Shape optimization of elastic structures using a level-set based mesh evolution method

We propose a method for structural optimization that combines two different ways of depicting shapes : the considered domain is exactly meshed at each iteration when it comes to performing shape or topological sensitivity analysis of the considered cost functional (which often requires one or several finite element computations), while we resort to a level-set description of the domain for describing its evolution along the derived gradient velocity field. The cornerstone of this method is a meshing algorithm for building a mesh, suitable for mechanical computations, out of a piecewise linear level-set function on an unstructured mesh. The proposed method thus enjoys an accurate description of the shapes at hand, and still allows for topological changes thanks to the versatility of level-set methods.