Investigation On The Buckling Of Rectangular Plates Subjected To Nonlinearly Distributed In-plane Loads Along Their Edges

The buckling behavior of thin rectangular elastic plates, widely used in engineering structures, has been given a lot of attention. And with the increasing usages of composite materials in the field of aerospace, construction, mechanical and marine engineering, the buckling of composite plates should be concerned by designers. However, most of the available literature on the buckling of rectangular plates due to compressive loads deals only with cases where such loads are uniformly or linearly distributed along the edges. There have been few previous researches on the case of nonlinearly distributed edge loads, even fewer for composite plates. Therefore, this thesis is to study such an issue based on the theory of elasticity. Firstly, a detailed solution for the in-plane stresses of the rectangular plates under nonlinearly distributed edge loads is given. Stress functions which satisfy all stress boundary conditions are provided for both same and different load distributions along opposite sides. The stress distributions within the plate for several loads cases are analyzed and compared with numerical results given by the differential quadrature (DQ) method and finite element method (FEM). The analytical solution given herein is proved to have the same precision as ones obtained by the two numerical methods. Then, buckling loads of the isotropic rectangular plates and symmetrically laminated rectangular plates are computed. Displacement functions are taken in the form of polynomials for isotropic plates which contain clamped edges and for symmetrically laminated plates. The effects of the aspect ratio, fiber orientation, number of plies and boundary conditions on the buckling loads are discussed. The obtained results agree well with numerical ones given by the DQ method and FEM, thus, verifies the validity and accuracy of the proposed method. In addition, it is found that the use of double sine (or cosine) series for simply supported symmetrically laminated plates having bending-twisting coupling in some literature overestimates the stiffness of plates thus provides larger buckling loads.