(An) immersed finite element method for the elasticity problems with cracks = 크랙이 있는 탄성문제에 대한 경계함유 유한요소법

We propose a finite element method (FEM) for solving planar elasticity problems involving of heterogeneous materials using uniform grid. Since the interface is allowed to cut through the element, we modify the standard Crouzeix-Raviart (CR) $P_1$-nonconforming basis functions so that they satisfy the jump conditions along the interface. It is well-known that the nonconforming piecewise linear FEM does not satisfy the discrete Korn’s inequality. To ensure the coercivity of the bilinear form arising from using the nonconforming finite elements, we add stabilizing terms as in the discontinuous Galerkin (DG) method. Numerical experiments for various problems show that second order convergence in $L^2$ and first order in $H^1$-norms. Moreover, the convergence order is very robust for nearly incompressible case.
Advisors
Kwak, Do Youngresearcher곽도영researcher
Publisher
한국과학기술원
Issue Date
2016
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2016.8 ,[iii, 51 p. :]

Keywords

elasticity problems; immersed finite element method; stability term; Crouzeix-Raviart element; displacement discontinuity; 탄성 문제; 경계함유 유한요소법; 안정성 항; Crouzeix-Raviart 원소; 불연속 변위

URI
http://hdl.handle.net/10203/222188
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=663136&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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