Research On The Method Of Dynamic Analysis For Flexible Multi-beams System Based On Rational Absolute Nodal Coordinate Formulation Finite Element

Absolute nodal coordinate formulation(ANCF) has become a hot-topic in the field of fexible multi-body system dynamics due to its advantage such as the brief expression of system motion equations and the mass matrices are constant real matrices. Recently, the similarity of mathematical form between ANCF and NURBS has been found so that the concept of rational absolute nodal coordinate formulation(RANCF) was proposed. This formulation can enhance the descriptive ability of element for structural configuration and improve the analytical accuracy. While RANCF and NURBS have good compatibility which can promote the integration of computer aided design(CAD) and computer aided analysis(CAA).This dissertaion researchs the methods of dynamic analysis for flexible multibeam system which based on RANCF. The characteristic of two different kinds of RANCF planar beam elements are discussed. Meanwhile, the influence of weight coefficients and rational shape functions on the configuration of elements is discussed. Furthermore, based on the defination expression of rational curves, the pioneering approach of RANCF mesh scheme is researched as well as the physic meaning of different schemes.With the help of continuum mechanics theory and structure mechanics theroy, two general methods to calculate the elastic force of elements are discussed based on which the explict expression of stiffness matrices and corresponding tangent stiffness matrices of these two RANCF elements are also given. Furthermore, the difference and relationship between these two methods are demonstrated by the means of mathematical derivation. The nonlinear static characteristics of RANCF beam elements are researched by utilizing stiffness matrix and tagent stiffness matrix as well as iterative algorithm. The numerical examples show that both of these two elements can convergent to the correct solution no matter it’s small deformation case or strong geometic nonlinear case. However, one-dimensional element has better convergence while the two-dimensional one suffers from locking problem and shows poor convergence as the result of different intepolation order between axis and transverse. In order to overcome shear locking, the selective integral procedu re is adopted which means using incomplete integral to calculate the energy of shear deformation. The small deformation solution shows this measure can obviously improve the behavior of element by the fact that the accuracy and convergence are all improved.In flexible multi-body dynamic analysis, the motion equation of RANCF beam elements and its setup process is discussed. In order to establish the dynamic equation, the treatment of constrain equations is also researched. There are two numerical examples to demenstrate the nonlinear dynamic characterise of these elements at last. Simailer to the static analysis, one-dimensional element has better convergence while the two-dimensional one is not so good which is close to the traditional FEM(Finite Element Method) by the reason of locking problem. However, the consuming time of RANCF is much less than FEM. It shows that RANCF elements have better precision and convergence when analysis the structure with initial configuration when compare RANCF elements with ANCF elements.