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EVALUATION OF THE STRESS TENSOR IN 3‐D ELASTOPLASTICITY BY DIRECT SOLVING OF HYPERSINGULAR INTEGRALS
Author(s) -
HUBER O.,
DALLNER R.,
PARTHEYMÜLLER P.,
KUHN G.
Publication year - 1996
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/(sici)1097-0207(19960815)39:15<2555::aid-nme966>3.0.co;2-6
Subject(s) - mathematics , mathematical analysis , boundary (topology) , cauchy stress tensor , domain (mathematical analysis) , regularization (linguistics) , singular integral , tensor (intrinsic definition) , point (geometry) , singular boundary method , singularity , boundary value problem , singular point of a curve , displacement (psychology) , boundary element method , integral equation , geometry , finite element method , physics , psychology , artificial intelligence , computer science , psychotherapist , thermodynamics
A 3‐D hypersingular Boundary Integral Equation (BIE) of elastoplasticity is derived. Using this formulation the displacement rate gradients and the complete stress tensor on the boundary can be evaluated directly as opposed to the classical approach, where the shape functions derivatives are to be calculated. The regularization of strongly singular and hypersingular boundary integrals, as well as strongly singular domain integrals for a source point positioned on the boundary is carried out in a general manner. Arbitrary types of elements and arbitrary positions of the source point with respect to continuity requirements can be used. Numerical 3‐D elastoplastic examples (notch and crack problems) illustrate the advantages of the proposed method.