Structural optimization by the level-set method

In the context of structural optimization, we describe a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We have implemented this method in two and three space dimensions for models of linear or non-linear elasticity, with various objective functions and constraints on the volume or on the perimeter. 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.