On Influence Coefficients and Nonlinearity for Thin Shells of Revolution

1959 ◽  
Vol 26 (1) ◽  
pp. 69-72
Author(s):  
Eric Reissner
Keyword(s):  
Linear Theory ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Nonlinear Formulation ◽  
Elastic Shells ◽  
Edge Zone ◽  
Influence Coefficients ◽  
Rotationally Symmetric

Abstract The paper is concerned with a nonlinear formulation of the problem of rotationally symmetric deformations of thin elastic shells of revolution, which are acted upon by edge forces and moments. Determined are, in particular, nonlinear corrections to the known results of the linear theory, for edge displacements and rotations. The calculations are for cases for which thickness and curvature of the shell are such as to insure that stresses and deformations are effectively contained within a narrow edge zone of the shell.

On the Accuracy of Some Shell Solutions

1959 ◽  
Vol 26 (4) ◽  
pp. 577-583
Author(s):  
G. D. Galletly ◽  
J. R. M. Radok
Keyword(s):  
Negative Curvature ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence

Abstract R. B. Dingle’s method [1] for finding asymptotic solutions of ordinary differential equations of a type such as occur in the bending theory of thin shells of revolution is presented in outline. This method leads to the same results as R. E. Langer’s method [2], recently used for problems of this kind, and permits a simple analytical and less formal interpretation of the asymptotic treatment of such equations. A comparison is given of edge influence coefficients due to bending loads, obtained by use of these asymptotic solutions and numerical integration of the equilibrium equations, respectively. The particular shells investigated are of the open-crown, ellipsoidal, and negative-curvature toroidal types. The results indicate that the agreement between these solutions is satisfactory. In the presence of uniform pressure, the use of the membrane solutions for the determination of the particular integrals appears to lead to acceptable results in the case of ellipsoidal shells. However, in the case of toroidal shells, the membrane and the numerical solutions disagree significantly.

Saint-Venant’s Principle and the Torsion of Thin Shells of Revolution

1976 ◽  
Vol 43 (4) ◽  
pp. 663-667 ◽  
Author(s):  
C. O. Horgan ◽  
L. T. Wheeler
Keyword(s):  
Maximum Principle ◽  
Exponential Decay ◽  
Elliptic Equations ◽  
Second Order ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Quantitative Characterization ◽  
Elastic Shells ◽  
The Maximum Principle

This paper is concerned with obtaining stress estimates for the problem of axisymmetric torsion of thin elastic shells of revolution subject to self-equilibrated end loads. The results are obtained in the form of explicit pointwise stress bounds exhibiting an exponential decay with distance from the ends, thus supplying a quantitative characterization of Saint-Venant’s principle for this problem. In contrast to arguments using energy inequalities, here we apply a technique, recently developed by the authors, based on the maximum principle for second-order uniformly elliptic equations.

Influence Coefficients for Thin Smooth Shells of Revolution Subjected to Symmetric Loads

1962 ◽  
Vol 29 (2) ◽  
pp. 335-339 ◽  
Author(s):  
B. R. Baker ◽  
G. B. Cline
Keyword(s):  
Differential Equations ◽  
Asymptotic Integration ◽  
Asymptotic Solutions ◽  
Thin Shells ◽  
Uniform Thickness ◽  
Shells Of Revolution ◽  
Influence Coefficients ◽  
Independent Variable

The differential equations governing the deformation of shells of revolution of uniform thickness subjected to axisymmetric self-equilibrating edge loads are transformed into a form suitable for asymptotic integration. Asymptotic solutions are obtained for all sufficiently thin shells that possess a smooth meridian curve and that are spherical in the neighborhood of the apex. For design use, influence coefficients are derived and presented graphically as functions of the transformed independent variable ξ. The variation of ξ with the meridional tangent angle φ is given analytically and graphically for several common meridian curves—the parabola, the ellipse, and the sphere.

Maysel's formula generalized for piezoelectric vibrations - Application to thin shells of revolution

1996 ◽  
Author(s):  
Hans Irschik ◽  
Franz Ziegler ◽  
Hans Irschik ◽  
Franz Ziegler
Keyword(s):  
Thin Shells ◽  
Shells Of Revolution

scholarly journals Large Creep Deformations of Thin Shells of Revolution

1973 ◽  
Vol 39 (327) ◽  
pp. 3304-3312
Author(s):  
Shigeo TAKEZONO ◽  
Masafumi NAKATSUKASA ◽  
Masami USUI
Keyword(s):  
Thin Shells ◽  
Shells Of Revolution ◽  
Creep Deformations

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.

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