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.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

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.

Thermoelastic bending analysis of laminated composite plates according to various shear deformation theories

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Atteshamuddin Shamshuddin Sayyad ◽  
Bharati Machhindra Shinde ◽  
Yuwaraj Marotrao Ghugal
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Plate Theory ◽  
Thermal Response ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates

AbstractThis study presents the thermoelastic analysis of laminated composite plates subjected to sinusoidal thermal load linearly varying across the thickness. Analytical solutions for thermal displacements and stresses are investigated by using a unified plate theory which includes different functions in terms of thickness coordinate to represent the effect of shear deformation. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Governing equations of equilibrium and associated boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates has been developed. Numerical results are presented to demonstrate the thermal response of the laminated composite plates.

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.

Thermal Bending of Thick Rectangular Plates of Bimodulus Composite Materials

1980 ◽  
Vol 22 (6) ◽  
pp. 297-304 ◽  
Author(s):  
J. N. Reddy ◽  
C. W. Ber ◽  
Y. S. Hsu ◽  
V. S. Reddy
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Fibre Direction ◽  
Thermal Bending ◽  
Good Agreement

Closed-form and finite-element solutions are presented for thermal bending and stretching of laminated composite plates. The material of each layer is assumed to be elastically and thermoelastically orthotropic and bimodular, i.e., having different properties depending upon whether the fibre-direction normal strain is tensile or compressive. The formulations are based on the thermoelastic version of the Whitney-Pagano laminated plate theory, which includes thickness shear deformations. Numerical results are obtained for deflections and neutral-surface positions associated with normal strains in both of the in-plane coordinates. The closed-form and finite-element results are found to be in good agreement.

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