On the application of the generalized Plemelj formulas to crack problems
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Ioakimidis, Nikolaos
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Abstract
The singular integral equation for the simple plane elasticity problem of a straight crack under a known normal pressure distribution is derived by using the first generalized Plemelj formula (where a finite-part integral appears) on the basis of the complex-variable formulation of plane elasticity problems. The present results are believed to prove useful in a lot of more complicated elasticity problems, to which they can easily be applied, and to lead to the wide use of singular integral equations with finite-part integrals in elasticity problems.
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Keywords
Crack problems, Fracture mechanics, Plane elasticity, Isotropic elasticity, Generalized Plemelj formulas, Principal value integrals, Cauchy-type integrals, Singular integral equations, Finite-part integrals, Hadamard-type integrals, Hypersingular integrals, Hypersingular integral equations, Analytic functions, Complex variables, Complex potentials