The tangential differential operator applied to a stress boundary integral equation for plate bending including the shear deformation effect

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.