The Study Of The Displacement Model Of Planar Beam Element That Based On The Absolute Nodal Coordinate Formulation

The research background of this paper is based on absolute nodal coordinates of flexible multibody systems, for the problem of the deformation of a cantilever beam is difficult to quantitative analysis, absolute nodal coordinate method is used to analyze the dynamic response problem of large displacement of flexible beam systems. First, analyze the dynamic response displacement of the selected beam element in the vertical and horizontal coordinates. Then, based on the absolute nodal coordinates method, considering the geometric nonlinear and shear deformation of a cantilever beam to put forward a new beam element. Derive the mass matrix, stiffness matrix and generalized force array of a cantilever beam, to establish a dynamic model of two-dimensional planar flexible beam. Finally, program for the dynamic response of beam in the whole deformation process. In this paper, through the study of beam element displacement under the geometric nonlinear model that based on the absolute nodal coordinates method, to solve the dynamic equation of motion, and through the deformation analysis for flexible cantilever beam element, to research dynamics response that under the condition of big rotational displacement of the beam. Comparing the dynamic responses of the proposed displacement model and the other known displacement models, to assess whether the model is superior to obtain the deformation response of the beam under external force.In this article, on the basis of proposed researches, the displacement model is analyzed and compared, which based on absolute nodal coordinate method, as follows:(1) Respectively, analyze the two-dimensional shear deformation of beam element that based on the absolute nodal coordinate formulation, the linear finite element that based on the absolute nodal coordinate formulation, and a new locking-free shear deformable finite element based on absolute nodal coordinates, analyze the displacement models and the dynamic responses, then compare the results with each other.(2) Find out the solving method for the differential nonlinear equations. In this paper, the Maple and MATLAB methods are used to solve the equations.(3) Try to establish a new displacement mode, analyze the dynamic response, etc. Then compare the result with the above three models in the same numerical example, the main process is to analyze the effect of interpolation polynomial of the displacement mode.