Element connectivity parameterization for topology optimization of geometrically nonlinear structures

In the current element density-based topology optimization, element stiffness is penalized to yield either solid or void (or very weak) materials, but low-density elements appear during and even after optimization iterations. Especially when nonlinear problems involving large deformation are considered, low-density finite elements cause serious numerical problems as their tangent stiffness matrices lose positive definiteness. To completely eliminate the problem caused by low-density elements, we propose a new method: all finite elements are kept solid throughout the optimization process; zero-length elastic links are introduced to parameterize inter-element connectivity; the link stiffness is penalized. In this approach, the design variables are defined on the links, and vary from 0 and 1 corresponding to the unconnected and rigidly-connected states. Since the finite elements used to discretize the analysis domain always remain solid, typical numerical problems encountered by the standard element density-based formulation disappear. To implement the present method, several issues such as the handling of the mass constraint and raster imaging are also investigated. (C) 2004 Elsevier Ltd. All rights reserved.