Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis

1987 ◽  
Vol 54 (3) ◽  
pp. 578-584 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Shear Deformation ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Normal Strain ◽  
Shells Of Revolution ◽  
Incompressible Hyperelastic Material ◽  
Large Elastic Deformation ◽  
Spherical Caps ◽  
Transition Points ◽  
Thick Shells

Large axisymmetric deformation of pressurized shells of revolution is studied. The governing equations include the effects of transverse normal strain and transverse shear deformation for shells composed of an incompressible, hyperelastic material. Asymptotic solutions to the equations are developed which are valid for moderately large strains. Application to Mooney-Rivlin clamped spherical caps reveals that, for large enough bending and stretching, the consequences of shear deformation include: (1) bending moments can decrease at the edge after the load passes a critical point; (2) even thick shells can behave as membranes; (3) transition points can occur in the shell which divide regions of shell-like behavior from regions of membrane-like behavior.

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.

Large Elastic Deformation of Shear Deformable Shells of Revolution: Numerical and Experimental Results

1988 ◽  
Vol 55 (3) ◽  
pp. 629-634 ◽  
Author(s):  
M. H. Kempski ◽  
L. A. Taber ◽  
Fong-Chin Su
Keyword(s):  
Numerical Solution ◽  
Elastic Deformation ◽  
Tensile Tests ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Strain Energy Density Function ◽  
High Inflation ◽  
Large Elastic Deformation ◽  
Shell Equations ◽  
Shear Deformable

Through an integrating matrix approach, a numerical solution is obtained to the equations governing large elastic deformation of a clamped circular cylinder due to internal pressure. The shell equations include the effects of large strains, thickness changes, and transverse shear deformation. The numerical solution is compared to results from an asymptotic analysis and from experiments on rubber cylinders. A specialized Rivlin-Saunders strain-energy density function is assumed for the rubber, with material constants determined from tensile tests and deformed cylinder profiles at a high inflation pressure.

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

A Refined Theory for Laminated Anisotropic, Cylindrical Shells

1974 ◽  
Vol 41 (2) ◽  
pp. 471-476 ◽  
Author(s):  
J. M. Whitney ◽  
C.-T. Sun
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Theory Of Elasticity ◽  
Small Radius ◽  
Refined Theory ◽  
Normal Strain ◽  
Governing Equations ◽  
Transverse Normal Strain ◽  
Anisotropic Cylindrical Shell ◽  
Good Agreement

A set of governing equations and boundary conditions are derived which describe the static deformation of a laminated anisotropic cylindrical shell. The theory includes both transverse shear deformation and transverse normal strain, as well as expansional strains. The validity of the theory is assessed by comparing solutions obtained from the shell theory to results obtained from exact theory of elasticity. Reasonably good agreement is observed and both shear deformation and transverse normal strain are shown to be of importance for shells having a relatively small radius-to-thickness ratio.

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