A Q4/Q4 continuum structural topology optimization implementation

Abstract

A node-based design variable implementation for continuum structural topology optimization in a finite element framework is presented and its properties are explored in the context of solving a number of different design examples. Since the implementation ensures C0 continuity of design variables, it is immune to element-wise checkerboarding instabilities that are a concern with element-based design variables. Consequently, the proposed implementation can in most cases be applied to a wide range of structural design applications without ad-hoc assumption of spatial filtering parameters or perimeter constraints to control checkerboarding. Nevertheless in a small subset of design examples considered, especially those involving compliance minimization with coarse meshes, the implementation is found to introduce a new phenomenon that takes form of "layering" or "islanding" in the material layout design. In the examples studied, this phenomenon disappears with mesh refinement or the enforcement of sufficiently restrictive design perimeter constraints, the latter of which are sometimes necessary in design problems involving bending to assure convergence with mesh refinement. Based on its demonstrated performance characteristics, the authors conclude that the proposed node-based implementation is viable for continued usage in continuum topology optimization