Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Free Vibration Analysis of Arches Using Higher-Order Mixed Curved Beam Elements

고차 혼합 곡선보 요소에 의한 아치의 자유진동해석

  • 박용국 (대구가톨릭대학교 기계자동차공학부) ;
  • 김진곤 (대구가톨릭대학교 기계자동차공학부)
  • Published : 2006.01.01
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Abstract

The purpose of this research work is to demonstrate a successful application of hybrid-mixed formulation and nodeless degrees of freedom in developing a very accurate in-plane curved beam element for free vibration analysis. To resolve the numerical difficulties due to the spurious constraints, the present element, based on the Hellinger-Reissner variational principle and considering the effect of shear deformation, employed consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees. The stress parameters were eliminated by the stationary condition, and the nodeless degrees were condensed by Guyan Reduction. Several numerical examples indicated that the property of the mass matrix as well as that of the stiffness matrix have a great effect on the numerical performance. The element with consistent mass matrix produced best results on convergence and accuracy in the numerical analysis of Eigenvalue problems. Also, the higher-order mixed curved beam element showed a superior numerical behavior for the free vibration analyses.

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References

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