• Composites Research
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• v.23 no.3
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• pp.19-30
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• 2010

The present study describes a method for analytical solution to elastic field in structural elements of general symmetric laminated composite materials. The two dimensional plane stress elasticity problems under mixed boundary conditions are reduced to the solution of a single fourth order partial differential equation, expressed in terms of a single unknown function, called displacement potential function. In addition, all the components of stress and displacement are expressed in terms of the same displacement potential function, which makes the method suitable for any boundary conditions. The method is applied to obtain analytical solutions to two particular problems of structural elements consisting of an angle-ply laminate and a cross-ply laminate, respectively. Some numerical results are presented for both the problems with reference to the glass/epoxy composite. The results are highly accurate and reliable as all the boundary conditions including those in the critical regions of supports and loads are satisfied exactly. This verifies the method as a simple and reliable one as well as capable to obtain exact analytical solution to elastic field in structural elements of composite materials under mixed and any other boundary conditions.

• Journal of Korean Association for Spatial Structures
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• v.6 no.4 s.22
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• pp.81-92
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• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.