WIT Press

BIEs For Modelling Of Discontinuities In Linear Multi-field Half-space


Free (open access)





Page Range

125 - 137




459 kb

Paper DOI



WIT Press


T. N. Pham, J. Rungamornrat, W. Pansuk, Y. Sato


This paper presents an efficient and accurate boundary integral equation method for solving a linear, multi-field, half-space containing a surface of discontinuity and subjected to symmetrical and anti-symmetrical conditions on the boundary. Responses of the half-space are governed by a set of linear partial differential equations which are formulated in a general framework allowing the treatment of Laplace equation, linear elasticity problems, and problems involving multi-field materials such as piezoelectric, piezomagnetic, and piezoelectromagnetic solids. In the formulation, a systematic regularization procedure via the integration by parts, symmetrical and anti-symmetrical properties, and special representations of strongly singular and hyper singular kernels is employed to derive a set of singularity-reduced boundary integral relations. A pair of weak-form boundary integral equations involving both the sum and relative crack-face state variable and surface flux across the discontinuity surface is finally established and they contain only weakly singular kernels. A standard symmetric Galerkin boundary element method (SGBEM) is then implemented to solve those weakly singular integral equations for unknown data on the discontinuity surface. In numerical implementations, continuous local interpolation functions are employed in the approximation of solutions and an efficient means for both the kernel evaluation and the numerical integration is adopted to enhance the accuracy and computational efficiency of the developed scheme. The proposed numerical technique is then verified with various, reliable benchmark cases and a selected set of results is presented to demonstrate its capability and robustness.


half-space, discontinuity, SGBEM, SIFs, T-stress, weakly singular