The large deflection of a rectangular orthotropic plate subjected to the combined action of edge compression and transverse load is investigated on the basis of von KBrmbn-type large-deflection equations. The cdgcs of the plate are assumed to be either all clamped or all simply supported. A solution is obtained in the form of double Fourier scries consisting of beam eigenfunctions for both transverse deflection and force function. The postbuckling of the plate is treated as a special case. Taking the first nine terms in each truncated series, numerical results in loaddcflection relations and bending moments are graphically presented for three types of fibre-reinforced composite plates with various aspect ratios. The three types of transverse load considered in the combined loading are central patch load, eccentric patch load and hydrostatic pressure. The present results for postbuckling and large deflection of isotropic and orthotropic plates are in good agreement with available data.
This paper is concerned with an analytical investigation of free flexural large-amplitude vibrations of rectangular composite plates. Solutions of the dynamic von Karman-type equations of these plates in conjunction with different boundary conditions are obtained by use of generalized double Fourier series and the method of harmonic balance. Numerical calculations for multimode vibrations of unsymmetric cross-ply and angle-ply plates having various material properties and lamination geometry were performed for all-clamped and all-simply supported stress-free edges. The present results indicate that the effect of coupling of vibrating modes on nonlinear frequencies is not appreciably significant for isotropic plates but considerably significant for composite plates, especially for clamped high-modulus laminates.
SummaryA double Fourier series solution is presented for the buckling of simply supported orthotropic and isotropic skew plates, subjected to in-plane compressive and shear edge loads. All the boundary conditions, including the vanishing of the normal bending moment along the edges, are satisfied. Numerical results, suitable for design purposes, are presented graphically for a number of independent parameters such as skew angle, ratio of flexural rigidities and aspect ratio. The results show that the buckling strength is substantially effected by the skew angle, and to a lesser extent, by the ratio of the flexural rigidities and aspect ratio. In contrast with positive shear edge loads, which tend to decrease the skew angle, negative shear edge loads appear to reduce the buckling strength of orthotropic and isotropic skew plates.
An analysis for the postbuckling behavior of unsymmetrically layered rectangular anisotropic plates is presented. Each layer is assumed to have arbitrary thickness, elastic properties, and orientation of orthotropic axes with respect to the plate axes. The governing nonlinear differential equations in the sense of von Karman are solved in conjunction with boundary conditions for clamped edges by use of the multiple Fourier method. In the case of simply supported edges, a solution based on the method is also obtained for unsymmetrical angle-ply plates. In the examples, a nine-term approximation to each series is used and load-deflection relations, bending moments, membrane forces are presented for clamped cross-ply and angle-ply and simply supported angle-ply plates with various aspect ratios. Numerical results obtained from the present solution are, in special cases, compared with available data.
An analysis is presented for the post-buckling behaviour of a simply supported, rectangular, orthotropic plate subjected to biaxial compression. The solution of von Karman-type large deflection equations of the plate satisfying the prescribed boundary conditions is expressed in the form of a double Fourier series for the transverse deflection and a double series for the stress function consisting of the appropriate beam functions. The effect of plate properties on stresses and deflections has been studied for three fibre-reinforced materials. Numerical results indicate good convergence of the present series solution and are compared with the available data. INTRODUCTION THIN PLATESin which resistances to mechanical actions are different in different directions have found wide applications in modern technology, particularly in aircraft construction. These materials such as fibre-reinforced epoxy resins, plywood, and deltawood show a great difference in elastic moduli and flexural rigidities in principal directions. Thus it is incorrect to investigate the structural behaviour of these materials by formulae intended for isotropic materials.Unlike simple columns, rectangular plates which are supported on all the four edges carry considerable load beyond their critical buckling load when the latter occurs in the elastic range. Thus it is of great importance to investigate the buckling of the plate by the theory of large deflections. The post-buckling behaviour of rectangular isotropic plates has been studied by a large number of workers. Exact solutions have been obtained by Coan (I)$ and Yamaki (2) (3) using Fourier series, by Stein (4) using the perturbation technique, and by Walker (5) using the method of Fourier series together with the perturbation technique about the critical buckling load. Approximate solutions have been obtained by Timoshenko (6), by Cox (7), and by Marguerre (8). For the case of orthotropic plate, an investigation has been done by Yusuff (9) modifying Coan's method but no details have been given for the effect of the plate material properties on the stresses and deflections. There exist a few investigations on the large deflection of rectangular orthotropic plates under transverse loading, but to the authors' knowledge not many numerical results can be found regarding the postbuckling behaviour of rectangular orthotropic plates subjected to edge loading.The object of this paper is therefore to present a detailed investigation of deflections and stresses of rectangular orthotropic plates in the post-buckling range. For static problems of orthotropic plates, the governing differential equations have been given by Leknitskii (10). A solution of these equations is, in this work, obtained by modifying the solution given by Sundara Raja Iyengar and Naqvi (XI) for isotropic plates. The edge compression is assumed to Journal Mechanical Engineering Science be uniformly distributed. This differs from the problem considered by Yusuff in which the edges have a constant in-plane displacement and the edge ...
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