Explicit Local Buckling Analysis of Rotationally Restrained Composite Plates Under Biaxial Loading

Abstract

A variational formulation of the Ritz method is used to establish an eigenvalue problem for the local buckling behavior of composite plates elastically restrained (R) along their four edges (the RRRR plates) and subjected to biaxial compression, and the explicit solution in terms of the rotational restraint stiffness (k) is presented. Based on the different boundary and loading conditions, the explicit local buckling solution for the rotationally restrained plates is simplified to several special cases (e.g. the SSSS, SSCC, CCSS, CCCC, SSRR, RRSS, CCRR, and RRCC plates) under biaxial compression (and further reduced to uniaxial compression) with a combination of simply-supported (S), clamped (C), and/or restrained (R) edge conditions. The deformation shape function is presented by using the unique harmonic functions in both the axes to account for the effect of elastic rotational restraint stiffness (k) along the four edges of the orthotropic plate. A parametric study is conducted to evaluate the influences of the loading ratio (α), the rotational restraint stiffness (k), the aspect ratio (γ), and the flexural-orthotropy parameters (α OR and β OR ) on the local buckling stress resultants of various rotationally restrained plates, and design plots with respect to these parameters are provided. The present explicit local buckling solution of the elastically restrained composite plates and the associated design plots can be employed to facilitate design analysis of composite structures (e.g. stiffened panels, thin-walled structures, and honeycomb cores).

Theoretical Study on Local Buckling of Steel Plate in Concrete-filled Tube Column under Axial Compression

“…In applying the variational formulation of this approach, Qiao and his research group [5][6][7][8] conducted extensive analyses to develop the explicit local buckling of composite plates with rotational restraint under uniaxial compression, uniform shear, and biaxial loading, and fully restrained under combined linearly varying axial and in-plane shear loadings. Kang and Leissa 9) proposed an exact buckling solution of plates subjected to linearly varying normal stresses and with two opposite edges simply supported, and the other two edges may be clamped, simply supported, free, or elastically supported.…”

Explicit local buckling analysis of rotationally restrained composite plates under uniaxial compression

“…(12) or (17)) is considered, Eqs. (21) and (22) are the solution for a particular plate with minimum buckling resistance, and they could be used to determine the critical aspect ratio and its corresponding critical buckling coefficient.…”

“…The explicit local buckling solutions of composite plates with the elastic restraints along the unloaded edges were formulated by Qiao and Shan [26], and the generic formulas for the rotational restraint stiffness (k) of different FRP shapes were developed. Most recently, the local buckling solution of the rotationally restrained composite plates (the RRRR plate) subjected to biaxial loading (including biaxial compression-compression and biaxial compression-tension) was obtained by Qiao and Shan [21].…”

Optimizing the buckling characteristics and weight of functionally graded circular plates using the multi-objective Pareto archived simulated annealing algorithm (PASA)

“…Brush and Almorth [1] have comprehensively analyzed the buckling problems of columns, plates and shells and studied various methods for formulating the governing nonlinear equilibrium equations in buckling. In addition, many researchers have provided analytical and numerical solution for study of the buckling behavior of circular and annular FG plates based on thin, first and higher order shear deformation theories [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”