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

Part of:Elastic materialsPartial differential equations, boundary value problemsNumerical methods

Published online by Cambridge University Press:  09 January 2017

Daehyeon Kyeong and
Do Young Kwak
Daehyeon Kyeong*
Affiliation:
Korea Advanced Institute of Science and Technology, Daejeon, Korea 305-701, Korea
Do Young Kwak*
Affiliation:
Korea Advanced Institute of Science and Technology, Daejeon, Korea 305-701, Korea
*
*Corresponding author. Email:huff@kaist.ac.kr (D. Kyeong), kdy@kaist.ac.kr (D. Y. Kwak)
*Corresponding author. Email:huff@kaist.ac.kr (D. Kyeong), kdy@kaist.ac.kr (D. Y. Kwak)

Abstract

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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.

Keywords

Elasticity problemsfinite element methodCrouzeix-Raviart elementdisplacement discontinuity

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods74S05: Finite element methods74B05: Classical linear elasticity

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017, pp. 407 - 428
Copyright
Copyright © Global-Science Press 2017 

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