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 Rayleigh-Ritz 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.