Transverse shear effect in a circumferentially cracked cylindrical shell

Abstract

Abstract.The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment for values of 0 < \2 = [12(1 -^)]'/4. a(Rh)'/2 < 10 and 0 < a/h < 10, where 2a, h, and R are, respectively, the crack length, the thickness, and the (mean) radius of the cylinder. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are also presented.

A cylindrical shell with an arbitrarily oriented crack

“…This was shown to be the case for the classical shell results (see, for example, the review article [7]). Recent studies using a Reissner-type shell theory [8J, [9] shows that similar agreement is also obtained between shell results and those given by the plane elasticity and a sixth order plate bending theory [10]- [13].…”

“…1. As in [11]- [13] the material is assumed to be specially orthotropic, that is the elastic constants defined by €11 = t-(a11-v l a 22) , €22 = t-(a 2 2-v 2 a l1) ,…”

“…The derivation of the differential equations for a specially orthotropic shallow shell based on a transverse shear theory [8], [9] may be found in [11]- [13] and will not be repeated in this paper •. Referring to Appendix A for notation and to [11]- [13] for details, in terms of a stress function ~ and the z-component of the displacement w the problem may be formulated as fo11<Ms:…”

“…Referring to Appendix A for notation and to [11]- [13] for details, in terms of a stress function ~ and the z-component of the displacement w the problem may be formulated as fo11<Ms:…”

Fracture mechanics evaluation of railroad tank cars containing circumferential cracks

“…The solution has the following accuracy: (i) better than 2% for & /n < 0.05 as compared to the results in Ref. 9, and (ii), the solution is increasingly conservative for 0 /n > 0.05.…”