Multi-connected boundary conditions in solid mechanics and surgery theory

authored by
Huilong Ren, Xiaoying Zhuang, Cosmin Anitescu, Timon Rabczuk
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.

Organisation(s)
Institute of Continuum Mechanics
External Organisation(s)
Bauhaus-Universität Weimar
Tongji University
Ton Duc Thang University
Type
Article
Journal
Computers and Structures
Volume
251
ISSN
0045-7949
Publication date
15.07.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Civil and Structural Engineering, Modelling and Simulation, Materials Science(all), Mechanical Engineering, Computer Science Applications
Electronic version(s)
https://doi.org/10.1016/j.compstruc.2021.106504 (Access: Closed)
 

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