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 C 0 continuity of design variables, it is immune to elementwise checkerboarding instabilities that are a concern with element-based design variables. Nevertheless, in a subset of design examples considered, especially those involving compliance minimization with coarse meshes, the implementation is found to introduce a new phenomenon that takes the 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 sometimes being necessary in design problems involving bending to ensure convergence with mesh refinement. Based on its demonstrated performance characteristics, the authors conclude that the proposed nodebased implementation is viable for continued usage in continuum topology optimization.

Robust Topology Optimization for Compliant Mechanisms Considering Uncertainty of Applied Loads

“…Also note that similar formulations based on the SIMP method were presented in Refs. (21) and (22). Although they pointed out some numerical problems such as "layering" and "islanding" when using coarse meshes, the numerical examples obtained by the method proposed here will show clear optimal configurations given sufficiently fine meshes, without the above problems.…”

Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes

“…Also note that similar formulations based on the SIMP method were presented by Rahmatalla and Swan [42,43]. Although they pointed out some numerical problems such as 'layering' and 'islanding' using coarse meshes [43], the numerical examples obtained by the method proposed here will show clear optimal configurations, without the above problems. The reason why such phenomena do not occur in our proposed method is not clear, and we plan to investigate this in detail in the future.…”

Regular solution to topology optimization problems of continua

“…However, numerical instabilities such as checkerboard patterns or mesh-dependencies are observed if the parameters of micro-structure or the density is constructed by a constant function in each finite element and they are varied using a gradient method [6,7]. If the design parameters are approximated by continuous functions [8], it is known that a numerical instability, such as the socalled island phenomena, is observed [9]. In addition, although many numerical schemes have been proposed to overcome such numerical instabilities [10,11], regularity in the sense of functional analysis has not been shown.…”