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.

摘要 本文针对受拉伸载荷作用、含中心裂纹的有限尺寸薄板，提出了其对称与反对称局部屈曲的解析分析方法。基于最小总势能原理，针对对称与反对称屈曲模态分别采用仅含2个和1个自由度的高效经典解法，并通过瑞利-里兹法（Rayleigh-Ritz method）求解线弹性屈曲载荷。在屈曲前阶段，本文通过经验公式定义了有限尺寸含裂纹薄板的峰值压应力修正系数，并将其应用于屈曲解析解的求解中。为验证该解析方法，本文提供了大量基于有限元法（Finite Element Method, FEM）的数值计算结果，并将理论结果与其他研究者的实验工作进行了对比。数值与实验结果均证实了本文所提出解析模型的准确性与有效性。