Optimized/adapted finite elements for structural shape optimization

Abstract

A methodology for geometry-based structural shape optimization with adaptive meshing is developed. This method uses a two-level optimization problem where the first level is focussed on generation of good-quality finite elements/meshes and the second level deals with optimization of the overall structural shape based on responses computed on the adapted mesh. The first-level optimization problem uses the finite element nodal coordinates as design variables whereas the second-level problem uses design-oriented, geometry-based parameters for modifying the structural shape. An error indicator, based on effective stress variations in an element, is used to refine the finite element mesh. It is seen from initial investigation that, with mesh adaptation, the accuracy of the structural responses (displacements and stresses) are increased, resulting in a more accurate evaluation of the design objective and constraints, and therefore resulting in more conservative designs.