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 引用本文: 杜超凡, 章定国, 洪嘉振. 径向基点插值法在旋转柔性梁动力学中的应用[J]. 力学学报, 2015, 47(2): 279-288.
Du Chaofan, Zhang Dingguo, Hong Jiazhen. A MESHFREE METHOD BASED ON RADIAL POINT INTERPOLATION METHOD FOR THE DYNAMIC ANALYSIS OF ROTATING FLEXIBLE BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288.
 Citation: Du Chaofan, Zhang Dingguo, Hong Jiazhen. A MESHFREE METHOD BASED ON RADIAL POINT INTERPOLATION METHOD FOR THE DYNAMIC ANALYSIS OF ROTATING FLEXIBLE BEAMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288.

## A MESHFREE METHOD BASED ON RADIAL POINT INTERPOLATION METHOD FOR THE DYNAMIC ANALYSIS OF ROTATING FLEXIBLE BEAMS

• 摘要: 将无网格径向基点插值法用于旋转柔性梁的动力学分析. 利用无网格方法对柔性梁的变形场进行离散,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类拉格朗日方程推导得到系统刚柔耦合动力学方程. 将无网格径向基点插值法的仿真结果有限元法和假设模态法进行比较分析,说明假设模态法的局限性,并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性,并讨论了径向基形状参数的影响. 同时运用3 种求解系统动力学方程的方法:纽马克方法、4阶龙格库塔法、亚当姆斯预报校正法,并比较各方法的计算效率, 结果表明纽马克方法最快.

Abstract: A meshfree method based on radial point interpolation method (RPIM) is proposed for dynamic analysis of a rotating flexible beam. The RPIM is used to describe the deformation of the flexible beam. The longitudinal and transverse deformations of the beam are both considered, and the coupling term of the deformation which is caused by the transverse deformation is included in the longitudinal deformation of the beam. The rigid-flexible coupling dynamic equations of the system are derived via employing Lagrange's equations of the second kind. Simulation results of the RPIM are compared with those obtained by using finite element method (FEM) and assumed modes method and show the limitations of assumed modes method. It is demonstrated that the meshfree method as a discrete method of the flexible body can be extended in the field of multibody system dynamics. Meanwhile, the influence of the radial basis shape parameters is discussed. What's more, three integration methods (Newmark method, fourth-order Runge—Kutta method and Adams prediction correction method) are used to solve the dynamic equations, and it shows that the Newmark method is the fastest with the computational effciency.

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