Journal of the Chinese Institute of Engineers · 1999 · 60 citations · 5 references
EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisRock MechanicsElasticity TheoryFracture MechanicsIntegral Equation FormulationsIntegral EquationsSingularity AnalysisSolid Mechanics ApplicationsBoundary Integral Equation FormulationsBoundary Integral EquationsHypersingular Boundary Integral EquationsSingular Integral EquationsSingular Integral EvaluationSingular Integral RegularizationSingular IntegralsSingularities
Abstract This article considers weakly singular, singular and hypersingular integrals which arise when the boundary integral equations (BIE) are used to solve problems in the theory of elasticity and fracture mechanics. For their regularization, an approach based on the application of the Gauss‐Ostrogradskii and the Green theorems has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals for any convex polygon, have been constructed. Such an approach may be generalized easily and applied for the calculation of multidimensional integrals with various singularities.
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