大挠度缺陷旋转壳数值分析

借助于微分几何、矢量分析的工具,导出了小应变、大转动、大位移薄壳考虑初始几何缺陷的非线性几何方程,用双向样条试函数及离散最小二乘配点法给出了残值表达式,采用联合法求解,以降低初值要求,减少求逆运算及避免奇异出现,算例证明:本文方法未知量少、精度好、计算速度快、占用计算机内存少。

The Nonlinear Data Analysis of Rotational shell with Arbitrary Initial Geometrical Imperfections

In this paper, the nonlineer geometric equations for the thin shell of small strain, large rotation, large deflection are deduced by means of the differential geometry and vector analysis, considering arbitrary initial geometric imperfections. Using the least square collocation method and taking B-spling functions along orthogonal directions as trial functions of displacement, the residuals formulas are given. In order to reduce the demand of initial values, the calculations of inverse matrix and avoid the singular character of inverse matrix, the united method is adopted. The examples show that the method have advantages of less unknous, high precision, more rapid computation and less storage required in computer.