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

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.

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.

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.

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.

On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation

1972 ◽  
Vol 39 (4) ◽  
pp. 1091-1097 ◽  
Author(s):  
S. B. Dong ◽  
F. K. W. Tso
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Plane Waves ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Correction Factors ◽  
Natural Oscillations ◽  
Orthotropic Shells

A constitutive relation for laminated orthotropic shells which includes transverse shear deformation is presented. This relation involves composite correction factors k112, k222 which are determined from an analysis of plane waves in a plate with the same layered construction. The range of applicability of the present theory and the quantitative effect of transverse shear deformation are evinced in a problem concerned with the natural oscillations of a three-layered freely supported cylinder.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

2011 ◽  
Vol 44 (10) ◽  
pp. 1960-1966 ◽  
Author(s):  
Farhang Daneshmand ◽  
Esmaeal Ghavanloo ◽  
Marco Amabili
Keyword(s):  
Wave Propagation ◽  
Transverse Shear ◽  
Shear Deformations ◽  
Elastic Shells

A General Theory of Shells and the Complementary Potentials

1986 ◽  
Vol 53 (4) ◽  
pp. 881-885 ◽  
Author(s):  
G. Wempner
Keyword(s):  
Finite Elements ◽  
General Theory ◽  
Linear Function ◽  
Transverse Shear ◽  
Surface Deformation ◽  
Reference Surface ◽  
Shear Deformations ◽  
Theory Of Shells

This theory incorporates the attributes which are essential to the approximation of shells by finite elements. It is limited only by one assumption: Displacement is a linear function of distance along the normal to a reference surface. Deformation is decomposed into rotation and strain; the rotation carries elements of the reference surface to the same surface in any subsequent state. Transverse-shear deformations accommodate simple elements. The theory is couched in the potential Pv and in the complementary potential Pc; these have the property, Pv + Pc= 0 for all admissible (equilibrated) states. The theory is also cast in the complementary functional P¯c of stress and displacement, and the functional P¯v of displacement, strain and stress; P¯c and P¯v are akin to the functionals of Hellinger-Reissner and Hu-Washizu. These alternate functionals provide the means to develop various hybrid elements.

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