Structural optimization using sensitivity analysis and a level-set method

Authors:
Grégoire Allaire;François Jouve;Anca-Maria Toader
Affiliations:
Centre de Mathématiques Appliquées (UMR 7641), Ecole Polytechnique, 91128 Palaiseau, France;Centre de Mathématiques Appliquées (UMR 7641), Ecole Polytechnique, 91128 Palaiseau, France;CMAF, Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa, Portugal
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

In the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or nonlinear elasticity. We consider various objective functions with weight and perimeter constraints. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a fixed Eulerian mesh. Although this method is not specifically designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess.