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Structural Engineering and Mechanics
  Volume 19, Number 1, January10 2005 , pages 73-96
DOI: https://doi.org/10.12989/sem.2005.19.1.073
 


Exact dynamic element stiffness matrix of shear deformable non-symmetric curved beams subjected to initial axial force
Nam-Il, Kim and Moon-Young, Kim

 
Abstract
    For the spatially coupled free vibration analysis of shear deformable thin-walled non- symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact 14 ?14 dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS\' shell elements.
 
Key Words
    thin-walled; curved beam; dynamic stiffness matrix; free vibration; shear deformation.
 
Address
Department of Civil and Environmental Engineering, Sungkyunkwan University, Cheoncheon-Dong, Jangan-Ku, Suwon 440-746, S. Korea
 

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