Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method

Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges

“…The analysis of vibration and buckling of plates has been the subject of the research of structural and mechanical engineering [18][19][20][21][22][23][24][25][26]. Long list of references and detailed formulation on buckling and vibration of rectangular plates are given, for example, in Refs.…”

Accurate buckling loads of plates with different boundary conditions under arbitrary edge compression

“…9) in form σ[(2y/b) 2 À 1]. For this particular case it is possible to compare analytically obtained results with some interesting numerical solutions [13,14]. Four types of boundary conditions and eight different aspect ratios in range ϕ¼0.5-3 has been analyzed in this example.…”

“…In order to achieve that, some loads which are not so common in Notation a plate length (measured along the x-axis) A o , A n , A m Fourier-series coefficients for arbitrary external loadings f(y), f(x) b plate width (measured along the y-axis) B n , B 0 unknown group of coefficients defined by Eqs. (13) and (14) …”

“…(12) i,j,k,l positive integers l 1 , l 2 load length on the edges x ¼ 7a/2 and y¼ 7b/2 respectively K buckling coefficient N 1 , N 2 analytical solutions for direct stresses along x and y axis respectively P total applied edge load p x , p y load intensity in x and y direction respectively t thickness of the web T 3 analytical solution for shear stress in the plane x-y u, v displacements along the x and y directions respectively U strain energy due to bending V potential energy associated with the work done by external loads w out-of-plane deflection function W ij coefficients for deflection function α¼(λþ2μ)⧸μ constant defined in terms of Lame's parameters β m , β 0 unknown group of coefficients defined by Eqs. (13) and (14) γ x ¼l 1 /b patch-load ratio on the edges x ¼ 7 a/2 γ y ¼l 2 /a patch-load ratio on the edges y ¼ 7b/2 Δ civil engineering practice were used. Afterwards, previously checked stress functions, which were implemented in Ritz energy procedure in combination with suggested deflection functions, were controlled in numerous analyses of stability of plates with different boundary conditions.…”

The stability analysis of a rectangular plate supported at points of the corners

“…Research methods about the stability problem of thin elastic rectangular plates are abundant [1][2][3][4][5]. However, there aren't many studies of the exact solution for the stability problem of rectangular plates with complex boundary conditions.…”