The general type of finite-part singular integrals and integral equations with logarithmic singularities used in fracture mechanics |
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Authors: | E G Ladopoulos |
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Affiliation: | (1) Department of Theoretical and Applied Mechanics, The National Technical University of Athens, GR-15773 Athens, Greece |
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Abstract: | Summary A new method is proposed, by using some special quadrature rules, for the numerical evaluation of the general type of finite-part singular integrals and integral equations with logarithmic singularities. In this way the system of such equations can be numerically solved by reduction to a system of linear equations. For this reduction, the singular integral equation is applied to a number of appropriately selected collocation points on the integration interval, and then a numerical integration rule is used for the approximation of the integrals in this equation. An application is given, to the determination of the intensity of the logarithmic singularity in a simple crack inside an infinite, isotropic solid.With 1 Figure |
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