三角形单元协调与非协调位移的能量正交关系  

The Energy Orthogonal Relation Between Conforming and Non_Conforming Displacements of Triangular Element

作　　者：聂玉峰[1,2] 周天孝[1,2] 聂铁军[1,2] 

机构地区：[1]西北工业大学应用数学系 [2]中国航空计算技术研究所

出　　处：《应用数学和力学》1999年第6期619-624,共6页Applied Mathematics and Mechanics

摘　　要：基于组合稳定化变分原理，周天孝提出的组合杂交法是绝对收敛和稳定的，它给出了一种系统化的增强应力／应变方法，并建立了一簇低阶仿射等价的ｎ＿ｃｕｂｅ（ｎ＝２，３）单元·本文论证了单元上应力插值为线性，位移插值为协调线性部分和非协调二次部分之和的三角形组合杂交单元其协调部分与非协调部分的能量正交关系，进而得到此三角形单元刚度矩阵等同于协调的三角形线性元刚度矩阵。Based on the variational principle of combinative stability, combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower_order elements which are affine_equivalent to n _cube( n =2,3). The energy orthogonal relation between the conforming part and the non_conforming part of displacements interpolation functions in triangular element is given, in which the stress is interpolated by linear polynomials on each element, but the displacements are interpolated by the sum of conforming linear and non_conforming quadratic polynomials. Furthermore, this element is equivalent to the conforming triangular linear element, that is, the non_conforming parts have no contribution to enhanced strains.

关 键 词：能量正交 应力 位移 三角形单元协调 非协调位移 

分 类 号：O343[理学—固体力学] O242.21[理学—力学]