• Title/Summary/Keyword: Hellinger-Reissner 변분이론

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3-Node Relaxed-Equiribrium Hybrid-Mixed Curved Beam Elements (완화된 평형조건을 만족하는 응력함수를 가지는 3절점 혼합 곡선보요소)

  • Kim, Jin-Gon
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.21 no.2
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    • pp.153-160
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    • 2008
  • In this study, we propose a new three-node hybrid-mixed curved beam element with the relaxed-equiribrium stress functions for static analysis. The proposed element considering shear deformation is based on the Hellinger-Reissner variational principle. The stress functions are carefully chosen from three important considerations: (i) all the kinematic deformation modes must be suppressed, and (ii) the spurious constraints must be removed in the limiting behaviors via the field-consistency, and (iii) the relaxed equilibrium conditions could be incorporated because it might be impossible to select the stress functions and parameters to fully satisfy both the equiribrium conditions and the suppression of kinematic deformation modes in the three-node curved beam hybrid-mixed formulation. Numerical examples confirm the superior and stable behavior of the proposed element regardless of slenderness ratio and curvature. Besides, the proposed element shows the outstanding performance in predicting the stress resultant distributions.

A New Higher-Order Hybrid-Mixed Element for Curved Beam Vibrations (곡선보의 자유진동해석을 위한 고차 혼합요소)

  • Kim Jin-Gon;Park Yong-Kuk
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.19 no.2 s.72
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    • pp.151-160
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    • 2006
  • In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and introduces additional nodeless degrees for displacement field interpolation in order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.