Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection

TL;DR

This paper introduces a novel element removal and reintroduction strategy in density-based topology optimization, significantly reducing computational costs and improving numerical stability while maintaining high-quality design results.

Contribution

It proposes a new method combining element removal with Heaviside projection to enhance efficiency and stability in topology optimization, allowing reintroduction of elements and promoting boundary material reactivation.

Findings

Achieves comparable or better design quality with reduced computational time.

Effectively mitigates numerical instabilities in low-density regions.

Demonstrates applicability in 2D and 3D structural optimization problems.

Abstract

We present a strategy grounded in the element removal idea of Bruns and Tortorelli [1] and aimed at reducing computational cost and circumventing potential numerical instabilities of density-based topology optimization. The design variables and the relative densities are both represented on a fixed, uniform finite element grid, and linked through filtering and Heaviside projection. The regions in the analysis domain where the relative density is below a specified threshold are removed from the forward analysis and replaced by fictitious nodal boundary conditions. This brings a progressive cut of the computational cost as the optimization proceeds and helps to mitigate numerical instabilities associated with low-density regions. Removed regions can be readily reintroduced since all the design variables remain active and are modeled in the formal sensitivity analysis. A key feature of the proposed approach is that the Heaviside functions promote material reintroduction along the structural boundaries by amplifying the magnitude of the sensitivities inside the filter reach. Several 2D and 3D structural topology optimization examples are presented, including linear and nonlinear compliance minimization, the design of a force inverter, and frequency and buckling load maximization. The approach is shown to be effective at producing optimized designs equivalent or nearly equivalent to those obtained without the element removal, while providing remarkable computational savings.