基于本征梁理论的非线性大挠度柔性梁无网格动力学计算

摘要

本征梁方程是一种建立在Frenet标架上的,具有精确几何变形描述能力的梁的动力学控制方程,具有非线性阶数低、方程形式简洁的优点.提出了一种与本征梁方程相适应的无网格离散和相应的计算方法.针对本征梁方程的特点,引入配点型无网格方法对本征梁方程进行离散化处理,推导出了仅具有一阶导数和二阶非线性项的本征梁运动控制方程.采取此方法建立的大柔性梁在动力学计算过程中无需背景网格,避免了常规有限元建模所需的网格积分.利用这一特性,无需像传统非线性有限元分析那样在每一个计算时间步上进行的网格积分运算,简化了计算步骤.数值算例结果表明此方法具有很好的计算精度.%The intrinsic beam formula which is defined in the Frenet frame is one of the geometrically exact beam theories.This means that the deformation or the configuration of the beam can be described by the intrinsic beam theory exactly.By using the intrinsic beam theory,the equations of the beam can be expressed by lower order nonlinear terms with elegant form.This paper presents a meshless method for dynamic analysis of the large deflection flexible beam based on the intrinsic beam theory.The point interpolation meshless method is combined with the intrinsic beam formula to obtain the discretization equation of motion for the large deflection curved beam.Owing to the advantages of the intrinsic beam theory,the resulted equations are expressed in the first order partial differential form with second order nonlinear terms.With application of the presented method,the equation of motion of the large deflection flexible beam can be easily constructed without using integration with background cells,which the finite element always require.Thus,the present method does not need the integration process for every element during each time step.Finally,numerical example shows that the results predicted with the proposed method have good agreement with those generated using the commercial finite element software ABAQUS.