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Structural optimization using sensitivity analysis and a level-set method. (English) Zbl 1136.74368
Summary: 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.

MSC:
74P15 Topological methods for optimization problems in solid mechanics
49Q12 Sensitivity analysis for optimization problems on manifolds
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
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