Flux and traction boundary elements without hypersingular or strongly singular integrals

Abstract

SUMMARYThe present paper deals with a boundary element formulation based on the traction elasticity boundary integral equation (potential derivative for Laplace's problem). The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require any change of co-ordinates and the resulting integrals can be numerically evaluated in a simple and e cient way. The formulation presented is completely general and valid for arbitrary shaped open or closed boundaries. Analytical expressions for all the required hypersingular or strongly singular integrals are given in the paper. To fulÿl the continuity requirement over the primary density a simple BE discretization strategy is adopted. Continuous elements are used whereas the collocation points are shifted towards the interior of the elements. This paper pretends to contribute to the transformation of hypersingular boundary element formulations as something clear, general and easy to handle similar to in the classical formulation.

Numerical solution of the variation boundary integral equation for inverse problems

“…Twelve (M = 12) measurements are provided, three points on each side. Speciÿcally, the 'experimental' potential or ux is given at nodes 2, 5,8,11,13,15,19,20,23,27,29 and 31 (see Figure 3 for the discretization. )…”

“…The number of equations is therefore greater than in the standard collocation scheme (which nevertheless can not be applied to this BIE), and greater than the number of unknowns, but can be easily reduced in order to arrive to a square system of equations (see Section 5), therefore, avoiding a costly least-squares solver. Gallego and Dominguez [24;25] employed this approach for fracture dynamic problems, Saez et al [28] for static fracture and Dominguez et al [29] extended it to 3D elastostatic fracture cases.…”

Three-Dimensional Be-Fe Model of Bucket Foundations in Poroelastic Soils

“…Using this fact, a meaningful HBIE can be obtained once a regularization process based on the work of Domínguez et al [14] is performed.…”

“…Aliabadi and co-workers [15,16] use discontinuous boundary elements with nodes already located at points where this condition is fulfilled. Another approach is that of Domínguez et al [14], where standard continuous boundary elements with multiple non-nodal collocation is used. The latter is considered in the present work since, as it will become clear in the next section, continuous boundary elements are much more appropriate for the proposed coupling.…”

Symmetric collocation BEM/FEM coupling procedure for 2-D dynamic structural-acoustic interaction problems

“…The main difficulty for SGBEM is the existence of hypersingular integrals. Although numerous papers can be found in dealing with the hypersingular integrals [17][18][19], there are still some spaces that need more research works. The double boundary integration can increase the accuracy for SGBEM, but with a cost of computing time [20].…”