Nonlinear Dynamics Of Elastic Thin Rod With Finite Element Method And Its Application

Air assisted spinning is a process to use air directly or by twisting scheme of air assisted twisting.In the air assisted spinning process,airflow on the fiber bundle,namely dispersion and twisting,plays a decisive role.So it is necessary to study the law of motion and behavior of the fiber in the air flow field,and the numerical simulation method is essential to the study of the air assisted spinning and its improvement.This paper is a study of the movement in the process of spinning fiber in the flow,establishes physical and mathematical models suitable for fiber,fiber geometry in general stress state under large deformation of static and dynamic numerical simulation.Because the fiber has a very large length to diameter ratio,even if the whole fiber geometry deformation,the strain of the fiber material is not very large.In this paper,we assume that the material is still in a small strain state,and the fibers are considered as elastic thin rods.In this paper,the finite element method is used to solve the static and dynamic problems of nonlinear large deformation of elastic thin rod.The bar element finite element method is used in structural mechanics are used to solve the linear static problems of geometric rod structure of small deformation,nonlinear large deformation mechanics can not be applied to solve the elastic thin rod.In this paper,Solution method based on finite element method can apply to the numerical calculation of nonlinear static and dynamic problems of large deformation of elastic thin rod,so it can be said that in a certain sense of innovation.The work done in this paper can be divided into two parts: elastic thin rod statics and elastic rod dynamics.The main work done in the static part is as follows:1.Considered the axial force on the bending effect in bar element thin elastic rod whole large deformation.Based on hermite interpolation and parabolic interpolation and considering the rod unit based on tension compression,torsion and bending deformation the stiffness matrix of space bar element is derived.2.In order to determine the position of each node in the finite element of the rod element in the finite element of the elastic thin rod,The spatial position of each step of each unit is set up with the body coordinates,i.e.,the local coordinates.Using euler quaternion to represent the position of body coordinates in general coordinates,and the coordinate transformation relation between the angular displacement of the small Euler four element increment and the angular displacement increment in the Descartes coordinate system is derived.3.In the calculation method of load step by step,to the total displacement increment equation of the static equilibrium analysis of the system corresponding to each load increment step,an iterative acceleration method for solving the equations is proposed.The main work done by the dynamic part is as follows:1.In the dynamic problem of elastic thin rod,the elasticity and the mass of the elastic thin rod are separately treated.The treatment method of the elastic part is the same as the static method.In this paper,the quality of the micro segment of each unit is considered as a rigid body which is fixed to the joint section,and it is guaranteed that the length of each unit is small enough.2.According to the rigid rigid body dynamics in relative coordinates integral Euler dynamic equations of fixed-point rotation,and the rigid body movement theorem,is derived for a rigid body in general space motion with respect to the dynamic equations of global coordinates.3.In the dynamic problems of the whole process of the elastic thin rod,In this paper,the differential equations of motion for the finite element dynamic analysis of elastic thin rods are derived,The numerical solution of The explicit difference schemes and implicit difference schemes of the differential equations of motion are introduced.4.For the contact problem of elastic thin rod,it is treated as elastic contact constraint with large enough rigidity.In this paper,several numerical examples are calculated by using MATLAB and ANSYS software programming,which verify the feasibility and accuracy of this method.