任意边界下多跨梁弯曲计算及其工程应用

Bending calculation of multi-span beam under arbitrary boundary conditions and engineering application thereof

    摘要
  • 摘要:
      目的  为了快速寻找到甲板结构在轮印载荷下的最危险工况，
      方法  针对任意边界条件下多跨梁弯曲问题，首先利用改进的傅里叶级数方法（IFSM）描述多跨梁的位移函数，列出位移函数需满足的边界方程，并求解得到级数中各系数间的关系式；然后，基于哈密顿原理得到能量控制方程，采用伽辽金方法求解出满足边界条件的梁结构位移函数，通过算例，与有限元结果进行对比，验证此方法的正确性；最后，将该方法应用于轮印载荷下多跨梁最危险工况的计算中。
      结果  结果表明，所用方法的计算结果与有限元结果的误差小于0.05%，具有很好的精度。
      结论  相比有限元法，所用方法求解多跨梁最危险工况的速度得到极大提高，同时结合遗传算法，可获得更为精确的轮印载荷最危险工况的作用位置。

     

    Abstract:
      Objectives  To find the worst-case of a deck structure under patch loading quickly.
      Methods  For the bending of a multi-span beam under arbitrary boundary conditions, an Improved Fourier Series Method(IFSM)is used to describe the displacement functions of the multi-span beam, list the boundary equations that the displacement functions need to meet and solve such equations to obtain the relational expressions of coefficients; and then an energy control equation is obtained on the basis of the Hamilton principle, the displacement functions of beam structure satisfying the boundary conditions is acquired with the Galerkin method, and the functions are compared with the finite element results by means of example analysis. Finally, this method is applied to the calculation of the worst-case analysis of multi-span beam under patch loading.
      Results  The results show that the error between the result of this paper and the finite element analysis is less than 0.05%, indicating good accuracy.
      Conclusions  Compared with finite element method, the speed of solving the worst-case of the multi-span beam is greatly reduced by using this method, and a more accurate location to which the worst-case of patching loading is applied is obtained by combining the genetic algorithms.

     

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