Generalized Mangler-type principal value integrals with an application to fracture mechanics

摘要

A generalized interpretation of the classical Mangler-type principal value integrals is proposed. This new interpretation in general is not equivalent to the classical one. Several formulae for this new class of integrals are proved, concerning their relationship to Cauchy-type, generalized Cauchy-type and ordinary Mangler-type principal value integrals. Moreover, the Plemelj formulae and quadrature rules are considered for the same class of integrals. Finally, the present results are applied to the hypersingular integrodifferential equation of an interface crack in the classical theory of plane elasticity, which takes now the form of a simple hypersingular integral equation.