构造杂交应力单元的柔度矩阵H对角化方法

证明了杂交元柔度矩阵 H非奇异的充分必要条件是假设应力模式线性无关 ;以及等价应力模式形成相同的杂交元。在此基础上建立了假设应力模式的 Hilbert子空间 ,从而可以利用 Schmidt方法简单地得到等价的正交应力模式 ,实现了柔度矩阵 H对角化 ,使得杂交元形成过程中完全避免了繁杂的矩阵求逆运算 ,提高了杂交元分析的计算效率 ,特别在柔度矩阵不容易显式求逆的材料非线性分析中更具有实际意义

A method of flexibility matrix H diagonalization for constructing hybrid stress finite elements

Following two theorems are proved in this paper: (1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix H. (2) The equivalent assumed stress modes construct the same hybrid element stiffness matrix. Based on the theorems, the Hilbert subspace of the assumed stress modes is established, therefore, by Schmidt's method, the equivalent orthogonalized stress modes can be easy to obtain. Because flexibility matrix is diagonal with the orthogonal stress modes, the complex matrix inverse can be avoided and the hybrid efficiency is improved greatly. The more advantage can be found particularly in the analysis for nonlinear material behavior where the inverse for flexibility matrix cannot be obtained in the explicit form.