A hybrid-stress element based on Hamilton principle |
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Authors: | Cen Song Zhang Tao Chen-Feng Li Xiang-Rong Fu and Yu-Qiu Long |
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Institution: | Song Cen · Tao Zhang · Chen-Feng Li · Xiang-Rong Fu · Yu-Qiu Long Department of Engineering Mechanics,School of Aerospace,Tsinghua University,Beijing 100084,China AML,China Civil and Computational Engineering Centre,School of Engineering,Swansea University,Swansea SA2 8PP,UK College of Water Conservancy and Civil Engineering,China Agriculture University,Beijing 100083,China Department of Civil Engineering,China |
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Abstract: | A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the
new element is denoted as HH4-3β here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger–Reissner variational
principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from
3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly,
the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the
stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element
stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is
less than that in the Hellinger–Reissner variational principle, and no additional incompatible displacement modes are considered,
the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress
solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying
that the proposed technique is an effective way for developing simple finite element models with high performance. |
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Keywords: | Finite element · Hybrid-stress element · Hamilton variational principle · Post-processing schemes |
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