Extracting generalized edge flux intensity functions by the quasidual function method along circular 3-D edges

Samuel Shannon, Zohar Yosibash, Monique Dauge, Martin Costabel

August 2012. Prépublication IRMAR, 12-62.

International Journal of Fracture 181, 1 (2013) 25-50 DOI: 10.1007/s10704-013-9817-4

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Explicit asymptotic series describing solutions to the Laplace equation in the vicinity of a circular edge in a three-dimensional domain was recently provided in Yosibash et al, Int. Jour. Fracture, 168 (2011), pp. 31-52 . Utilizing it, we extend the quasidual function method (QDFM) for extracting the generalized edge flux intensity functions (GEFIFs) along circular singular edges in the cases of axisymmetric and non-axisymmetric data.

This accurate and efficient method provides a functional approximation of the GEFIFs along the circular edge whose order is adaptively increased so to approximate the exact GEFIFs. It is implemented as a post-solution operation in conjunction with the p-version of the finite element method. The mathematical analysis of the QDFM is provided, followed by numerical investigations, demonstrating the efficiency, robustness and high accuracy of the proposed quasi-dual function method. The mathematical machinery developed in the framework of the Laplace operator is important to realize its possible extension for the elasticity system.