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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 im- plementations with respect to that employed for the displacement BIE. The use of the tangen- tial differential operator (TDO) in conjunction with the integration by parts is one way to reduce the order of strong singularities in these fundamental solution kernels. Stress and trac- tion BIEs using the TDO for plate bending models including the shear deformation effect are studied in this work. A Kelvin-type fundamental solution is the main requirement for applying the TDO in conjunction with integration by parts to reduce the singularities. The TDO and integration by parts were applied to all fundamental solution kernels involving the multiplica- tion of generalized displacements in traction BIEs to reduce the singularities, and the result- ing kernels were combinations of those from the displacement BIE, i.e. the numerical imple- mentation requires the same effort employed for displacement BIEs. Plate problems were solved with traction BIEs employing the TDO instead of the displacement BIEs to the behav- ior evaluation with singularity reduced.

blucher mechanical engineering proceedings

A SIMPLIFIED FORMULATION FOR STRESS AND TRACTION BOUNDARY IN-TEGRAL EQUATIONS USING THE TANGENTIAL DIFFERENTIAL OPERATOR FOR PLATE BENDING INCLUDING THE SHEAR DEFORMATION EFFECT