A combined FEM and three-dimensional asymptotic solution based analysis on stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in stretched plates

Abstract

a b s t r a c t C 0 -type triangular ''layered'' plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST) are employed to investigate the weakening effects of localized elliptical (circular being a special case) cylindrical surface flaws in isotropic plates. Numerical results indicate severe transverse shear deformation in the vicinity of a surface flaw boundary. In addition, a recently developed asymptotic solution to the problem pertaining to the stress fields in the neighborhood of the circumferential corner line or line of intersection of a circular cylindrical external partthrough open hole and an interior surface of an isotropic plate, subjected to far-field extension (mode I), in-plane shear (mode II) loadings, is presented. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening plates, are numerically assessed, because of their role in crack initiation.

On three-dimensional asymptotic solution, and applicability of Saint–Venant’s principle to pie-shaped wedge and end face (of a semi-infinite plate) boundary value problems

“…The interaction of this singularity with end or edge face (free edge in two dimension) stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of Saint-Venant's principle) in regards to testing of laminated composite specimens have also been thoroughly investigated [13][14][15]. For homogeneous plates weakened by similar internal and surface part-through flaws, there is no violation of SaintVenant's principle, because of absence of such an edge face singularity [14,16,17]. This notwithstanding, a rigorous theoretical basis of such violations or lack thereof is still absent in the literature, which is an important focus of the present study.…”

Effects of Surface-Parallel Edge Restraints and Inter-laminar Shear on the Responses of Doubly Curved General Cross-Ply Panels

“…Finally, reliability of the finite element method, based on the assumed displacement potential energy approach, in the neighborhood of stress discontinuities and stress singularities has been discussed by Whitcomb, et al [128] (at the free edge in a laminated composite), and Chaudhuri and co-workers [129][130][131][132][133][134][135][136][137] (at the circumferential corner line of an internal circular cylindrical hole). Whitcomb, et al [128] have concluded that "the finite element method yielded accurate solutions everywhere except in a region involving the elements closest to the stress discontinuity or singularity and that this region can be made arbitrarily small by refining the finite element model".…”

“…Whitcomb, et al [128] have concluded that "the finite element method yielded accurate solutions everywhere except in a region involving the elements closest to the stress discontinuity or singularity and that this region can be made arbitrarily small by refining the finite element model". Chaudhuri [129][130][131][132][133] has probed into the issue much deeper. His conclusion re-affirms, to a rather milder degree, the conclusion reached in the case of its laminate counterpart [133][134][135][136][137] in regards to the accuracy (or lack thereof) of the stresses (more accurately, the stress gradients) computed using the conventional (assumed displacement potential energy based) finite element analysis and computed FEM-based post-processing analysis results for transverse shear stresses in the vicinity of a stress singularity, such as the circumferential corner line of an internal circular/elliptical cylindrical hole.…”

“…Second, a boundary-value formulation based on trigonometric shear deformation theory [90] for laminated anisotropic doubly curved panels of various ply-orientations, subjected to arbitrary boundary constraints, can also solved using the present approach. Third and more important, the present and future TSDT-based results for laminated anisotropic doubly curved panels can be compared with their counterparts computed using the zig-zag theory (or layer-wise constant shear angle theory (LCST))-based FEM [30,[110][111][112][113][114][129][130][131][132][133][134][135][136][137].…”

“…both internal [114,[129][130][131][133][134][135][136] and external [132,137], have not been investigated like their flat and cylindrical panel counterparts. This is an extremely important area for further research.…”