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Engineering Analysis with Boundary Elements, Volume 36, Issue 8, August 2012, Pages 1213-1225
Leandro Palermo Jr.
Faculty of Civil Engineering, Architecture and Urban Design, University of Campinas, Brazil
Abstract
Boundary integral equations (BIEs) for stresses are widely used in elastic and inelastic analyses, and those for tractions are essential in fracture mechanics problems. The existence of strong singularities in the fundamental solution kernels of BIEs for stresses at boundary points and for traction forces requires additional care in numerical implementations with respect to that employed for a displacement BIE. The use of the tangential differential operator (TDO) in conjunction with integration by parts is one way to reduce the order of strong singularities in these fundamental solution kernels when Kelvin-type fundamental solutions are used. Two formulations for stress and traction BIEs using the TDO are presented in this study. The TDO and integration by parts were employed in the first formulation only to reduce the strong singularity without changing other fundamental solution kernels. In the second formulation, the TDO was applied to all fundamental solution kernels involving the multiplication of generalized displacements to reduce the singularities, and the resulting kernels were combinations of those from the displacement BIE. Finally, plate problems were solved with both traction BIEs employing the TDO instead of the displacement BIEs to evaluate the accuracy of these formulations.
Additional Information:
A traction boundary integral equation (BIE) without hypersingular fundamental solution kernels is presented to perform plate bending analyses including the shear deformation effect. The tangential differential operator (TDO) and integration by parts were applied to all fundamental solution kernels involving the multiplication of generalized displacements to reduce the singularities, and the resulting kernels were combinations of those from the displacement BIE. Furthermore, the use of non-conformal interpolation in traction BIEs with TDO is allowed according to the formulation presented and it is shown the numerical implementation of TDO in the boundary element method is simplified beyond the point of benefiting from singularity reduction, i.e. the numerical implementation requires the same effort employed for displacement BIEs.