Stress constrained optimization using X-FEM and Level-Set description

in Proceedings of III European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering (2006)

This paper presents and describes an intermediate approach which takes its place between the two classical methods of shape and topology optimization. It is based on using the recent Level Set description ... [more ▼]

This paper presents and describes an intermediate approach which takes its place between the two classical methods of shape and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (X-FEM). The method benefits from the fixed mesh work using X-FEM and from the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation remains small whereas various global and local constraints can be considered. A key problem which is investigated here is the sensitivity analysis and the way it can be carried out precisely and efficiently. Numerical applications revisit some classical 2D (academic) benchmarks from shape optimization and illustrate the great interest of using X-FEM and Level Set description together. The paper presents the results of stress constrained problems using the proposed X-FEM and Level Set based formulation. A central issue is the sensitivity analysis (related to the compliance and/or the stresses) and the way it can be carried out efficiently. A special attention is also paid to stress constrained problems which are often neglected in other Level Set Methods works. [less ▲]