scholarly journals Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal ◽  
N. S. Naik
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Bending Analysis

AbstractA trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

A Unified Shear Deformation Theory for the Bending of Isotropic, Functionally Graded, Laminated and Sandwich Beams and Plates

2017 ◽  
Vol 09 (01) ◽  
pp. 1750007 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Present Theory ◽  
Functionally Graded ◽  
Shear Stresses

In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy’s theory, but trigonometric, hyperbolic and exponential functions are first time used in the present displacement field. The present theory is accounted for an accurate distribution of transverse shear stresses through the thickness of plate, therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived from the principle of virtual work. Navier type closed-form solutions are obtained for simply supported boundary conditions. To verify the global response of the present theory it is applied for the bending of both one-dimensional (beams) and two-dimensional (plates) functionally graded, laminated composite and sandwich structures. The present results are compared with exact elasticity solution and other higher order shear deformation theories to verify the accuracy and efficiency of the present theory.

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.

On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation

1972 ◽  
Vol 39 (4) ◽  
pp. 1091-1097 ◽  
Author(s):  
S. B. Dong ◽  
F. K. W. Tso
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Plane Waves ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Correction Factors ◽  
Natural Oscillations ◽  
Orthotropic Shells

A constitutive relation for laminated orthotropic shells which includes transverse shear deformation is presented. This relation involves composite correction factors k112, k222 which are determined from an analysis of plane waves in a plate with the same layered construction. The range of applicability of the present theory and the quantitative effect of transverse shear deformation are evinced in a problem concerned with the natural oscillations of a three-layered freely supported cylinder.

On the Analysis and Fundamental Frequency of Slightly Curved Sandwich Beams With a Delamination

1995 ◽  
Author(s):  
John N. Rossettos
Keyword(s):  
Shear Deformation ◽  
Fundamental Frequency ◽  
Transverse Shear ◽  
Transverse Shear Deformation ◽  
Sandwich Beams ◽  
Combined Effects ◽  
High Modulus ◽  
Curved Beams ◽  
Initial Curvature ◽  
The Core

Abstract An analysis of the vibration of sandwich beams with small iinitial curvature and a delamination between the core and face sheet is presented. The combined effects of initial curvature, transverse shear deformation and extent of delamination are evaluated and discussed. It is shown that the sensitivity to delamination damage is greater for straight beams than for initially curved beams. It is also greater for high modulus cores (less shear deformation). Also the influence of shear deformation on the fundamental frequency becomes smaller as the curvature increases.

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