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Special finite elements with holes and internal cracks
Author(s) -
Piltner R.
Publication year - 1985
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.1620210809
Subject(s) - conformal map , computation , finite element method , boundary value problem , mathematics , mathematical analysis , stiffness , boundary (topology) , elasticity (physics) , a priori and a posteriori , stress functions , displacement (psychology) , geometry , structural engineering , engineering , physics , algorithm , psychology , philosophy , epistemology , psychotherapist , thermodynamics
For the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.