一种弹性薄板分析的非协调矩形单元

A non-conforming rectangular element for elastic thin plate analysis

为了简化传统的4结点弹性薄板矩形单元,提出了一种8结点矩形单元。根据虚功原理,推导出了这种单元的单元刚度矩阵及等效结点荷载的显式,并对其协调性和收敛性加以概括说明。利用Matlab强大的矩阵处理功能,编制了利用这种单元进行弹性薄板分析的计算机程序,并对编程加以简要说明。通过典型算例,将采用这种单元所得结果与传统4结点单元加以比较。结果表明:这种单元不但能大大简化传统的4结点单元,使单元结点位移分量数由原来的12降至8,相应的单元刚度矩阵由12×12降至8×8,而且仍具有较快的收敛速度;特别是当网格加密时,计算精度与前者基本相当;同时也具有节约计算机内存、编程容易等优点。

In order to simplify the conventional 4-node rectangular element for the analysis of elastic thin plate, a kind of 8-nodes rectangular element was introduced. According to the virtual work principle, its element stiffness matrix and equivalent node forces were formulated explicitly, and its compatibility and convergence were summarized briefly. By using the powerful matrix-operation functions of Matlab, a program was compiled for plate analysis with the element, and the programming procedures were simply described. A typical example was used to compare the new 8-nodes rectangular element with the conventional 4-nodes one. The results show that the former not only greatly simplifies the latter, reducing the number of nodal displacements from 12 to 8 and corresponding element stiffness matrix from 12 × 12 to 8 × 8, but also has fast rate of convergence; especially, with fine meshes, its accuracy can be almost equivalent to that of the latter, it can save the computer memory and the ease of programming. 1 tab, 2 figs, 7refs.