Experimental investigation of cylindrical shells with an opening under an external pressure pulse

The results of experimental investigation of the deformation of a shell with a circular opening under a pulse of uniform external pressure are presented. A multifactor regression equation is derived on the basis of experimental data. The resultant equation is analyzed statistically. Relationships suitable for the practical computation of the residual deflection and critical pulse are given.Translated from Problemy Prochnosti, No. 2, pp. 68–71, February, 1990.     

Dynamic pulse buckling of composite shells subjected to external blast

Dynamic pulse buckling of woven E-Glass/Vinyl Ester and laminated E-Glass/Epoxy cylindrical shells subjected to uniform overpressure and asymmetric pressure pulse (side-on explosion) were examined. The solutions for the radial shell deformations were represented by Mathieu differential equations. The dynamic instability of the shells was determined from a Mathieu stability diagram. It was found that the stability of the shells depended on lay-up, aspect ratio as well as impulse distribution. The stable vibration response of the shells with side-on explosion compared well with finite element solutions using a Dynamic, Implicit analysis in ABAQUS Standard. First-ply failure of the woven E-Glass/Vinyl Ester shell with side-on explosion was predicted using a modified Hashin–Rotem failure criterion. It was shown that the thinner woven E-Glass/Vinyl Ester shells were more likely to fail by dynamic instability, whereas the thicker woven E-Glass/Vinyl Ester shells were more likely to fail by first-ply failure.     

Nonlinear behavior and buckling of cylindrical shells subjected to localized external pressure

Buckling loads and postbuckling behavior of cylindrical shells subjected to localized external pressure are considered. The modified extended Kantorovich method with path-tracing technique is applied to determine the buckling loads of the cylindrical shells. It is found that the load is dependent nonmonotonically on geometrical parameters of the area subjected to external pressure. Respective postbuckling shapes show correlation with the shapes corresponding to secondary bifurcation paths for the cases of a cylindrical shell under uniform external pressure and a cylindrical shell under uniform axial load.     

On the stability of thin-walled, corrugated, circular cylindrical shells under external pressure

Summary Thin-walled, corrugated, circular cylindrical shells under external pressure have repeatedly buckled at much lower values than has been predicted from simple orthotropic shell theory, where a flexural mode of buckling is assumed, in-plane to the cross-section of the tube. In the present paper it is shown that there exists always a combined, torsional–flexural, out-of-plane mode of buckling, frequently corresponding to an extremely low critical pressure. The need to design these tubes also with respect to torsional stiffness is emphasized, and a formula for the buckling pressure is proposed. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually.     

Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure

This article focuses on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. First, combining the method of separation of variables, perturbation method, and Fourier series expansion, an analytical method for the buckling analysis of cylindrical shells with axisymmetric thickness variation subjected to external pressure is established. The method is verified by comparing with the previous results. Then, the stepwise variable thickness of cylindrical shells is described exactly by the arc tangent function. Finally, using the presented method, a general formula for the critical buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure is derived. This general formula is compared and discussed with some empirical formulae in the current design standards. This study lays a theoretical foundation for the calculation of the buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Moreover, it provides a reference and guidance for the further revision of related standards.     

Dynamic buckling of functionally graded cylindrical thin shells under non-periodic impulsive loading

Summary.  This paper is concerned with the study of the amplitude of the steady-state vibration in a right finite cylinder made of a mixture consisting of three components: an elastic solid, a viscous fluid and a gas. An exponential decay estimate of Saint-Venant type in terms of the distance from one end of the cylinder is obtained from a first-order differential inequality for a cross-sectional area measure associated with the amplitude of the steady-state vibration. The decay constant depends on the excitation frequency, the constitutive coefficients and the first positive eigenvalue for the fixed membrane problem for the cross-sectional geometry. The paper also indicates how to extend the results to a semi-infinite cylinder. Received October 24, 2002 Published online: April 17, 2003     

Dynamic buckling of metal matrix composite plates and shells under cylindrical bending

A micro-to-macro analysis is offered to investigate the dynamic response and buckling of metal matrix composite cylindrical shells and plates under cylindrical bending. The micromechanical analysis relies on the elastic fibers and inelastic matrix material properties, and provides the bulk behavior of the metal matrix composite at room and elevated temperatures. The macromechanical analysis employs the classical and higher order plate theories in conjunction with a spatial finite difference and temporal Runge-Kutta integrations to provide the dynamic response of the structure. The effects of the metallic matrix inelasticity, material rate sensitivity, shear deformation, fiber orientation, and initial geometrical imperfection on the behavior of the metal matrix composite structures are studied.     

Elasticity, shell theory and finite element results for the buckling of long sandwich cylindrical shells under external pressure

The buckling of a sandwich cylindrical shell under uniform external hydrostatic pressure is studied in three ways. The simplifying assumption of a long shell is made (or, equivalently, ‘ring’ assumption), in which the buckling modes are assumed to be two-dimensional, i.e. no axial component of the displacement field, and no axial dependence of the radial and hoop displacement components. All constituent phases of the sandwich structure, i.e. the facings and the core, are assumed to be orthotropic. First, the structure is considered a three-dimensional (3D) elastic body, the corresponding problem is formulated and the solution is derived by solving a set of two linear homogeneous ordinary differential equations of the second-order in r (the radial coordinate), i.e. an eigenvalue problem for differential equations, with the external pressure, p the parameter/eigenvalue. A complication in the sandwich construction is due to the fact that the displacement field is continuous but has a slope discontinuity at the face-sheet/core interfaces, which necessitates imposing ‘internal’ boundary conditions at the face-sheet/core interfaces, as opposed to the traditional two-end-point boundary value problems. Second, the structure is considered a shell and shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are employed, one based only on the core, and the other based on an effective shear modulus that includes the face-sheets. Third, finite element results are generated by use of the ABAQUS finite element code. In this part, two types of elements are used: a shear deformable shell element and a solid 3D (brick) element. The results from all these three different approaches are compared.     

Tests on ring–stiffened cylindrical shells with external pressure

External pressure tests were conducted on thin multi–bay cylindrical shells to investigate the significance of out-of-roundness in relation to elastic and collapse behaviour.
Conclusions are drawn about the developing elastic deflection profiles of the shells during loading and suggestions are proposed for the prediction of the collapse mode and the collapse pressure.     

Buckling optimization of hybrid-fiber multilayer-sandwich cylindrical shells under external lateral pressure

This paper describes a method of analyzing the maximum buckling strength of hybrid-fiber multilayer-sandwich cylindrical shells under external lateral pressure with respect to fiber orientations and weighting factors. Formulae for optimizing these parameters are presented and conditions for the application of these formulae are discussed. A discriminant is derived for assessing whether the hybrid sandwich cylindrical shells for given different unidirectional composites should reach the extreme value of critical pressure.     

Delamination buckling of cylindrical shells under axial compression

A model is developed for the study of delamination buckling of axially loaded cylindrical shells. Delamination is assumed to exist before load application, it spans the entire circumference, and it lies on the contact surface of neighboring laminae. The mathematical model employs Donnell-type kinematic relations and linearly elastic material behavior. Furthermore, each lamina is assumed isotropic, and the emphasis is on studying the effect of delamination size and position on the critical load. Two sets of boundary conditions are used with the model: simply supported and clamped. The study reveals several important conclusions. Among them, one may list the following: (a) the critical load is primarily controlled by the position of the delamination from the reference surface, provided that the delamination is not very close to the boundaries; and (b) for long delaminations (relative to the cylinder length), the critical load is not appreciably affected by the boundary conditions.     

Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells

A thermal buckling analysis is presented for laminated cylindrical shells with surface mounted piezoelectric actuators under combined action of thermal and electrical loads. Derivations of the equations are based on the classical laminated shell theory, using the Sanders nonlinear kinematic relations. The analysis uses the Galerkin method to obtain closed form solutions for the buckling loads of shallow and nonshallow piezolaminated cylindrical shells. Temperature dependency of material properties is taken into account. Illustrative examples are presented to verify the accuracy of the proposed formulation. The effects of the various design parameters on thermal buckling loads are investigated.     

Dynamic response of pre-stressed fibre metal laminate (FML) circular cylindrical shells subjected to lateral pressure pulse loads

Dynamic response of fiber metal laminate cylindrical shells subjected to initial combined axial load and internal pressure were studied in this paper. First order shear deformation theory (FSDT) was utilized in the shell’s equilibrium equations and strain–displacement relations were based on Love’s first approximation theory. Equilibrium equations for buckling, free and forced vibration problems of the shell were solved using Galerkin method. The influences of FML parameters such as material properties lay up, Metal Volume Fraction (MVF), fiber orientation and initial stresses on dynamic response were investigated. The results were indicated that the FML lay up, has a significant effect on natural frequencies as well as transient dynamic response with respect to various values of MVF as well as pre-stress.