X-CAD: Optimizing CAD Models with Extended Finite Elements

C. Hafner, C. Schumacher, E. Knoop, T. Auzinger, B. Bickel, M. Bächer, ACM Transactions on Graphics 38 (2019).

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Journal Article | Published | English
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Abstract
We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.
Publishing Year
Date Published
2019-11-06
Journal Title
ACM Transactions on Graphics
Volume
38
Issue
6
Article Number
157
ISSN
IST-REx-ID

Cite this

Hafner C, Schumacher C, Knoop E, Auzinger T, Bickel B, Bächer M. X-CAD: Optimizing CAD Models with Extended Finite Elements. ACM Transactions on Graphics. 2019;38(6). doi:10.1145/3355089.3356576
Hafner, C., Schumacher, C., Knoop, E., Auzinger, T., Bickel, B., & Bächer, M. (2019). X-CAD: Optimizing CAD Models with Extended Finite Elements. ACM Transactions on Graphics, 38(6). https://doi.org/10.1145/3355089.3356576
Hafner, Christian, Christian Schumacher, Espen Knoop, Thomas Auzinger, Bernd Bickel, and Moritz Bächer. “X-CAD: Optimizing CAD Models with Extended Finite Elements.” ACM Transactions on Graphics 38, no. 6 (2019). https://doi.org/10.1145/3355089.3356576.
C. Hafner, C. Schumacher, E. Knoop, T. Auzinger, B. Bickel, and M. Bächer, “X-CAD: Optimizing CAD Models with Extended Finite Elements,” ACM Transactions on Graphics, vol. 38, no. 6, 2019.
Hafner C, Schumacher C, Knoop E, Auzinger T, Bickel B, Bächer M. 2019. X-CAD: Optimizing CAD Models with Extended Finite Elements. ACM Transactions on Graphics. 38(6), 157.
Hafner, Christian, et al. “X-CAD: Optimizing CAD Models with Extended Finite Elements.” ACM Transactions on Graphics, vol. 38, no. 6, 157, ACM, 2019, doi:10.1145/3355089.3356576.
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