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.

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.

Untwist of Rotating Blades

1975 ◽  
Vol 97 (2) ◽  
pp. 180-187 ◽  
Author(s):  
M. Ohtsuka
Keyword(s):  
Cross Section ◽  
Virtual Work ◽  
Axial Flow ◽  
Arbitrary Cross Section ◽  
Principle Of Virtual Work ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Compressor Rotor ◽  
Flow Compressor ◽  
Good Agreement

This paper deals with the deformation and the stress of an axial flow compressor rotor blade under the loading of centrifugal forces. Coupled deformation of extension, bending, torsion and transverse shear of a pretwisted curved bar with arbitrary cross section is considered. Governing equations derived by means of the principle of virtual work are solved numerically by finite difference method. The warping functions used in the analysis were obtained by the use of finite element method. Measurement of the untwist angles and the stresses were carried out for the verification of the numerical analysis and they were found to be in good agreement.

Torsion of Pretwisted Beams Due to Axial Loading

1980 ◽  
Vol 47 (2) ◽  
pp. 393-397 ◽  
Author(s):  
D. H. Hodges
Keyword(s):  
Virtual Work ◽  
Axial Loading ◽  
Tensile Loading ◽  
Present Theory ◽  
Present Formulation ◽  
Principle Of Virtual Work ◽  
Torsional Deformation ◽  
Curvilinear Coordinate ◽  
Coupling Terms ◽  
Beam Approximation

The equations for static torsional deformation of a pretwisted beam under axial loading are obtained from the principle of virtual work. Theory appropriate for a curvilinear coordinate system is used, and warp is included in the analysis from the outset. The present formulation yields the expected result that a pretwisted beam of noncircular cross section will untwist under tensile loading. A slender-beam approximation of the present theory is offered, and the resulting torsion-extension coupling terms are similar but not identical to those in common use in analyses of rotating blades. Numerical results indicate that the effect is not negligible when the ratio of shear modulus to extension modulus is small.

Analytical solution for bending and buckling response of laminated non-homogeneous plates using a simplified-higher order theory

2017 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Ferruh Turan ◽  
Muhammed Fatih Başoğlu ◽  
Zihni Zerin
Keyword(s):  
Virtual Work ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Principle Of Virtual Work ◽  
Rotation Tensor ◽  
Buckling Loads ◽  
Simply Supported ◽  
Higher Order Theory ◽  
Bending Response

In this study, analytical solutions for the bending and buckling analysis of simply supported laminated non-homogeneous composite plates based on first and simplified-higher order theory are presented. The simplified-higher order theory assumes that the in-plane rotation tensor is constant through the thickness. The constitutive equations of these theories were obtained by using principle of virtual work. Numerical results for the bending response and critical buckling loads of cross-ply laminates are presented. The effect of non-homogeneity, lamination schemes, aspect ratio, side-to-thickness ratio and in-plane orthotropy ratio on the bending and buckling response were analysed. The obtained results are compared with available elasticity and higher order solutions in the literature. The comparison studies show that simplified-higher order theory can achieve the same accuracy of the existing higher order theory for non-homogeneous thin plate.

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.

scholarly journals Bending of functionally graded plates via a refined quasi-3D shear and normal deformation theory

2018 ◽  
Vol 5 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Asharf M. Zenkour ◽  
Rabab A. Alghanmi
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Three Dimensional ◽  
Present Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Normal Strain ◽  
Equilibrium Equations ◽  
Normal Deformation

Abstract Bending of functionally graded plate with two reverse simply supported edges is studied based upon a refined quasi three-dimensional (quasi-3D) shear and normal deformation theory using a third-order shape function. The present theory accounts for the distribution of transvers shear stresses that satisfies the free transverse shear stresses condition on the upper and lower surfaces of the plate. Therefore, the strain distribution does not include the unwanted influences of transverse shear correction factor. The effect of transverse normal strain is included. Unlike the traditional normal and shear deformation theories, the present theory have four unknowns only. The equilibrium equations are derived by using the principle of virtual work. The influence of material properties, aspect and side-to-thickness ratios, mechanical loads and inhomogeneity parameter are discussed. The efficiency and correctness of the present theory results are established by comparisons with available theories results.

REISSNER-MINDLIN EXTENSIONS OF KIRCHHOFF ELEMENTS FOR PLATE BENDING

2005 ◽  
Vol 02 (01) ◽  
pp. 127-147 ◽  
Author(s):  
FUMIO KIKUCHI ◽  
KEIZO ISHII ◽  
HIDEYUKI TAKAHASHI
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Plate Thickness ◽  
Special Technique ◽  
Test Problems ◽  
Element Approximation ◽  
Plate Bending ◽  
Wide Range ◽  
Shear Strains ◽  
Transverse Shear Strains

A method of extending various existing Kirchhoff elements to Reissner-Mindlin elements for plate bending is developed and tested. The essential idea is to use independent transverse shear strains and a special mixed formulation. The Nedelec edge element is effective for assuming the shear strains. Furthermore, the displacements are carefully constructed so that the strain-displacement relations are strictly satisfied for the transverse shear strains. We present our approach for displacement-based three-node triangular elements including both conforming and non-conforming ones as the base Kirchhoff elements. It is also possible to reduce the shear variables from the element degrees of freedom by means of a special technique called the beam element approximation. Numerical results are obtained for some fundamental test problems and are generally reasonable over wide range of plate thickness. In particular, it is observed that the tested elements actually reduce to the base Kirchhoff element in the thin plate range and are free from transverse shear locking.

Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler–Pasternak foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 169-190 ◽  
Author(s):  
AM Zenkour ◽  
AF Radwan
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Plate Thickness ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Soft Core ◽  
Sandwich Plates

Free vibration of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations using four-variable refined plate theory are presented. The theory accounts for the hyperbolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the dynamic version of the principle of virtual work. Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply, angle-ply, and soft core laminates or soft core sandwich plates resting on elastic foundations. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate, but also efficient in predicting the natural frequencies of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

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