WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 9, 2014
Mixed Finite Element Method for Linear Elasticity in a Cracked Domain
Authors: , ,
Abstract: A mixed finite element procedure for plane elasticity system in a cracked domains is introduced and analyzed. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order approximation. The simplest element pair involves 24 local degrees of freedom for the stress and 6 for the displacement. We also construct a lower order element involving 21 stress degrees of freedom and 3 displacement degrees of freedom which is, we believe, likely to be the simplest possible conforming stable element pair with polynomial shape functions. The mixed formulation is used in elasticity for incompressible materials such as rubber, its use for linear elasticity has been discussed by many researchers, in this section we will study the compatibility of the mixed formulation cracked domains and compare it with the conventional method.The numerical results are compared with some previously published works or with others coming from commercial code.
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Keywords: Elasticity problem, mixed finite element method, Lower order element, linear fracture mechanics
Pages: 167-178
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 9, 2014, Art. #14