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.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

BENDING OF FGM PLATES BY A SIMPLIFIED FOUR-UNKNOWN SHEAR AND NORMAL DEFORMATIONS THEORY

2013 ◽  
Vol 05 (02) ◽  
pp. 1350020 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Present Theory ◽  
Normal Strain ◽  
Principle Of Virtual Work ◽  
Governing Equations ◽  
Shear Strains ◽  
Transverse Normal Strain ◽  
Transverse Shear Strains ◽  
Bending Response

The bending response of FGM plates is presented based upon a simplified shear and normal deformations theory. The present simplified theory is accounted for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free on the plate surfaces. The effect of transverse normal strain is also included. The number of unknown functions involved here is only four as against six in case of other shear and normal deformations theories. The principle of virtual work is employed to derive the governing equations. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all stresses are investigated through-the-thickness of the FGM plate.

On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints

1975 ◽  
Vol 42 (1) ◽  
pp. 127-132 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
General Problem ◽  
Transverse Shear ◽  
Beam Theory ◽  
Transverse Shear Deformation ◽  
Normal Strain ◽  
Rectangular Section ◽  
Surface Constraints ◽  
Transverse Normal Strain

The general problem of a beam of rectangular section with displacement components prescribed over portions of its top and bottom surfaces is considered. A beam theory which includes the effect of transverse normal strain (as well as the effect of transverse shear deformation) is developed and the advantages of applying this theory to the class of problems considered is examined by means of an example.

Impulsive Deformation of Mirsky-Herrmann’s Thick Cylindrical Shells by a Numerical Method

1973 ◽  
Vol 40 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
M. Ziv ◽  
M. Perl
Keyword(s):  
Shell Theory ◽  
Pulse Velocity ◽  
Normal Strain ◽  
Finite Difference Technique ◽  
Characteristics Method ◽  
Transverse Normal Stress ◽  
Infinite Cylindrical Shell ◽  
Shell Equations ◽  
Thickness Parameter ◽  
Transverse Normal Strain

The transient response of a thick elastic semi-infinite cylindrical shell subjected to impulsive step loads is obtained. This work presents solutions to two boundary-value problems. First, the shell is exposed to an axially step pulse velocity load while second, the pulse is applied radially to the shell. The influence of the transverse normal stress and the transverse normal strain on the deformation is being studied in great detail. The shell theory employed is based on the thick-shell equations derived by Mirsky and Herrmann, which comprise these transversal effects. These equations are solved by the characteristics method, while integration is carried out by the finite-difference technique. The results also present the influence of the thickness parameter (h/R) on the solution. Comparisons are made to solutions of other shell theories which neglect the transversal effects. Major conclusions show the existence of an important influence of the transverse normal strain on the deformation.

Refined hyperbolic shear deformation plate theory

2014 ◽  
Vol 229 (15) ◽  
pp. 2675-2686 ◽  
Author(s):  
K Nareen ◽  
RP Shimpi
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Dimensional Theory ◽  
Classical Plate Theory ◽  
Shear Deformation Plate Theory ◽  
Elasticity Solutions

The paper presents a novel shear deformation plate theory involving only two variables. Taking a cue from exact three-dimensional theory of elasticity solutions for a plate, hyperbolic functions are used for describing displacement variation across plate thickness. The theory involves only two governing equations, which are uncoupled for statics and are only inertially coupled for dynamics. The shear stress free surface conditions are satisfied. No shear correction factor is required. The theory is variationally consistent, has a strong similarity with classical plate theory, and is simple, yet accurate. Illustrative examples for free vibration and for static flexure demonstrate the effectiveness of the theory.

On Free Vibrations of an Embedded Anisotropic Spherical Shell

1997 ◽  
Vol 119 (4) ◽  
pp. 481-487 ◽  
Author(s):  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Spherical Shell ◽  
Elastic Medium ◽  
Shell Theory ◽  
Three Dimensional ◽  
Homogeneous Solution ◽  
Free Vibrations ◽  
Normal Strain ◽  
Auxiliary Variables ◽  
Transverse Normal Strain ◽  
Isotropic Spherical Shell

In this paper, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a six-mode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain. The separable homogeneous solution for displacements and stresses in a deep spherical shell is derived and two classes of vibrations are obtained by the introduction of five auxiliary variables. Numerical results are compared with those predicted by two simpler shell theories mentioned in the paper and those by three-dimensional elastic theory.

STRESS ANALYSIS OF THICK LAMINATED PLATES USING TRIGONOMETRIC SHEAR DEFORMATION THEORY

2013 ◽  
Vol 05 (01) ◽  
pp. 1350003 ◽  
Author(s):  
YUWARAJ M. GHUGAL ◽  
ATTESHAMUDDIN S. SAYYAD
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Strain Effect ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Deformation Effect ◽  
Line Load ◽  
Transverse Normal Strain

A trigonometric shear deformation theory (TSDT) taking into account transverse shear deformation effect as well as transverse normal strain effect is presented. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in thickness coordinates is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The results of displacements and stresses for static flexure of simply supported symmetric and anti-symmetric cross-ply laminated square plates subjected to parabolic load and line load are obtained. The results obtained by present theory are compared with those of classical, first-order and higher-order plate theories.

A Composite Plate Theory With Rotatory Inertia, Transverse Shear, and Normal Stress Effects

1991 ◽  
Vol 113 (2) ◽  
pp. 127-132 ◽  
Author(s):  
G. Z. Voyiadjis ◽  
P. D. Panera
Keyword(s):  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Composite Plates ◽  
Offshore Structures ◽  
Refined Theory ◽  
Normal Strain ◽  
Rotatory Inertia ◽  
Stress Effects ◽  
Transverse Normal Strain

A refined theory for the flexural motions of composite plates is presented. The theory incorporates rotatory inertia in addition to the influence of transverse normal strain, transverse normal stress, and transverse shear. This is of primary interest for the analysis of offshore structures as well as piping analysis. The classical wave propagation problem is used to test the proposed theory. The results indicate the influence of the transverse normal strain on the wave speed for large values of h/λ. The shear coefficient obtained from the proposed theory has a constant magnitude as opposed to the undetermined coefficient form in previous flexural motion formulations.

A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

1988 ◽  
Vol 55 (3) ◽  
pp. 611-617 ◽  
Author(s):  
R. Schmidt ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Shell Theory ◽  
Plate Theory ◽  
Small Strain ◽  
Present Theory ◽  
Shell Structures ◽  
Governing Equations ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Principle Of Virtual Displacements

A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Ka´rma´n type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

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