A tangential differential operator applied to stress and traction boundary integral equations for plate bending including the shear deformation effect

Stress boundary integral equations (BIEs) are required in elastic or inelastic analyses of plate bending problems to obtain distributed shear, bending and twisting moments. Traction BIE, which is important to perform fracture analyses, is directly related to stress BIE. The collocation point position and the strategy to treat improper integrals are essential features studied in BIE for tractions or stresses at boundary points. The tangential differential operator (TDO) is used in stress and traction BIEs to reduce the strong singularities in the fundamental solution kernels and remaining singularities can be treated with the Cauchy principal value sense or the first order regularization. This study presents the application of the TDO for stress and traction BIEs used in plate bending models considering the shear deformation effect. The results in bending problems are obtained with traction BIE using TDO, instead of displacement BIE, and are compared to those in the literature where the problem was solved with traction BIE containing the strong singularity or with displacement BIE.