An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump

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In this paper, we propose a finite element method for the elasticity problems which have displacement discontinuity along the material interface using uniform grids. We modify the immersed finite element method introduced recently for the computation of interface problems having homogeneous jumps [20, 22]. Since the interface is allowed to cut through the element, we modify the standard Crouzeix-Raviart basis functions so that along the interface, the normal stress is continuous and the jump of the displacement vector is proportional to the normal stress. We construct the broken piecewise linear basis functions which are uniquely determined by these conditions. The unknowns are only associated with the edges of element, except the intersection points. Thus our scheme has fewer degrees of freedom than most of the XFEM type of methods in the existing literature [1,8,13]. Finally, we present numerical results which show optimal orders of convergence rates.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2017-04
Language
English
Article Type
Article
Keywords

ELLIPTIC INTERFACE PROBLEMS; LINEAR ELASTICITY; DISCONTINUOUS GALERKIN; EQUATIONS; FORMULATION; SIMULATION

Citation

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, v.9, no.2, pp.407 - 428

ISSN
2070-0733
DOI
10.4208/aamm.2016.m1427
URI
http://hdl.handle.net/10203/222678
Appears in Collection
MA-Journal Papers(저널논문)
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