A Simplified Displacement-Rotation Form for the Equations of Motion of Nonlinearly Elastic Shells of Revolution Undergoing Combined Bending and Torsion

1996 ◽  
Vol 63 (2) ◽  
pp. 539-542 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Equations Of Motion ◽  
Shell Of Revolution ◽  
Shells Of Revolution ◽  
Elastic Shells ◽  
Axisymmetric Bending ◽  
Nonlinearly Elastic

By appropriately defining two displacements and a rotation, it is shown that the equations of motion of a shell of revolution undergoing combined axisymmetric bending and torsion, in which the extensional strains and the rotations may be arbitrarily large, can be given a form in which there are three effective extensional strains and two effective bending strains, each of which is only linear or quadratic in the displacements and rotation.

The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques

1998 ◽  
Vol 65 (1) ◽  
pp. 99-106
Author(s):  
T. J. McDevitt ◽  
J. G. Simmonds
Keyword(s):  
Anisotropic Material ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Large Rotation ◽  
Elastic Tubes ◽  
Axisymmetric Bending ◽  
Combined Parameters ◽  
Nonlinearly Elastic

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

Problems of Nonlinear Multiple-Mode Vibrations of Thin Elastic Shells of Revolution

2000 ◽  
Author(s):  
Veniamin D. Kubenko ◽  
Piotr S. Kovalchuk
Keyword(s):  
Degrees Of Freedom ◽  
Asymptotic Methods ◽  
Nonlinear Resonance ◽  
Shells Of Revolution ◽  
Elastic Shells ◽  
Resonance Amplitude ◽  
Multiple Degrees Of Freedom ◽  
Free And Forced Vibrations ◽  
Multiple Mode ◽  
Averaged Equations

Abstract A method is suggested for the calculation of nonlinear free and forced vibrations of thin elastic shells of revolution, which are modeled as dynamic systems of multiple degrees of freedom. Cases are investigated in which the shells are characterized by two or more closely-spaced eigenfrequencies. Based on an analysis of averaged equations, obtained by making use of asymptotic methods of nonlinear mechanics, a number of new first integrals is obtained, which state a regular energy exchange among various modes of cylindrical shells under conditions of nonlinear resonance. Amplitude-frequency characteristics of multiple-mode vibrations are obtained for shells subjected to radial oscillating pressure.

Asymptotic shapes of inflated spheroidal nonlinearly elastic shells

1985 ◽  
Vol 97 (3) ◽  
pp. 541-549 ◽  
Author(s):  
Stuart S. Antman ◽  
M. Carme Calderer
Keyword(s):  
Hydrostatic Pressure ◽  
Asymptotic Behaviour ◽  
Large Volume ◽  
Large Parameter ◽  
Spherical Shells ◽  
Elastic Shells ◽  
Nonlinearly Elastic

In this paper we study the asymptotic behaviour of large axisymmetric deformations of closed axisymmetric nonlinearly elastic shells under internal hydrostatic pressure. These shells can suffer flexure, extension, and shear. Since there are spherical shells that can enclose an arbitrarily large volume at a finite pressure (cf. [1]), we take the volume rather than the pressure as the large parameter.

Fiber Trajectories on Shells of Revolution—An Engineering Approach

2011 ◽  
pp. 49-64
Author(s):  
Sotiris Koussios
Keyword(s):  
Coefficient Of Friction ◽  
Shell Of Revolution ◽  
Shells Of Revolution ◽  
Engineering Approach

Abstract This chapter outlines a method for mathematically describing fiber trajectories on a shell of revolution. After a short outline of the basic geometry of shells of revolution, the focus shifts to fiber trajectories and their characteristic metrics, angles, and vectors. Next, the chapter focuses on the determination of various kinds of curvatures that eventually lead to the derivation of (non-) geodesic fiber trajectories according to a predetermined coefficient of friction. It concludes with the analysis of nongeodesics on conical segments, annuli, and cylinders.

Nonaxisymmetric bulging of nonhollow elastic shells of revolution

1983 ◽  
Vol 19 (2) ◽  
pp. 131-137
Author(s):  
I. M. Bermus ◽  
L. S. Srubshchik
Keyword(s):  
Shells Of Revolution ◽  
Elastic Shells

Mixed functionals in the theory of nonlinearly elastic shells

2004 ◽  
Vol 40 (11) ◽  
pp. 1226-1262 ◽  
Author(s):  
V. A. Maksimyuk ◽  
I. S. Chernyshenko
Keyword(s):  
Elastic Shells ◽  
Nonlinearly Elastic
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