结构自动离散的一种新方法

本文采用等参元素中的几何插值方法,以少量的输入数据,自动生成全部元素的节点坐标;采用“棋盘”网格,使元素和节点的编号简单易行;同时,采用“波前法”解方程组,使编号的程序简化。 本方法具有输入数据少,改变网格容易,边界节点坐标足够准确等优点,已用于轴对称体二维网格及透平叶片的三维网格,结果满意。

A NEW METHOD OF FINITE ELEMENT STRUCTURE DISCRETIZATION

It is well known that automatic discretization of a structure in FEM contains:1. automatic generation of nodal point coordinates;2. numbering of nodal points;3. numbering of elements.In this paper, the concept of mapping in iso-parametric elements is adopted to generate the nodal point coordinates of the mesh. First of all, the structure is divided properly into several parts according to the profile of its cross-section. For each part an appropriate parent element is selected and its nodal locations in global coordinate system are chosen for interpolation. Then, by the following equationsthe coordinates of any nodal point in mesh may be obtained from its local coordinates（ξ ,η ,ζ ） given.In general, the numbering of nodal points is a troublesome task in programming. In consideration of the storage capacity of a computer, the Front Solver is adopted in solution of the simultaneous equations. The aim is twofold: first, the Front Solver itself requires much less storage than ordinary bandwidth solver; secondly, it is unnecessary to keep the order of nodal point numbers in continuous sequence, i. e. "dummy" nodal points are allowable which make the programming much easier and simpler.In numbering of nodal points and elements, the author presents a so-called "Chessboard" mesh in which the elements are arranged in a more regular form, so that the order of numbers of nodal points and elements can be exhibited more intuitively.This method has been applied in mesh generation of 2- and 3-dimensional structures such as disks and turbine blades, the results confirm adequate accuracy of the nodal point coordinates at the boundary and less effort in preparation of input data. Finally, when the mesh has to be altered or refined, all we need do is to change several controlling parameters.