薄壳问题的一种数值解法

A Numerical Method for Solving Thin Shells Problems

本文直接从三维弹性力学微分方程出发,依据三维的Kelvin解,应用最小二乘法建立了三维虚边界无法解薄壳问题的一般方法。本方法的显著优点是:不论求解何种壳体问题,思想是不变的,均以三维的Kelvin解来建立方程,而勿需对不同几何形状的壳体采用不同的基本解。文中给出了数值算例,以作为本方法的应用。本文方法与边界元直接法相比,优点在于无需处理奇异积分,且系数阵是对称的;再者,本文方法思想简单,程序实现容易。

In the present paper, based on the differential equation of three-dimension theory of elasticity, in accordance with kelvin solution and least square method a numerical method of thin shells with three-dimension virtual boundary element is presented. The advantage of this method is that the different basic solution is not needed for solving the problems of thin shells with different geometry. For the application, a numerical example of shallow thin-shell is computed by this method. Comparing with the direct formulation of boundary elements method, the treatment of singular integration is rendered unnecessary and the coefficient matrix is a symmetrical one. In addition, the method is simple in ideas, and the programme is easy to carry out.