Research On The Development Of Flexible Beams Finite Element Using Absolute Nodal Coordinate Formulation And Its Numerical Method

Flexible beam is an important structure in the aerospace and mechanical fields,also it is a typical object in the research of flexible multi-body system dynamics.The development of its dynamical model can give an important theoretical basis for the design and analysis of complex flexible multi-body system.With the development of science and technology,many systems are arising that have a large-scale rigid-body motion and large flexibility.Absolute Nodal Coordinate method(ANCF)is a non-incremental method,and can accurately describe the coupling dynamic behavior of the flexible system when it experiences a large range of motion and deformation.In this thesis,the flexible beam that experiences the large-scale motion and large deformation is the research object,the study on the development of flexible beam,the numerical solution method of differential and algebraic equations of multi-body system,and their application are investigated systematically with the use of ANCF method.The main innovative works are as follows:1.The improvement and verification of the two-dimensional ANCF shear beam(2D ANCF shear beam)element is studied.Since the high-frequency deformation coupling in 2D ANCF shear beam element,the numerical convergence accuracy is not accurate and the computational efficiency is expensive.Two kinds of improved ANCF shear beam finite elements are proposed via improving the calculation method of elastic force.The decoupling elastic force formulations are developed by combining the new curvature formulations and the elastic centerline method(ECM),and the high-frequency coupling on the beam deformations is eliminated.In the new elastic force formulation,two new exact curvature formulations are derived using differential geometry theory,which are displacement field curvature and rotation field curvature.These two formulations contain fully nonlinear term of deformation that can accurately describe the bending potential energy of the flexible beam.Finally,the proposed shear beam elements are valiadated using static,characteristic frequency and dynamics examples.2.The development and verification of ANCF beam with the angle coordinate.Two kinds of two-dimensional ANCF/CRBF beam(2D ANCF/CBRF euler beam)elements are developed.Based on the rigid cross-section assumption,the nonlinear constraint equation is imposed on the gradient vector at the nodes for the traditional 2D ANCF euler beam element and ANCF shear beam element respectively.This constraint equation is related to the rotation angle,thereby introduces the rotational angle coordinate.Then,the velocity transformation matrix from the time derivative of the gradient vector to the time derivative of the rotation angle is derived,and two new ANCF/CRBF beam elements are achieved using this transformation matrix.The new ANCF/CRBF shear beam reduces the degree of freedom of the system,and eliminates the high-frequency deformation mode of the cross-section.Finally,the new ANCF/CRBF euler beam are verified by static,characteristic frequency and dynamic examples.The development of the new ANCF/CRBF beam elements enriches the type of ANCF beam element.3.The implicit method for solving differential-algebraic equations of the multibody system is studied.A numerical algorithm(TLISMNI/Adams)based on high-order implicit Adams multi-step integration is proposed.The outer loop is used to solve the the equation of the differential motion,and the inner loop is used to solve the nonlinear constraint equation.The proposed algorithm has the ability of the variable step size,high order and numerical high frequencies elimination.The TLISMNI/Adams algorithm is verified systematically from multi aspects,such as the relative error,the initial step size,the number of corrector iterations,as well as the system stiffness with use of several multi-body system examples.4.The development of multibody system with hinge rolling and its dynamic analysis is studied.The finite element model of spacecraft solar panels and flexible track with hinge rolling structure are established respectively.The dynamic modeling and simulation were carried out by ANCF flexible beam element and TLISMNI/Adams algorithm.The new model can describe the inner deformation and strain changes of the rolling,also can be generated in the pre-processing stage,thereby helping to reduce the complexity and difficulty of the model.Several typical simluations of the spacecraft/tracked vehicle with a large-scale motion are used to verified the new model.