Optimal sizing for a class of nonlinearly elastic materials

The intention of this paper is to develop efficient algorithms for solving sizing optimization problems for a class of nonlinearly elastic materials (including, e.g., gray cast iron that is used in car engines) within the finite element programming package MSC/NASTRAN. The nonlinear material law is such that Young's modulus depends on the stresses. Therefore it is not possible to use standard software to perform sizing optimization, but new algorithms have to be found. We will develop and analyse algorithms to solve the nonlinear discrete equilibrium equations and the discrete design problem. Moreover, we test our algorithms for real-life problems, namely to minimize the volume, respectively to reach an even stress distribution, of a unit injector rocker arm made of gray cast iron.