三种六面体约束应力空间的相关性  

The Correlation of Three Kinds of Constrained Stress Spaces Suiting Hexahedron Element

作　　者：袁占斌[1] 聂玉峰[1] 周云[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2007年第2期229-236,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金重点项目(90405016).

摘　　要：弱平衡、正交性和能量协调条件是构造高性能杂交元的三种手段,三个条件同时满足是一种理想的应力设计方案,四边形单元CH(0-1)的应力是这种理想方案的一个代表。本文在剖析出三线性等参变换中众多参数的几何意义之后,研究了六面体情况下约束线性应力关于Wilson位移满足三种不同条件的应力设计方案,结论是对于一般网格,能量协调与正交性条件约束下的应力空间不一定相同,弱平衡条件不一定自然满足;只有当网格满足一定的条件时,这两种应力空间才相同;当采用折半剖分方案时,这两种约束下的应力模式相差高阶无穷小。数值试验结果也肯定了以上结论。Weak equilibrium condition （WEC）, orthogonality condition （OC） and energy compatibility condition （ECC） are used to construct high performance elements. An ideal approach is to suppose that stress satisfy these conditions simultaneously, such as the stress mode of CH （0-1） in 2-D case. After developing the geometrical explanation of the parameters used in the trilinear iso-parametric transform, the stress modes obtained by restricting the linear stress to satisfy the above-mentioned three conditions with Wilson bubbles are studied respectively. It is found that the three stress spaces are not the same ones generally except for some special meshes. For example, with parallelepiped or cube meshes being used, OC leads to the same stress space as ECC. Furthermore, if the bisection approach is used to re-mesh the grids, there is a higher order infinitesimal between the stress spaces constrained by OC and ECC. Finally some numerical results are given.

关 键 词：杂交元 能量协调条件 正交条件 弱平衡条件 WILSON BUBBLES 

分 类 号：O243[理学—计算数学]