Research On Discontinuous Dynamics Modeling And Simulation For Multibody System Of Large Deformational Thin Shell Based On Corotational Formulation

Due to loads and other reasons,spacecrafts use lightweight shell-like structures to form complex multibody systems.Such as solar arrays,antennas,solar sails and so on.When such systems entered orbits,they often need to be deployed from the state of transport to work.The system will present the following three important features in this process: 1)The deployment process produces a large motion and large deformation response.The components are often made of light-weight thin plate material.Under loads and drive,the structure produces large rotation and small strain characteristics.It is a geometric nonlinear problem which is one of the large deformation problems.2)The bodies of systems contacts with each other.Because of the large-scale movement of thin plates,the thin plates often come in contact with each other in different places.Contact will cause sudden changes in the system state,and the structure will generate high-frequency vibrations.3)Large-scale discontinuous processes.Due to the existence of contact,the state variables of the system will produce mutations,and continuous dynamic processes will become discontinuous dynamic processes.In order to build a model of a large deformational thin plate multibody system,the corotational formulation is an accurate and efficient method.Different from the inertial coordinate method,the strain energy can be described by the nonlinear strain function.The co-rotating coordinate method can greatly improve the efficiency through relatively simple strain description in the local coordinate system.However,there are still problems when dealing with large deformational multibody systems.If there exists rotation parameters,it will lead to singularity problem.The local coordinate system will cause the calculation to produce fictitious rigid body rotation,local bending deformation is not accurate and so on.The contact collision phenomenon in discontinuous problems is often handled in node-to-surface and surface-to-surface contact discretization in commercial software for multibody dynamics,and the calculation results are often unreasonable at the boundaries of low-order elements.In addition to the difficulties mentioned above,theoretically,there are also inefficiencies in the numerical solution of the large-deformation thin plate multibody system discontinuity problems,including numerical difficulties in contact detection,step length control,iterative strategy,and so on.Because of the enormous numerical difficulty in solving the problem of discontinuous problems of large deformational thin plate multibody systems,an efficient multibody dynamic model of large deformational thin plates is established and a reasonable and effective contact model between thin plates can be established.This paper combines the corotational formulation with the theory of rotation-free plates,and improves the accuracy of the local coordinate system based on polar decomposition theory.This paper adopts two different separation methods of rigid body motion and deformation: 1)Using element independent corotational formulation,the idea of the method is to use a local coordinate system to separate the rigid body motion and use the relative position in the local coordinate system to extract the deformed motion.And in the local coordinate system,a new type of thin plate bending element without rotational degrees of freedom is proposed to further improve the accuracy of the model.2)The derivative of rigid body motion is used to separate the rigid body motion from the local deformation,and then the element strain energy is described in the local coordinate system.A simple and efficient dynamics equation is obtained.Under these theories,the constraint equation of the joint kinematics is established,and the modeling theory of the large deformational thin plate multibody system is proposed.This paper combines the corotational formulation with the rotation-free shell and is used for the first time in the multibody system modeling theory.This paper supplements the contact-discretization type of node-to-surface contact,and increases the edge-to-edge contact model for low-order cell contact to avoid over-penetration in contact collisions.The edge-to-edge contact in contact is verifies in detail.The augmented Lagrange method is used to calculate the contact force,which avoids the sensitivity to the penalty factor and improves the contact force accuracy.Applying this method to practical applications of sheet contact has achieved reasonable results.In order to further improve the computational efficiency,a global multibody dynamics simulation strategy for large deformational thin plates is proposed.An efficient local contact detection method based on triangular elements is proposed.Two different control methods are used for continuous and discontinuous processes.The integration step length is estimated accurately and the numerical integration iteration flow is optimized.Based on this method,a general calculation code for the discontinuous motion problem of the large deformational thin plate multibody system is developed,which also provides a research platform for follow-up research.Through the theories and calculation techniques proposed in this paper,it is possible to simulate the discontinuous dynamics problem of a large deformational thin plate multibody system with high accuracy and efficiency.