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Numerical analysis of edge singularities in three‐dimensional elasticity
Author(s) -
Yosibash Zohar
Publication year - 1997
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(19971230)40:24<4611::aid-nme276>3.0.co;2-p
Subject(s) - elasticity (physics) , gravitational singularity , mathematics , numerical analysis , enhanced data rates for gsm evolution , geometry , mathematical analysis , computer science , materials science , composite material , artificial intelligence
A numerical method is described for the computation of eigenpairs which characterize the exact solution of linear elastostatic problems in three‐dimensions in the vicinity of edge singularities. These may be caused by re‐entrant corners, abrupt changes in boundary conditions or material properties. Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes. This paper addresses the problem of determining the edge eigenpairs numerically on the basis of the modified Steklov formulation (presented in Reference 1 in a 2‐D framework) in conjunction with the p ‐version of the finite element method. Numerical results are presented for several cases including isotropic as well as anisotropic multi‐material interfaces. © 1997 John Wiley & Sons, Ltd.