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A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions
Author(s) -
Zhang J.,
Katsube N.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620381004
Subject(s) - finite element method , degrees of freedom (physics and chemistry) , mixed finite element method , displacement (psychology) , extended finite element method , mathematical analysis , mathematics , elasticity (physics) , finite element limit analysis , element (criminal law) , boundary value problem , geometry , structural engineering , materials science , physics , engineering , composite material , psychology , quantum mechanics , political science , law , psychotherapist
A hybrid finite element approach is proposed for the mechanical response of two‐dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion. In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply‐connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense. The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freedom).