Investigation On Modeling Theory And Simulation Technique For Flexible Multi-body Systems With Large Deformation Beam Based On Element Recursive Method

With the development of aerospace science and technology,large deformation flexible beam structure in the spacecraft has been widely used,such as flexible space cable structure,coilable booms.This kind of flexible structure shows the characteristics of large displacement,large rotation and small strain.The existing multi-body dynamics theory based on small deformation assumption is no longer applicable.Therefore,it is necessary to carry out the research on the dynamic modeling theory and simulation technology of multi-body system for large deformation flexible beam system.It has important theoretical significance and good engineering value.The main problems in the numerical simulation of large deformation space beam dynamics are: singularity of rotation parameters;strain objectivity problem;path dependent problem.For the large numbers of flexible beam multi-body system,the main feature of high DOFs,discontinuous,variable topology make the dynamic numerical simulation face a huge calculation.The recursive method is a traditional multi-body dynamics modeling method,which combines the recursive concept with the floating frame to obtain the multi-body dynamics equation with the fewest DOFs composed of the joint coordinates and the deformation coordinates.It is widely used in the small deformation flexible multi-body system for the efficiency and precision of the method.But there are few researches on large deformation beam calculation.Based on previous research works,modeling theory and simulation technique is investigated for flexible multi-body systems with large deformation.This dissertation is funded by the National Natural Science Foundation of China(Grant No.’s 11132007),the main research and achievements are summarized as follows:1.Based on the hypothesis of Euler beam,Element Recursive Method for large deformation flexible Beam(ERMB)is proposed.ERMB is a method without singularity,strain invariance and path independent for space beam.ERMB integrates the recursive concept and the corotational frame,the recursion between adjacent bodies of the classical multi-body dynamics is extended to adjacent elements.The dynamics equation is composed with the element relative angular coordinates.Therefore,the method has following advantages:(a)Element strain and internal force are calculated in element corotational frame,the results will not change with the rigid rotation,which can effectively solve the strain objectivity problem of the large deformation space flexible beam.(b)The element attitude is described recursively by the relative angular of the nodes of the element,and ERMB can use the three parameters to describe rotation without singularity because the relative rotation of the elements is small.(c)The value of the relative angular in the corotational frame is close to zero,so the rotation parameter is similar to the linear relationship.Therefore,the relative rotation parameters are linearly interpolated in the element to obtain accurate results.Some typical examples are simulated by ERMB method and existing methods,and the results of different methods are compared.The results show that this method is strain objectivity without singularity for large deformation beam,and it has high precision and efficiency.2.ERMB is extended to complex topology configuration of large deformation beam multi-body system.The position constraint equation,the velocity constraint equation and the acceleration constraint equation of ERMB under different constraint forms are derived.So ERMB can be used to the multi-body system with closed loop and large deformation beam,and has a good procedural format.For the contact problem of the beams in multi-body system,the contact detection method of the point-line contact and the line-line contact between the beam elements of ERMB method is given.3.The solution format of ERMB with implicit generalized ? method is investigated to improve the numerical calculation efficiency.In traditional multi-body dynamics recursive method,the Jacobi array of dynamical equations is difficult to derive.While the difference form of Jacobian accuracy is poor and the computational efficiency is low,so explicit solution was used to solve the recursive dynamic equation usually.In this dissertation,the analysis Jacobian is derived recursively for implicit solution of ERMB dynamic equation.Based on the dynamic implicit algorithm,the static equation of multi-body system with large deformation beam is given by ERMB method.The results show that ERMB has following advantages:(a)Without path dependent in static mechanics;(b)A more accurate solution can be obtained with less DOFs;(c)Efficiency is greatly improved when the generalized ? method is used to solve the dynamic,thus the complex multi-body system dynamics and statics equations could be solved.4.ERMB is used to solve the large scaled dynamic problem of multi-body system with large deformation beam in engineering.In the case of coiled boom,it is difficult to simulate because of its complex mechanical feature such as large scaled,large deformation,contact and variable topology.The coiled static process and the deployment dynamic process of the coiled boom are simulated by ERMB.It shows that ERMB has the ability to deal with complex dynamics problems including multi-body systems with large deformation beams.