Abstract: 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.

Key words: absolute nodal coordinate formulation;variable cross-section beam;dynamic model;kinematic behavior