两个三角形元形函数空间的能量正交化

The orthogonalizations of two triangular elements' shape function spaces

关于二阶椭圆边值问题,本文对三角形上二次Lagrange元和Carey元的形函数空间进行了能量正交化.能量正交的形函数空间使单元刚度矩阵为对角块:Ke=Krc+Kh,其中Krc只和形函数空间的常应变有关,Kh由高阶模态决定.

In this paper,we have changed the shape function spaces of the quadric Lagrange triangular element and Carey element into energy -orthogonal ones respectively, such that the stiffness matrices are block diagonal ：Ke = Krc ＋ Kh, where Krc corresponds to constant strain of shape function spaces only, Kh is determinded by high modes. The two energy - orthogonal elements are proved to be convergent and equivalent to quadrie Lagrange triangular element and Carey element.