中文摘要：

复杂变截面梁结构在运动过程中产生柔性变形对其运动精度与动力学性能有很大影响,因此建立准确的数学模型描述其柔性变形十分重要。基于绝对节点坐标法,考虑变截面梁单元边界特性,建立单元边界非线性函数关系,通过改变积分上下限,将其引入到单元质量矩阵、刚度矩阵的计算模型中。基于牛顿方程,建立变截面梁系统的柔体动力学模型。利用Matlab数值仿真,对不同单元数目、不同变截面参数的单摆梁进行动力学仿真分析。结果表明梁结构的刚度计算值与划分的单元数目相关,不同单元数目会影响系统仿真计算的效率和精度,使得运动变形仿真产生较大偏差。在保证梁体积相同的情况下,改变梁单元边界函数,可提高梁的刚度,减小其末端的运动变形,提高梁的动力学性能。在不影响梁刚度的前提下,通过改变梁截面参数,可有效降低梁的质量。

英文摘要：

The mathematical model of flexible deformation and its coupling effect with dynamic behavior are very important for the kinematic behavior of variable cross-section beams. The nonlinear functions are employed to describe the boundary features of variable cross-section beams. The model to calculate the mass matrix and the stiffness matrix of element of beam is proposed based on the absolute nodal coordinate formulation, in which upper and lower limits in the integral formula is considered as nonlinear function. The dynamic model of the variable cross-section beam is established by using Newton formulation. The dynamic behavior of a classic pendulums with different number of elements and different kinds of cross-sections are numerical investigation by using Matlab. The results show that the beam stiffness depends on the number of elements. Various numbers of elements could influence the efficiency and accuracy of numerical simulation as well as result in deviation to the simulation. The stiffness of beam increases and the deformation decreases with the decrease of element number of beam. The variation of boundary of beam may improve the stiffness and decrease its flexible deformation when the volume of beam is constant. In addition, it may light the weight of beam structures when the stiffness is constant.