Transverse shear stress distribution through thickness near an internal part-through elliptical hole in a stretched plate

A semi-analytical post-processing method, termed the equilibrium/compatibility method here, is used for computation of hitherto unavailable through-thickness variation of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of an internal part-through elliptical cylindrical hole weakening an edge-loaded rectangular plate. A C0-type triangular “composite” plate element, based on the assumptions of transverse inextensibility and piece (“layer”)-wise constant shear-angle theory (LCST), is employed to first compute the inplane stresses and “layer”-wise through-thickness average transverse shear stresses. These serve as the starting point for computation of through-thickness distribution of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of the internal part-through elliptical hole. As in the case of its circular counterpart, the transverse shear stresses computed by the conventional equilibrium method (EM) are, in contrast, in serious error in the presence of the circumferential re-entrant corner line singularity arising out of the internal part-through elliptical hole, and are found to violate the compatibility condition. The computed maximum transverse shear stress can be high enough to cause catastrophic transverse shear fracture in the shape of a cone, of elliptical cross-section starting from the circumferential re-entrant corner line of the internal part-through hole. The results computed by the present analysis are in line with a three-dimensional asymptotic analysis.