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| A method of flexibility matrix H diagonalization for constructing hybrid stress finite elements |
| Revised:December 26, 2000 |
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| DOI：10.7511/jslx20024087 |
| KeyWord:hybrid stress finite element method,Hilbert stress subspace, flexibility matrix H diagonalization,nonlinear material behavior |
| Zhang Canhui Feng Wei Huang Qian |
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| Abstract: |
| 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. |
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