边界元法在薄板稳定问题中的应用

 <正> 1.基本公式 弹性薄板的稳定方程为式中D是板的弯曲刚度;λ是临界载荷因子;为双Laplace算子;N_1,N_2,N_3为板的中而力。 首先确定基本解。即:在无穷域上某一点作用一个单位力时,双调和微分算子的解,即板的挠度。与板的挠度相对应的基本解对应于方程

APPLICATIONS OF BOUNDARY ELEMENT METHOD TO BUCKLING OF PLATES

The paper gives out boundary as well as area integral equations with which critical loadings of arbitrary-shaped thin elastic plates with smooth boundary or with boundaries containing a finite number of corner points under various kinds of boundary conditions can be obtained. Furthermore, by means of programming and calculations for a number of typical examples, especially, for the plates with free-edges, satisfactory results show that the method provided in this paper is applicable to the buckling analysis of the plates with the common boundary as well as the free boundary. Thus, the reliability and th e efficiency of the method are proved.