Buckling of Thick Orthotropic Cylindrical Shells Under Torsion

1999 ◽  
Vol 66 (1) ◽  
pp. 41-50 ◽  
Author(s):  
Y. S. Kim ◽  
G. A. Kardomateas ◽  
A. Zureick
Keyword(s):  
Critical Loads ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Wide Range ◽  
Classical Shell Theory ◽  
Torsional Loads ◽  
Elasticity Solutions ◽  
The Galerkin Method ◽  
Three Dimensional Elasticity

A three-dimensional elasticity solution to the problem of buckling of orthotropic cylindrical shells under torsion is presented. A mixed form of the Galerkin method with a series of Legendre polynomials in the thickness coordinate has been applied to solve the governing differential equations. The accuracy of existing shell theory solutions has been assessed through a comparison study for both isotropic and orthotropic cylinders. For isotropic cylinders the solutions based on the Donnell shell theory were found to predict nonconservative values for the critical loads. As the circumferential wave numbers increase, shell theory solutions provide more accurate values. For orthotropic cylinders, the classical shell theory predicts much higher critical loads for a relatively short and thick cylinder, while the shear deformation theories provide results reasonably close to the elasticity solutions. Detailed data are also presented for the critical torsional loads over a wide range of length ratios and radius ratios for isotropic, glass/epoxy, and graphite/epoxy cylinders.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Exact Elasticity Solution for Laminated Anisotropic Cylindrical Shells

1993 ◽  
Vol 60 (1) ◽  
pp. 41-47 ◽  
Author(s):  
K. Bhaskar ◽  
T. K. Varadan
Keyword(s):  
Shell Theory ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Elasticity Solution ◽  
Transverse Loading ◽  
Cylindrical Bending ◽  
Simply Supported ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
Anisotropic Cylindrical Shell

An exact three-dimensional elasticity solution is obtained for cylindrical bending of simply-supported laminated anisotropic cylindrical shell strips subjected to transverse loading. Displacements and stresses are presented for different angle-ply layups and radius-to-thickness ratios, so as to serve as useful benchmark results for the assessment of various two-dimensional shell theories. Finally, in the light of these results, the accuracy of the Love-type classical shell theory is examined.

Reissner’s New Mixed Variational Principle Applied to Laminated Cylindrical Shells

1992 ◽  
Vol 114 (1) ◽  
pp. 115-119 ◽  
Author(s):  
K. Bhaskar ◽  
T. K. Varadan
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Order Theory ◽  
Equilibrium Equations ◽  
Mixed Variational Principle ◽  
Elasticity Solutions ◽  
Transverse Stresses ◽  
Higher Order Theory ◽  
Displacement Approach ◽  
Three Dimensional Elasticity

Reissner’s new mixed variational theorem, which allows independent interpolation, through the thickness, of the three transverse stresses besides that of the three displacements, is applied here to derive a higher-order theory of laminated orthotropic cylindrical shells. The accuracy of the theory is verified by comparison with three-dimensional elasticity solutions. It is shown that Reissner’s principle does not directly lead to accurate transverse shear stress predictions, but requires the use of the equilibrium equations of three-dimensional elasticity as is common in the conventional displacement approach.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Analytical and 3D Finite Element Study of the Deflection of an Elastic Cantilever Bilayer Plate

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
M. Chekchaki ◽  
V. Lazarus ◽  
J. Frelat
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Mechanical Stresses ◽  
Linear Elastic ◽  
Wide Range ◽  
Finite Element Calculations ◽  
Analytical Formulas ◽  
Three Dimensional Elasticity

The mechanical system considered is a bilayer cantilever plate. The substrate and the film are linear elastic. The film is subjected to isotropic uniform prestresses due for instance to volume variation associated with cooling, heating, or drying. This loading yields deflection of the plate. We recall Stoney’s analytical formula linking the total mechanical stresses to this deflection. We also derive a relationship between the prestresses and the deflection. We relax Stoney’s assumption of very thin films. The analytical formulas are derived by assuming that the stress and curvature states are uniform and biaxial. To quantify the validity of these assumptions, finite element calculations of the three-dimensional elasticity problem are performed for a wide range of plate geometries, Young’s and Poisson’s moduli. One purpose is to help any user of the formulas to estimate their accuracy. In particular, we show that for very thin films, both formulas written either on the total mechanical stresses or on the prestresses, are equivalent and accurate. The error associated with the misfit between our theorical study and numerical results are also presented. For thicker films, the observed deflection is satisfactorily reproduced by the expression involving the prestresses and not the total mechanical stresses.

Methods of Analysis for Very Thick-Walled Cylindrical Shells

1975 ◽  
Vol 97 (1) ◽  
pp. 175-181 ◽  
Author(s):  
J. R. Vinson
Keyword(s):  
Boundary Conditions ◽  
Wall Thickness ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Explicit Solutions ◽  
Axially Symmetric ◽  
Various Boundary Conditions ◽  
First Approximation ◽  
Methods Of Analysis ◽  
Elasticity Solutions

Methods of analysis are presented for very thick-walled cylindrical, isotropic shells subjected to axially symmetric lateral and in-plane loads. These methods are developed for shells with ratios of wall thickness to mean radius as large as 0.5, as well as being applicable for thin classical shells which involve Love’s First Approximation. The present methods are elasticity solutions and employ no shell theory assumptions. Explicit solutions are presented for the shell subject to in-plane loads and laterally distributed loads which are constant or varying linearly axially for various boundary conditions at the ends.

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