基于能量法和有限元法的四边简支矩形薄板屈曲临界荷载分析
Buckling Critical Load Analysis of Simply Supported Rectangular Thin Plates on Four Sides Based on Energy Method and Finite Element Method

结构的稳定性能直接关系到安全性和经济性，尤其是近代以来高强材料和薄壁结构的使用，稳定问题显得更加重要。本文介绍了四边简支矩形薄板在纵向集中荷载作用下的压屈以及用能量法求临界荷载的方法，通过一个实例，采用能量法及有限元法分析了该结构的屈曲稳定性能。分别选取一项三角级数和两项三角级数作为挠度表达式代入能量法公式中进行计算，并讨论了选取两项三角级数作为挠度表达式时的取值方法。使用ABAQUS对矩形薄板进行了特征值计算，结果证明，数值计算结果略大于能量法的理论解，能量法的理论解更偏安全。
The stability performance of structures is directly related to safety and economy, especially with the use of high-strength materials and thin-walled structures in modern times, stability issues have become more important. This article introduces the buckling of simply supported rectangular thin plates under longitudinal concentrated loads and the method of calculating critical loads using the energy method. Through an example, the buckling stability performance of the structure is analyzed using the energy method and finite element method. One trigonometric series and two trigonometric series are selected as deflection expressions to be used in the energy method formula for calculation, and the method of selecting two trigonometric series as deflection expressions is discussed. Using ABAQUS to calculate the eigenvalues of rectangular thin plates, the results show that the numerical calculation results are slightly larger than the theoretical solution of the energy method, and the theoretical solution of the energy method is more biased towards safety.