A New Kind Of Thin-walled Beam Element Based On Absolute Nodal Coordinate Formulation

Due to their outstanding features such as light weight and deformability,machines with flexible component can perform tasks under complex conditions.As a familiar flexible body,thin-walled beam has been applied extensively in various machines with flexible component.It is a valuable research work to establish a thin-walled beam model that can meet both the requirement of the engineering precision and save computing resources.The new thin-walled beam element proposed in this dissertation is to give out a numerical solving of slender thin-walled beam under large rotation and deformation problem.This thin-walled beam element is established base on absolute nodal coordinate formulation method.The research work is summarized as follows,1.A new kind of thin-walled beam element based on reduced parameter beam element of absolute nodal coordinate formulation is established in this dissertation.Lagrange interpolating polynomials are employed to describe the motions of thin-walled beam element.Introducing Kirchhoff thin plate theory and considering the geometric nonlinearity of the element,the element strain energy is derived based on Green-Lagrange strain tensor.The dynamic equation for thin-walled beam element is established using Lagrange's equation.2.A finite element program is implemented using MATLAB.The deformation and stress field of thin-walled beams with rectangular and L-shape sections are simulated.Due to the properties of absolute nodal coordinate formulation,the stiffness matrix in dynamic equation must be the function of nodal coordinates and the dynamic equation is nonlinear.To ensure the convergence,the implicit algorithm is used and an iterative procedure is designed.3.The accuracy of the new kind of thin-walled beam element is verified through a comparison with result from S4 R element from ABAQUS.The mechanical performance of the new element is illustrated.The main properties of the thin-walled beam elements proposed in this dissertation are as follows.(1)It can describe the distortion of the cross section of the large deformation beam;(2)For different type of load applied on thin-walled beam,appropriate Lagrange interpolation can be selected to give a result using less elements and meet the accuracy.