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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1166-1175.

• 论文 • 上一篇    下一篇

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

虞爱民1, 易明2   

  1. 1. Key Laboratory of Solid Mechanics of MOE, Tongji University, Shanghai 200092, P.R. China;
    2. Institute of Automobile, Tongji University, Shanghai 200092, P.R.China
  • 收稿日期:2002-12-10 修回日期:2004-06-11 出版日期:2004-10-18 发布日期:2004-10-18
  • 通讯作者: WU Jia-long,Original Member of Editorial Committee,AMM

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

YU Ai-min1, YI Ming 2   

  1. 1. Key Laboratory of Solid Mechanics of MOE, Tongji University, Shanghai 200092, P.R. China;
    2. Institute of Automobile, Tongji University, Shanghai 200092, P.R.China
  • Received:2002-12-10 Revised:2004-06-11 Online:2004-10-18 Published:2004-10-18

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摘要： A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

关键词: naturally curved and twisted beam, St.Venant torsional warping function, generalized coordinate for warping, the minimum potential energy principal, variational equation

Abstract: A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

Key words: naturally curved and twisted beam, St.Venant torsional warping function, generalized coordinate for warping, the minimum potential energy principal, variational equation

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