On the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections

For the problem of axisymmetrically loaded shells of revolution with small elastic strains and arbitrarily large axial deflections, this paper suggests a group of state variable: radial displacement u, axial displacement w, angular, deflection of tangent in the meridian X, radial stress resultant H and meridional bending moment M_s, and derives a System of First-order Nonlinear Differential Equations under global coordinate system with these variables. The Principle of Minimum Potential Energy for the problem is obtained by means of weighted residual method, and its Generalized Variational Principle by means of identified Lagrange multiplier method.This paper also presents a Method of Variable-characteristic Nondimensionization with a scale of load parameter, which may efficientlky raise the probability of success for nonlinearity calculation. The obtained Nondimensional System of Differential Equations and Nondimensional Principle of Minimum Potential Energy could be taken as the theoretical basis for the numerical computation of axisymmetrical shells with arbitrarily large deflections.     

THE CREEP EFFECTS ON THE BUCKLING OF SHALLOW SHELLS

An analysis of the creep effects on the buckling of concreteshallow shells is presented in this paper.Based on the non-linear theory of thin elastic shells.it is found that forthose of the elliptical paraboloidal type.the upper cri-tical load of the load-deflection curve will decrease whilethe lower limit Will increase with time.As to the problemof local buckling of the shell.the critical load is de-pendent only upon the modulus of elasticity at the instantit occurs.     

Simple equations in terms of displacements for finite axisymmetric deflections of shells of revolution

A set of strain-displacement relations for finite axisymmetric deflections of shells of revolution is obtained in as simple form as is consistent with the basic assumptions of the first approximation shell theory. Corresponding field equations and boundary conditions are identified as the Euler-Lagrange equations of an associated variational problem. The equivalence to Reissner theory is established. Simplified versions of strain-displacement relations are analysed. The theoretical considerations are supported by various numerical examples.     

Comparisons of test and theory for nonsymmetric elastic-plastic buckling of shells of revolution

Experimental and analytical buckling pressures are presented for very carefully fabricated thin cylindrical shells with 45, 60 and 75° conical heads and for cylindrical shells with torispherical heads pierced by axisymmetric cylindrical nozzles of various thicknesses and diameters. Nonsymmetric buckling occurs at pressures for which some of the material is loading plastically in the neighborhoods of stress concentrations caused by meridional slope discontinuities. The buckling pressures for the cone-cylinder vessels are predicted within 2.6 per cent and for the pierced torispherical vessels within 4.4 per cent with use of BOSOR5, a computer program based on the finite difference energy method in which axisymmetric large deflections, nonlinear material properties and nonsymmetric bifurcation buckling are accounted for. The predicted buckling pressures of the pierced torispherical specimens are rather sensitive to details of the analytical model in the neighborhood of the juncture between the nozzle and the head. The buckling pressures of the cone-cylinder vessels can be accurately predicted by treatment of the wall material as elastic, enforcement of the full compatibility conditions at the juncture in the prebuckling analysis, and release of the rotation compatibility condition in the bifurcation (eigenvalue) analysis.     

Impact buckling of orthotropic shells of revolution with allowance for geometric nonlinearity

Scientific Research Institute of Mechanics, Gorky University, Gorky. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 43–50, May, 1990.     

Geometrical analysis of large elastic deflections of axially compressed cylindrical and conical shells

This paper presents an analysis of the post-buckling behaviour of isotropic cylindrical and conical shells under axial compression. The starting point of the paper is Lagrange's variational principle, the application of which consists in assuming a kinematically admissible strain and displacement field. The field is determined considering the geometry of quasi-isometric deformations of the shell after buckling. That permits solving the problem with no limitation on the magnitude of the displacements.     

Traveling waves vibrations and buckling of rotating anisotropic shells of revolution by finite elements

A quasi-analytical finite element procedure is developed which can obtain the frequency and buckling eigenvalues of prestressed rotating anisotropic shells of revolution. In addition to the usual centrifugal forces, the rotation effects treated also include the contribution of Coriolis forces. Furthermore, since a nonlinear version of Novoshilov's shell theory is employed to develop the element formulation, the effects of moderately large prestress deflection states can be handled. Due to the generality of solution procedure developed, the axisymmetric prestress states treated can also consist of torque loads. In order to illustrate the procedures capabilities, as well as the significant effects of Coriolis forces, torque prestress and material anisotropy, several numerical experiments are presented.     

Application of the extended Newton method to the creep analysis of shells of revolution

Summary The extended Newton method combined with the method of finite-differences is shown to be a powerful means to the steady-state creep analysis of shells of revolution. The creep theory of von Mises type and the power creep law are assumed. As numerical examples, a simply-supported circular cylindrical shell with open ends and a clamped spherical shell, subjected to internal pressure respectively, are analysed. The results of calculation of the cylindrical shell, in particular, are compared with those of semi-infinite sandwich shell obtained by Rabotnov.

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Übersicht Das erweiterte Newton-Verfahren bildet zusammen mit der Methode der finiten Differenzen ein wirksames Werkzeug zur Berechnung der Kriecheigenschaften von rotationssymmetrischen Schalen. Dabei wird eine Kriechtheorie nach v. Mises sowie ein Potenzgesetz für das Kriechen zugrunde gelegt. Als Beispiele werden eine einfach gelagerte kreiszylindrische Schale mit freien Rändern sowie eine eingespannte Kugelschale berechnet, die beide durch Innendruck belastet sind. Die Ergebnisse für die Zylinderschale werden mit den von Rabotnov erhaltenen Ergebnissen für eine halb-unendliche Sandwich-Schale verglichen.

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The present authors wish to express their gratitude to Professor Y. Ohashi of Nagoya University for his invaluable guidance and stimulating discussions.     

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear

The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.     

Finite axisymmetric deformation of shells of revolution with application to flexural buckling of circular plates

Summary A new theory is presented for shells of revolution undergoing axisymmetric arbitrarily large strain deformations. The material of the shell is assumed to be hyperelastic incompressible. The formulated theory is applied to analyse the flexural buckling of circular plates under uniform radial loads.

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Endliche achsensymmetrische Verformung von Rotationsschalen mit Anwendung auf das Beulen von Kreisplatten

Übersicht Eine neue Theorie zur Berechnung achsensymmetrischer Verformungen von Rotationsschalen unter Berücksichtigung beliebig großer Dehnungen wird angegeben. Das Material der Schale wird hyperelastisch und inkompressibel angenommen. Die Theorie wird zur Berechnung des Beulens von Kreisplatten unter gleichmäßiger Radialbelastung angewandt.

     

Calculation of shells with large rectangular holes in the presence of finite bending deflections

The stability of shells perforated by large holes has been investigated previously [1–6]. The results published in the cited papers lead to the conclusion that the problem of the stability of shells with large holes is in a stage of vigorous development. The application of standard numerical methods in these problems is impeded by the fact that they are incapable of refining the stress concentration and local stability in the vicinity of corners of the holes and give an approximate smoothed distribution pattern of the forces and torques. Methods of approximation of the solutions in terms of regular functions [2] are complicated by the poor convergence of the corresponding series near the edges of a hole.Structural Engineering Institute, St. Petersburg. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 41–48, February, 1994.     

The effect of variations in the creep exponent on the buckling of circular cylindrical shells

The senior author solved the problem of axially symmetrical creep buckling of thin circular cylindrical shells subjected to uniform axial compression. In that analysis the constitutive equation was a power law, and the exponent was taken to be equal to three. The purpose of this work was to extend the solution to a range of values of the creep exponent, n. To cope with the increasing algebraic complexity, a digital computer was employed in two ways: to generate the set of equations symbolically, and then to solve these equations. The computer programs were used to generate numerical solutions for the cases in which n was equal to 3, 5, 7 and 9. Two simple extrapolation techniques were then employed to obtain approximate solutions to the critical time problem for values of n up to 29.