On Finite Symmetrical Deflections of Thin Shells of Revolution

1969 ◽  
Vol 36 (2) ◽  
pp. 267-270 ◽  
Author(s):  
Eric Reissner
Keyword(s):  
Differential Equations ◽  
Nonlinear Theory ◽  
Transverse Shear ◽  
Shell Theory ◽  
Middle Surface ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Shear Deformations ◽  
Linear Shell Theory ◽  
Classical Subject

Recent simplifications of linear shell theory through consideration of transverse shear deformations and stress moments with axes normal to the shell middle surface suggest analogous approaches to the corresponding problem of nonlinear theory. As a first step in this direction consideration is given here to the classical subject of finite symmetrical deformations of shells of revolution. The principal new results of the present analysis concern the form of strain-displacement and compatibility differential equations.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Calculation of orthotropic plates for creep taking into account shear deformations

2018 ◽  
Vol 196 ◽  
pp. 01002 ◽  
Author(s):  
Anton Chepurnenko ◽  
Batyr Yazyev ◽  
Angelica Saibel
Keyword(s):  
Differential Equations ◽  
Transverse Shear ◽  
System Of Differential Equations ◽  
Orthotropic Plates ◽  
Shear Deformations ◽  
Tangential Stresses ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Basic Hypothesis

A system of differential equations is obtained for calculating the creep of orthotropic plates taking into account the deformations of the transverse shear. The basic hypothesis is a parabolic change in tangential stresses over the thickness of the plate. An example of the calculation is given for a GRP plate hinged on the contour under the action of a uniformly distributed load.

Orthotropic Cylindrical Shells Under Dynamic Loading

1979 ◽  
Vol 101 (2) ◽  
pp. 322-329 ◽  
Author(s):  
E. Mangrum ◽  
J. J. Burns
Keyword(s):  
Cylindrical Shell ◽  
Characteristic Equation ◽  
Transverse Shear ◽  
Constant Velocity ◽  
Shell Theory ◽  
Fourier Transforms ◽  
Axial Direction ◽  
Shear Deformations ◽  
Small Deflection ◽  
Partial Fractions

An orthotropic right cylindrical shell is analyzed when subjected to a discontinuous, finite length pressure load moving in the axial direction at constant velocity. The analysis utilizes linear, small deflection shell theory which includes transverse shear deformations, and external radial damping. The problem is solved using Fourier transforms. The inverse Fourier integrals are evaluated for the radial deflection, axial deflection and rotation by expanding the characteristic equation in partial fractions. The behavior of load velocity loci is studied for variations in material moduli and thickness to radius ratio. The deflection response is investigated.

Vibration of thick curved shells, with particular reference to turbine blades

1970 ◽  
Vol 5 (3) ◽  
pp. 200-206 ◽  
Author(s):  
S Ahmad ◽  
R G Anderson ◽  
O C Zienkiewicz
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Turbine Blades ◽  
Shell Element ◽  
Thin Shells ◽  
Thick Shell ◽  
Shear Deformations ◽  
Vibration Problems ◽  
Thin Shell Theory

The application of a new thick shell element is described with reference to vibration problems. The element is derived from the general isoparametric solid and therefore allows shear deformations to be included. It can take up highly distorted shapes and is useful in such studies as vibration of turbine blades for which it is superior to elements based on thin-shell theory. This element can also be used for thin shells with caution, excessive length/thickness ratios being avoided.

The shell theory including transverse shear deformations and thickness change

1997 ◽  
Vol 33 (6) ◽  
pp. 543-552
Author(s):  
H. Altenbach ◽  
G. I. L'vov ◽  
S. V. Lysenko
Keyword(s):  
Transverse Shear ◽  
Shell Theory ◽  
Shear Deformations ◽  
Thickness Change

Pure Bending, Stretching, and Twisting of Anisotropic Cylindrical Shells

1972 ◽  
Vol 39 (1) ◽  
pp. 148-154 ◽  
Author(s):  
E. Reissner ◽  
W. T. Tsai
Keyword(s):  
Recent Work ◽  
Cross Section ◽  
Transverse Shear ◽  
Constitutive Equations ◽  
Middle Surface ◽  
Transverse Shear Deformation ◽  
Thin Shells ◽  
Pure Bending ◽  
Explicit Formulas ◽  
Thin Walled

This paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The analysis, which generalizes recent work on the problem of torsion [1], is based on the differential equations of equilibrium and compatibility of thin shells in the form given by Gunther [2], together with constitutive equations given by the first-named author [3]. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an “ordinary” material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.

Analysis of Shells of Revolution Formed of Closed Box Section

1970 ◽  
Vol 92 (4) ◽  
pp. 818-826 ◽  
Author(s):  
Zenons Zudans ◽  
Frederick H. Gregory
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Differential Equations ◽  
Numerical Integration ◽  
Stiffness Matrix ◽  
Shell Theory ◽  
New Method ◽  
Analysis Method ◽  
Shells Of Revolution ◽  
Numerical Techniques

An exact analysis method is presented for shells of revolution formed of closed box sections. A consistent shell theory is used to develop the differential equations of the shell which in turn are solved by the use of numerical integration. A new method is introduced to generate a symmetrical stiffness matrix from the numerically obtained exact displacement functions. While the exact solution is generated at all times, the highly developed finite element numerical techniques are shown to be immediately applicable.

Elastic Response of a Thin Conical Shell to an Oblique Impact

1973 ◽  
Vol 40 (4) ◽  
pp. 1017-1022
Author(s):  
B. Albrecht ◽  
W. E. Baker ◽  
M. Valathur
Keyword(s):  
Differential Equations ◽  
Conical Shell ◽  
Shell Theory ◽  
Oblique Impact ◽  
Elastic Response ◽  
First Order ◽  
Strain Waves ◽  
Finite Difference Approximations ◽  
Linear Shell Theory ◽  
Truncated Conical Shell

Strain waves in a truncated conical shell generated by oblique impact of the small end of the shell are discussed. The analysis is based on the general first-order linear shell theory of Sanders with all pertinent variables expanded into Fourier series in circumferential direction, resulting in decoupled sets of ordinary differential equations. Finite-difference approximations to these differential equations are then solved by matrix techniques. Theoretical values compare well with experimental results for the angle of oblicity β = 0, 5, 10, and 15 deg, the range of the experimental work.

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
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