An efficient analytical model to evaluate the first two local buckling modes of finite cracked plate under tension

Abstract

The analytical approach is presented for both symmetric and anti-symmetric local buckling of the thin-plate in finite sizes and with a center crack under tension. An efficient classical solution based on the principle of minimum total potential energy was provided using only 2 and 1 degrees of freedom for symmetric and anti-symmetric modes and the linear elastic buckling loads are evaluated by the means of RayleighRitz method. In the pre-buckling state, a correction factor for the peak compressive stress in the finite cracked plates is defined with an empirical formula and used in the analytical solution of the buckling. To verify the analytical approach, a wide range of numerical results by aid of finite element method are provided herein and a comparison between theoretical results with the experimental work of other researchers has been done. Both numerical and experimental results accept the accuracy and validity of the presented analytical model. KeywordsCracked plate; tension; linear elastic buckling; RayleighRitz method.An efficient analytical model to evaluate the first two local buckling modes of finite cracked plate under tension INTRODUCTIONIn a cracked plate subjected to the tension load, perpendicular to the crack orientation, the developed compressive stress near the crack leads to buckling of crack edges. This phenomenon which can be called as local buckling of cracked plates under tension, has been studied by numerous researchers.The early works were the experimental studies such as the Air Force Flight Dynamics Laboratory (AFFDL) results in AFFDL- TR-65-146 (1965); Zielsdorff and Carlson (1972). Similarly, Dyshel (1990;1999;2002) has presented some variety of experimental results on the stability and fracture of plate with a central crack referred to as a non-classical problem. A.E. Seif and M.Z. Kabir / An efficient analytical model to evaluate the first two local buckling modes of finite cracked plate under tension

Peculiarities in the Material Design of Buckling Resistance for Tensioned Laminated Composite Panels with Elliptical Cut-Outs

“…However, it is impossible to characterize the influence of material properties on the buckling resistance with the use of simple analytical formulas. The above problems have also been discussed by Muc et al [ 37 , 38 , 39 ] and Seif and Kabir [ 34 ].…”

“…It demonstrates only that the stress concentration effects are not only the function of Young’s moduli but also, of the in-plane Kirchhoff’s modulus ( G xy ) and Poisson’s ratio ( ν xy ). The effects of the Poisson’s ratio on the buckling loads were investigated by Seif and Kabir [ 34 ].…”

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

“…Mittelstedt 11) presented an energy-based approach to obtain the local buckling loads of blade-stringer-stiffened and compressively loaded orthotropic composite plates. Seif and Kabir 12) developed an analytical approach for both symmetric and anti-symmetric local buckling of thin-plate in finite sizes and with a center crack under tension, the solution of which was based on the principle of minimum total potential energy. Recently, Galerkin method, which is a powerful numerical solution approach in solving differential equations, was used by Jaberzadeh and Azhari 13) to analyze the elastic and inelastic local buckling of flat rectangular plates with centerline boundary conditions under non-uniform inplane compression and shear stress.…”

Local Buckling of Steel Plates in Composite Structures under Combined Bending and Compression

“…(1). Seif and Kabir 13) used piecewise functions with minimum degrees of freedom to describe the buckling mode shapes of plate under tension, as given in Eq. 2, where w o is the maximum deflection.…”