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THE EVALUATIONS OF CAUCHY PRINCIPAL VALUE INTEGRALS AND WEAKLY SINGULAR INTEGRALS IN BEM AND THEIR APPLICATIONS
Author(s) -
ZHU J.,
SHAH A. H.,
DATTA S. K.
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(19960330)39:6<1017::aid-nme892>3.0.co;2-r
Subject(s) - cauchy principal value , singular integral , principal value , mathematics , cauchy distribution , mathematical analysis , slater integrals , order of integration (calculus) , volume integral , principal (computer security) , integral equation , computer science , boundary value problem , cauchy boundary condition , free boundary problem , operating system
A new technique is developed to evaluate the Cauchy principal value integrals and weakly singular integrals involved in the boundary integral equations. The boundary element method is then applied to analyse scattering of waves by cracks in a laminated composite plate. The Green's functions are obtained in discrete form through the thickness of the plate using a stiffness method. To circumvent the difficulties associated with the evaluation of hypersingular integrals due to the presence of cracks, the multidomain technique is applied. Numerical computations have shown the accuracy and reliability of the proposed technique. Scattered wave fields for a composite plate with a horizontal crack are computed. The numerical results show that the applications of the technique in non‐destructive evaluation of defects is very promising.