Analytical solutions for buckling of rectangular plates under non-uniform biaxial compression or uniaxial compression with in-plane lateral restraint

An exact solution for stability analysis of orthotropic rectangular thin plate under biaxial nonlinear in-plane loading resting on Pasternak foundation

“…In general, to solve the governing equation by substituting Eqs. (7) and (8) in (6), the following equation can be obtained:…”

“…Bret and Devarakonda examined the buckling of rectangular plates with simply-supported boundary conditions at the edges which are subjected to sinusoidal loading, using Galerkin method [7]. The buckling of rectangular plates subjected to a variety of non-uniform loadings such as concentrated, local, sinusoidal, and other loadings was studied by Jana and Bhaskar [8,9]. Wang et al utilized the differential quadrature method to calculate the buckling load of rectangular plates which are subjected to nonuniform load at the edges.…”

Buckling and Vibration of Non-Homogeneous Rectangular Plates Subjected to Linearly Varying In-Plane Force

“…In many practical situations, particularly in the ship buildings and automotive industry these plates may be subjected to in-plane dynamic loads of different types, which may induce buckling, a phenomenon which is highly undesirable. In this regard, efforts have been made by researchers to analyses the effect of uniformly/non-uniformly distributed in-plane loads on the vibration characteristics of rectangular plates and prominent ones are reported in references [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Out of these, Leissa and Kang [6] employed the power series method to obtain the exact solutions for vibration and buckling of rectangular plates having two opposite edges simply supported and these are subjected to linearly varying in-plane stresses while the other two are clamped.…”

“…Wang et al [11] obtained the numerical results for the buckling and vibration of isotropic rectangular plate subjected to linearly varying in-plane stresses along two opposite simply supported edges while the other two are clamped using differential quadrature method. Jana and Bhaskar [12] used Galerkin's approach to present the analytical solutions for buckling of rectangular plates under non-uniform biaxial compression. Wang et al [13] analyzed the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides using differential quadrature method.…”

Buckling Behaviour of Carbon/Epoxy Laminated Composite Plates under Biaxial Loading

“…Results showed that the critical buckling load decreases when the plate is subjected to uniform loading on one edge and non-uniform loading on the opposite edge. Jana and Bhaskar [10,11] have examined the influence of different edge load distributions for the case of biaxial compression of a simply supported plate. Plate with lateral restraint is considered as a special case.…”