Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization

The application of the element density-based topology optimization method to nonlinear continuum structures is limited to relatively simple problems such as bilinear elastoplastic material problems. Furthermore, it is very difficult to use analytic sensitivity when a commercial nonlinear finite element code is used. As an alternative to the element density formulation, the element connectivity parameterization (ECP) formulation is developed for the topology optimization of isotropic-hardening elastoplastic or hyperelastic continua by using commercial software. ECP varies the stiffness of zero-length linear elastic links that connect design domain-discretizing finite elements. Unloading was not considered. But the advantages of ECP in material-nonlinear problems were demonstrated: considerably simple analytic sensitivity calculation using a commercial code and simple link stiffness penalization regardless of nonlinear material behaviour. Copyright q 2006 John Wiley & Sons, Ltd.