Structural Engineering and Mechanics

  • 제31권4호
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  • Pages.383-392
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  • 2009
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Convergence studies on static and dynamic analysis of beams by using the U-transformation method and finite difference method

  • Yang, Y. (School of Civil Engineering and Transportation, South China University of Technology) ;
  • Cai, M. (Department of Mechanics, Zhongshan University) ;
  • Liu, J.K. (Department of Mechanics, Zhongshan University)
  • 투고 : 2006.03.03
  • 심사 : 2009.01.31
  • 발행 : 2009.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

키워드

참고문헌

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  8. Liu, J.K., Yang, Y. and Cai, C.W. (2006), "Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method", J. Sound Vib., 289, 66-76 https://doi.org/10.1016/j.jsv.2005.01.036
  9. Liu, J.K., Yang, Y. and Cai, M. (2003), "Convergence study of the finite difference method: a new approach", Acta Mech. Sinica, 35(6), 757-760
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