Details
| Original language | English |
|---|---|
| Article number | 106504 |
| Journal | Computers and Structures |
| Volume | 251 |
| Early online date | 24 Apr 2021 |
| Publication status | Published - 15 Jul 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.
Keywords
- Augmented Lagrange method, Continuum mechanics, Multi-element boundary, Nonlocal operator method, Topological surgery
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Computers and Structures, Vol. 251, 106504, 15.07.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multi-connected boundary conditions in solid mechanics and surgery theory
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Anitescu, Cosmin
AU - Rabczuk, Timon
N1 - Funding Information: The authors acknowledge the supports from RISE-BESTOFRAC.
PY - 2021/7/15
Y1 - 2021/7/15
N2 - 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.
AB - 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.
KW - Augmented Lagrange method
KW - Continuum mechanics
KW - Multi-element boundary
KW - Nonlocal operator method
KW - Topological surgery
UR - http://www.scopus.com/inward/record.url?scp=85104671137&partnerID=8YFLogxK
U2 - 10.1016/j.compstruc.2021.106504
DO - 10.1016/j.compstruc.2021.106504
M3 - Article
AN - SCOPUS:85104671137
VL - 251
JO - Computers and Structures
JF - Computers and Structures
SN - 0045-7949
M1 - 106504
ER -