Dynamic Simulation Of Geometric Nonlinear Spatial Beam

In aerospace, engineering designers must control the weight and volume ofstructures in order to reduce costs and difficulty of launch mission, while ensuring thedesired mechanical properties. Lightweight mechanisms and flexible retractablemechanisms are widely used in aerospace exploration missions to meet theserequirements, such as rod-shaped satellite antenna and coilable mast deploymentmechanism. Beam is a fundamental component of aerospace structure. Therefore, thedynamic modeling and analysis of flexible beam mechanisms in order to predict theirdynamic behavior is of great significance in engineering. Furthermore, beams made ofcomposite materials or with irregular shaped cross-section are widely used in aerospaceand automotive engineering, such as aircraft wings, etc. The elastic deformation theoryof composite beams differs from those of isotropic beams because of materialanisotropy. It is necessary to consider the out-plane warping of composite beams.Therefore, the investigation of the dynamic performance of the composite beams is ofimportant value in engineering application.In order to solve dynamic problems of spatial beam with large deformation andlarge rotational angle, geometric nonlinear dynamic model of spatial beam isestablished in this dissertation. Firstly, the absolute position coordinates of an arbitrarypoint on the central axis of the beam and three attitude angles of the cross-sectional areused to describe the position and attitude of cross-sectional and then the relationshipamong the strain, curvature, the position coordinates and the attitude angles isestablished. Based on the assumption that the tangential direction of axis of the beam isconsistent with normal direction of the cross-section, the number of attitude angles canbe reduced. According to the principle of virtual power, dynamic equations of motionof slender beam under large deformation are derived. The simulation results obtainedby geometrically nonlinear spatial beam method and engineering software LS-DYNA are compared in dynamic simulations of beam. In addition, the time cost of the presentformulation is compared with that of the software LS-DYNA. The efficiency of thegeometrically nonlinear spatial beam formulation is verified. Considering theout-of-plane warping deformation of the cross-section, the geometric nonlinearformulation is extended to composite thin-walled beam.The main contents of this paper are as follows:The first chapter introduces the engineering applications of beam structures,research status of beam theory and the analysis methods in beam modeling, and thenthe main objectives of this paper are proposed.The geometric nonlinear formulation of spatial beam is introduced in the secondchapter. Based on Euler-Bernoulli assumption for slender beam and the exactexpression of the axial strain and the curvature, and considering the stretch deformation,bending deformation and torsion deformation in the strain energy, dynamic equations ofmotion of a spatial beam are derived. Based on Hertz impact law, equations of motionof spatial beams with multiple contact-impact points are derived. A criterion for contactand separation is proposed. Finally, the numerical integration algorisms for dynamicsimulation are introduced.In chapter3, several numerical simulation examples are presented for verificationof the present formulation and dynamic analysis of elastic beams with largedeformation. Firstly, the deflection result of a static beam is compared with classicaltheoretical solution to verify the accuracy of the present formulation, and then thesimulation examples of a cantilevered planar beam and a cantilevered spatial beam arepresented. The comparison of the present results with those obtained by LS-DYNAverifies the efficiency of the geometric nonlinear formulation. Finally, a simulationexample of a flexible pendulum impacting a rigid cylinder is presented, which verifiesthe effectiveness of the dynamic formulation for solving contact-impact problems.In Chapter4, based on the basic assumptions of composite thin-walled beam andHamilton principle，and considering the out-of-plane warping deformation of thecross-section, the equations of motion of anisotropic thin-walled closed section beamare derived. Firstly, the influence of the layer angle on the modal frequencies of boxbeam is investigated, and then the simulation results of the composite thin-walled beamare compared with ANSYS software to verify the formulation. Finally, the equations ofmotion of geometric nonlinear composite thin-walled beam are derived and dynamicanalysis is carried out.In the last chapter, summary of all the work is made. The difficulties and challenges in beam modeling are presented and the prospect of future research isproposed.