Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection
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 fix...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2021
|
| Online Access: | https://hdl.handle.net/1721.1/132730 |
| _version_ | 1811094508864012288 |
|---|---|
| author | Behrou, Reza Lotfi, Reza Carstensen, Josephine Voigt Ferrari, Federico Guest, James K |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Behrou, Reza Lotfi, Reza Carstensen, Josephine Voigt Ferrari, Federico Guest, James K |
| author_sort | Behrou, Reza |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:01:27Z |
| format | Article |
| id | mit-1721.1/132730 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:01:27Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1327302024-05-31T20:33:24Z Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection Behrou, Reza Lotfi, Reza Carstensen, Josephine Voigt Ferrari, Federico Guest, James K Massachusetts Institute of Technology. Department of Civil and Environmental Engineering 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. 2021-10-06T13:57:01Z 2021-10-06T13:57:01Z 2021-04 2021-02 2021-10-05T18:40:34Z Article http://purl.org/eprint/type/JournalArticle 0045-7825 https://hdl.handle.net/1721.1/132730 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 en 10.1016/J.CMA.2021.113799 Computer Methods in Applied Mechanics and Engineering Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Behrou, Reza Lotfi, Reza Carstensen, Josephine Voigt Ferrari, Federico Guest, James K Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title | Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title_full | Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title_fullStr | Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title_full_unstemmed | Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title_short | Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection |
| title_sort | revisiting element removal for density based structural topology optimization with reintroduction by heaviside projection |
| url | https://hdl.handle.net/1721.1/132730 |
| work_keys_str_mv | AT behroureza revisitingelementremovalfordensitybasedstructuraltopologyoptimizationwithreintroductionbyheavisideprojection AT lotfireza revisitingelementremovalfordensitybasedstructuraltopologyoptimizationwithreintroductionbyheavisideprojection AT carstensenjosephinevoigt revisitingelementremovalfordensitybasedstructuraltopologyoptimizationwithreintroductionbyheavisideprojection AT ferrarifederico revisitingelementremovalfordensitybasedstructuraltopologyoptimizationwithreintroductionbyheavisideprojection AT guestjamesk revisitingelementremovalfordensitybasedstructuraltopologyoptimizationwithreintroductionbyheavisideprojection |