Do, Tien Tho (2006) Optimisation de forme en forgeage 3D. PhD thesis Mécanique Numérique, ENSMP - CEMEF Centre de Mise en Forme des Matériaux, ENSMP.

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Abstract

This study focuses on shape optimization for 3D forging process. The problems to be solved consist in searching the optimal shape of the initial work piece or of the preform tool in order to minimize an objective function F which represents a measure of non-quality defined by the designer. These are often multi optima problems in which the necessary time for a cost function evaluation is very long (about a day or more). This work aims at developping an optimization module that permits to localize the global optimum within a reasonable cost (less than 50 calculations of objective function per optimization).
The process simulation is carried out using the FORGE3® finite element software. The axisymmetric initial shape of the workpiece or die is parameterized using quadratic segments or Bspline curves. Several objective functions are considered, like the forging energy, the forging force or a surface defect criterion. The gradient of these objective functions is obtained by the adjoint-state method and semi-analytical differentiation. In this work, this gradient calculation (initiated in M. Laroussi's thesis) has been extended to another type of parameter "the parameters that control the shape of tool preform".
Different optimization algorithms are tested for 3D applications: a standard BFGS algorithm, a moving asymptote algorithm, an evolution strategies algorithm enhanced with a response surface method based on Kriging and two new hybrid evolutionary algorithms proposed during this work. This hybrid approach consists in coupling a genetic algorithm to a response surface method that uses gradient information to dramatically reduce the number of problem simulations. All studied algorithms are compared for two 3D industrial tests, using rather coarse meshes. They make it possible to improve the initial design and to decrease the total forming energy and/or a surface defect criterion. Numerical results show the feasibility of such approaches, i.e. the achieving of satisfactory solutions within a limited number of 3D simulations, less than fifty.

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