Multi-connected boundary conditions in solid mechanics and surgery theory

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Huilong Ren
  • Xiaoying Zhuang
  • Cosmin Anitescu
  • Timon Rabczuk

Organisationseinheiten

Externe Organisationen

  • Bauhaus-Universität Weimar
  • Tongji University
  • Ton Duc Thang University
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer106504
FachzeitschriftComputers and Structures
Jahrgang251
Frühes Online-Datum24 Apr. 2021
PublikationsstatusVeröffentlicht - 15 Juli 2021

Abstract

Boundary conditions are critical to the partial differential equations (PDEs) as they constrain the PDEs ensuring a unique and well defined solution. Based on combinatorial and surgery theory of manifolds, we develop multi-element boundary conditions as the generalization of the traditional boundary conditions in classical mechanics: Dirichlet boundary conditions, Neumann boundary conditions and Robin boundary conditions. The multi-element boundary/domain conditions glue the physical quantities at several points of different boundaries or domains on the fly, where the point-to-point correspondence (point mapping) on several boundaries are established on the common local coordinate system and the interactions are realized through the “wormhole” (i.e. the constraint equations). The study on weak form shows that the general multi-element boundary conditions are inconsistent with the variational principle/weighted residual method. To circumvent this dilemma, a numerical scheme based on augmented Lagrange method and nonlocal operator method (NOM) is proposed to deal with the mechanical problem equipped with general multi-element boundary conditions. Numerical tests show that the structures have completely different deformation modes for different multi-element boundary conditions.

ASJC Scopus Sachgebiete

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Multi-connected boundary conditions in solid mechanics and surgery theory. / Ren, Huilong; Zhuang, Xiaoying; Anitescu, Cosmin et al.
in: Computers and Structures, Jahrgang 251, 106504, 15.07.2021.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Ren H, Zhuang X, Anitescu C, Rabczuk T. Multi-connected boundary conditions in solid mechanics and surgery theory. Computers and Structures. 2021 Jul 15;251:106504. Epub 2021 Apr 24. doi: 10.1016/j.compstruc.2021.106504
Ren, Huilong ; Zhuang, Xiaoying ; Anitescu, Cosmin et al. / Multi-connected boundary conditions in solid mechanics and surgery theory. in: Computers and Structures. 2021 ; Jahrgang 251.
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AU - Zhuang, Xiaoying

AU - Anitescu, Cosmin

AU - Rabczuk, Timon

N1 - Funding Information: The authors acknowledge the supports from RISE-BESTOFRAC.

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