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.
Advances in the understanding of static large deflection, postbuckling, and nonlinear dynamic response by using the analytical method are summarized for laminated elastic plates. In the case of symmetric laminates, bending-stretching coupling vanishes. The classical nonlinear theory of orthotropic or anisotropic plates applies, and references are also presented for these plates. A nonlinear shear-deformable theory of generally laminated plates and a general method of solution are briefly reviewed for a wide class of boundary conditions. Several effects, which complicate the geometric nonlinear behavior of composite plates, discussed in this survey paper are: transverse shear and normal stresses, rotatory and in-plane inertia, initial in-plane edge forces, geometric imperfections, cutouts, and nonclassical boundary conditions.
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.
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