Hypersingularities and cracks in plane and three-dimensional elasticity
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Ioakimidis, Nikolaos
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Abstract
Crack problems in plane elasticity are often interpreted as edge dislocation arrays. Singular stress fields, such as those due to concentrated forces, dislocations and centres of rotation and dilatation, often prove useful in the interpretation and/or the solution of elasticity problems. Here a new kind of singular stress fields called hypersingularities, since these fields are straightforwardly related to hyperintegrals in mathematics, is introduced. The stress components of hypersingularities are seen to tend to infinity more rapidly than in other singular stress fields. The hypersingularities considered here are related to simple crack problems in plane and three-dimensional isotropic elasticity. Generalizations and further applications of the present results are quite possible.
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Keywords
Hypersingularities, Hyperintegrals, Hypersingular integrals, Finite-part integrals, Cracks, Fracture mechanics, Plane elasticity, Three-dimensional elasticity, Isotropic elasticity, Stresses, Displacements, Crack opening displacement, Potentials, Complex potentials, Singular stress fields, Hypersingular stress fields, Hypersingular integral equations