Abstract
The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modey by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly. The numerical examples show that the method is effective.
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Contributed by HUANG Qian
Foundation items: the Aid Funds of Ministry of Education to Returnee from Foreign; the Funds of Ministry of Education to Backbone Teachers in Institutions of Higher Education; the Down Program of Shanghai Foundation of Education (99SG38); the Key Project of Shanghai Education Committee
Biography: ZHANG Can-hui (1967-), Doctor
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Can-hui, Z., Wei, F. & Qian, H. The stress subspace of hybrid stress element and the diagonalization method for flexibility matrixH . Appl Math Mech 23, 1263–1273 (2002). https://doi.org/10.1007/BF02439457
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DOI: https://doi.org/10.1007/BF02439457