纯剪切矩形薄板屈曲理论分析及有限元计算

Theoretical Analysis and Finite Element Computing for Rectangular Plates Bucking under Shear Load

分别采用能量法和有限元法两种分析方法,利用数学分析软件Matlab和有限元分析软件ANSYS,对简支矩形薄板受纯剪切的弹性失稳问题进行了详尽的分析求解。通过增加挠度函数的三角级数项,提高计算精度,增补和修正了参考文献中的临界应力K值。通过大量有限元计算和分析,拟合给出了K值表达式,并论述了将薄板在小挠度理论限定挠度值下的剪应力,作为临界剪应力的合理性。两种分析方法结果表明,有限元分析给出的K值拟合函数,在工程应用中具有更为普遍的实用意义和安全性。

By adopting the energy and finite-element methods with analysis software MATLAB and ANSYS, a detailed and complete solution process for bucking of simply supported rectangular elastic plates is provided. By increasing the triangular series for the deflection function, the amendments have been made to the K values given in references. Through finite element analysis, the expression of K value is fitted out. It is ascertained that the shear stress, taken as a critical shear stress, is reasonable according to the small deflection theory under limited plate deflection. The results of two analytical methods show that the fitting curve of K values used by finite element analysis has more comprehensive practical significance.