薄板弯曲问题差分计算的图式

The Scheme of the Difference Calculation in the Sheet Bending Problems

在薄板小挠度弯曲问题计算中,有限差分法是一种有效的数值解法,文献[1]给出了求解薄板小挠度弯曲问题的基本差分方程,文章[2]在文献[1]的基础上推算了具有自由边界的薄板弯曲问题等间距差分网格的具体差分计算图式。本文在文献[1]和文章[2]的基础上,推求了具有自由边界薄板弯曲问题不等间距网格的差分计算图式,以便在工程实际中直接利用上述图式列出差分方程,不必再利用边界条件来消除虚结点的挠度而得差分方程,简便实用。

Finite difference method is an effctive numerical method in computing small deflection ocurring in the sheet. The basic difference equations to solve the problems of small deflection in the sheet bending were given by Xu zhilun [1]. Based on Xu Zhilun' s [equations] Shen Xiangdong [2] gives the difference scheme on equal spaced gride in the qroblems of sheet bending nuder te condition of free boundary. According to Xu Zhilun [1] and Shen Xiangdong [2] the paper gives the difference scheme in solving the problems of nuequal-spced grids of sheet bending nuder the conditions of free boundary, so that the difference equations can be directly given by the scheme in the actual engineering practices. Thus, it is not necessary to use the boundary conditions in offsetting the virtual deflection nodals, the difference scheme in this way is simple and practicable.