An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms

TLDR

In topology optimization, the material density field is distributed via nonlinear programming, but a small lower bound is usually imposed to avoid zero stiffness, which can cause computational issues in compliant mechanisms. The authors propose a systematic strategy to remove and reintroduce low‑density elements to mitigate these problems. The method operates on the finite‑element mesh, iteratively eliminating and reinstating elements based on their density while preserving structural integrity. Applying the strategy to several structures and compliant mechanisms yields significant improvements in design quality and computational efficiency compared to existing approaches. © 2003 John Wiley & Sons, Ltd.

Abstract

Abstract A method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined. The material density field which defines the topology and the local ‘stiffness’ of the structure is optimally distributed via non‐linear programming techniques. To prevent elements from having zero stiffness, an arbitrarily small lower bound on the material density is typically imposed to ensure that the global stiffness matrix does not become singular. While this approach works well for most minimum compliance problems, the presence of low density elements can cause computational problems, particularly in structures that exhibit geometric non‐linearities, e.g. in compliant mechanisms. To resolve this problem, a systematic approach for removing and reintroducing low density elements is presented, and the substantial performance improvements both in design and computational efficiency of the method over current methods are discussed. Several structures and compliant mechanisms are designed to demonstrate the method. Copyright © 2003 John Wiley & Sons, Ltd.