal-00536350⟩