The DOI matches its Crossref record.
Filters in topology optimization
Abstract
In this article, a modified (‘filtered’) version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ‘filtering’ technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs. Copyright © 2001 John Wiley & Sons, Ltd.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Topology optimization approaches: A comparative review
Sigmund, O., & Maute, K. (2013) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-013-0978-6 · Cited by 2,890
Giga-voxel computational morphogenesis for structural design
Aage, N., Andreassen, E., Lazarov, B. S., & Sigmund, O. (2017) · Nature · doi:10.1038/nature23911 · Cited by 772
Topology optimization for nano‐photonics
Jensen, J. S., & Sigmund, O. (2011) · Laser & Photonics Reviews · doi:10.1002/lpor.201000014 · Cited by 767
Length scale and manufacturability in density-based topology optimization
Lazarov, B. S., Wang, F., & Sigmund, O. (2016) · Archive of Applied Mechanics · doi:10.1007/s00419-015-1106-4 · Cited by 319
Robust topology optimization accounting for spatially varying manufacturing errors
Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2011.08.006 · Cited by 286
Metadata
- Authors
- Bourdin, B.
- Venue
- International Journal for Numerical Methods in Engineering
- Publisher
- Wiley
- Published
- 2001-02-14
- Volume
- 50
- Issue
- 9
- Pages
- 2143-2158
- ISSN
- 0029-5981 (ISSN-L)
- 1097-0207
- OpenAlex
- W2110696842
- Cited by
- 1,221
- References
- 0
- FWCI
- 54.25
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Filters in topology optimization. https://app.cochat.ai/papers/10.1002/nme.116
- The paper
- Bourdin, B. (2001). Filters in topology optimization. International Journal for Numerical Methods in Engineering. https://doi.org/10.1002/nme.116
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
