Buckling of imperfect, anisotropic, ring-stiffened cylinders under combined loads

Abstract

The objective of this study is to develop an analysis to predict buckling loads of ring-stiffened anisotropic cylinders subject to axial compression, torsion, and internal pressure. This structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to an exact solution within each branch. Axisymmetric geometric imperfections are included. Buckling displacements are represented by a Fourier series in the circumferential coordinate and the finite-element method in the axial coordinate. Application of the Trefftz criterion to the second variation of the total potential energy leads to a nonlinear eigenvalue problem for the buckling load and mode. Results are presented for both unstiffened and ring-stiffened cylinders in the form of buckling interaction diagrams. Imperfections can cause an unexpected buckling mode in the ring web which would not occur for the perfect structure, and pressurization diminishes the benefit of adding rings to the unstiffened shell to increase the buckling load. The implementation of the analysis methodology into a structural sizing algorithm is discussed.

Governing equations of a stiffened laminated inhomogeneous conical shell

“…It will be shown that the homogeneous linear governing equations possess only the zero solution; that is, the two sets of solutions (23) are equivalent under the pertinent boundary and initial conditions. In so doing, we introduce a relation of the form r - (26) in terms of the difference set of the solutions. Using the straindisplacement equations (3) in Eq.…”

“…Using the straindisplacement equations (3) in Eq. (26) and integrating the equation by parts, one arrives at the rate of the form (27) In this equation, the quantities of the form…”

“…Langley 25 applied a dynamic stiffness technique to the vibration of the stiffened shell structures. Ley et al 26 examined the buckling of the stiffened Received Nov. 30, 1994; revision received Jan. 16,1996; accepted for publication May 11, 1996. Copyright © 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.…”

Combined load buckling for cylindrical shells based on a symplectic elasticity approach

“…Tafreshi (2006) and Vaziri and Estekanchi (2006) investigated buckling and post-buckling cylindrical shells subjected to pressure and axial compression by means of the finite-element method. By employing the semi-analytical finite-element method, Ley et al (1994) studied buckling loads of ring-stiffened anisotropic cylinders subjected to axial compression, torsion, and internal pressure.…”

Optimum Design of Stiffened Panels With Substiffeners

“…Other contributions to the field of buckling and postbuckling of panels include works by Weaver and his colleagues [5][6][7], Hilburger, et al [8], Baruch and Singer [9], the creators of the STAGS general purpose program, Almroth, Rankin, Brogan, and Riks [10][11][12], Arbocz and his colleagues [13][14][15], Stein [16], Leissa [17], Arnold and Parekh [18], Starnes, Knight, and Rouse [19], Spier [20,21], Khot and Bauld [22,23], Zhang and Matthews [24], Gurdal and his colleagues [25][26][27][28][29][30], Haftka and his colleagues [30][31][32], Librescu and his colleagues [33][34][35], Sridharan and his colleagues [36,37], Myers and Hyer [38], Nemeth [39], and Noor, Starnes, and Peters [40], to identify but a few in a vast literature.…”