Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection
Name
2012.02860.pdf
Description
Accepted version
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4.74 MB
Format
Adobe PDF
Checksum (MD5)
d502dbc48c1db7281c36677f380aaf92
Author(s)
Behrou, Reza
Lotfi, Reza
Carstensen, Josephine Voigt
Ferrari, Federico
Guest, James K
Date Issued
April 2021
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Citation
Reza Behrou, Reza Lotfi, Josephine Voigt Carstensen, Federico Ferrari, James K. Guest,
Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection, Computer Methods in Applied Mechanics and Engineering, Volume 380, 2021
Version
Author's final manuscript
Abstract
We present a strategy grounded in the element removal idea of Bruns and Tortorelli (2003) 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 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 projection promotes 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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.CMA.2021.113799
