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The shifted boundary method for solid mechanics

Publication ,  Journal Article
Atallah, NM; Canuto, C; Scovazzi, G
Published in: International Journal for Numerical Methods in Engineering
October 30, 2021

We propose a new embedded/immersed framework for computational solid mechanics, aimed at vastly speeding up the cycle of design and analysis in complex geometry. In many problems of interest, our approach bypasses the complexities associated with the generation of CAD representations and subsequent body-fitted meshing, since it only requires relatively simple representations of the surface geometries to be simulated, such as collections of disconnected triangles in three dimensions, widely used in computer graphics. Our approach avoids the complex treatment of cut elements, by resorting to an approximate boundary representation and a special (shifted) treatment of the boundary conditions to maintain optimal accuracy. Natural applications of the proposed approach are problems in biomechanics and geomechanics, in which the geometry to be simulated is obtained from imaging techniques. Similarly, our computational framework can easily treat geometries that are the result of topology optimization methods and are realized with additive manufacturing technologies. We present a full analysis of stability and convergence of the method, and we complement it with an extensive set of computational experiments in two and three dimensions, for progressively more complex geometries.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

October 30, 2021

Volume

122

Issue

20

Start / End Page

5935 / 5970

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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ICMJE
MLA
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Atallah, N. M., Canuto, C., & Scovazzi, G. (2021). The shifted boundary method for solid mechanics. International Journal for Numerical Methods in Engineering, 122(20), 5935–5970. https://doi.org/10.1002/nme.6779
Atallah, N. M., C. Canuto, and G. Scovazzi. “The shifted boundary method for solid mechanics.” International Journal for Numerical Methods in Engineering 122, no. 20 (October 30, 2021): 5935–70. https://doi.org/10.1002/nme.6779.
Atallah NM, Canuto C, Scovazzi G. The shifted boundary method for solid mechanics. International Journal for Numerical Methods in Engineering. 2021 Oct 30;122(20):5935–70.
Atallah, N. M., et al. “The shifted boundary method for solid mechanics.” International Journal for Numerical Methods in Engineering, vol. 122, no. 20, Oct. 2021, pp. 5935–70. Scopus, doi:10.1002/nme.6779.
Atallah NM, Canuto C, Scovazzi G. The shifted boundary method for solid mechanics. International Journal for Numerical Methods in Engineering. 2021 Oct 30;122(20):5935–5970.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

October 30, 2021

Volume

122

Issue

20

Start / End Page

5935 / 5970

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering