Abstract
In this paper, the buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory are examined by using a refined shear deformation theory. This theory is based on the assumption that the transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies the conditions of zero shear stresses at the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In this analysis, the equations of motion for simply supported thick laminated rectangular plates are derived and obtained through the use of Hamilton’s principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. Numerical results of the present study are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling and free vibration behaviors of laminated composite plates.
Highlights
The most interesting feature of this theory is that it allows for parabolic distributions of transverse shear stresses across the plate thickness and satisfies zero shear stress conditions at the top and bottom surfaces of the plate without using shear correction factors
∂y w(x, y, z, t) = wb(x, y, t) + ws(x, y, t) where u and v are the mid-plane displacements of the plate in the x and y direction, respectively; wb and ws are the bending and shear components of transverse displacement, respectively, while f (z) represents shape functions determining the distribution of the transverse shear strains and stresses along the thickness and is given as the present model; the function f (z) is an hyperbolic shape function (Hyperbolic Shear Deformation Theory): f (z) = z 1 + 3π sech2 1 − 3π h tanh z (4b)
The Navier solutions for free vibrations of laminated composite plates are found by solving eigen value equations
Summary
Of these theories for the analysis of laminated composite plates is available in references [15,16,17,18,19]. The most interesting feature of this theory is that it does not require shear correction factors, and has strong similarities with the classical plate theory in some aspects such as governing equation, boundary conditions and moment expressions. A refined and simple theory of plates is presented and applied to the investigation of buckling and free vibration behavior of laminated composite plates. This theory is based on the assumption that the in-plane and transverse displacements consist of bending and shear components where the bending components do not contribute to shear forces, and likewise, the shear components do not contribute to bending moments. The results obtained by the present method are compared with solutions and results of the first-order and the other higher-order theories
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