Modeling And Numerical Solution For Dynamic System Of Spatial Multi Rigid Bodies And Shell Structure With Large Deformation

The deformable mechanism-structure system where the thin-walled structure can be forced by the mechanism system has important applications in engineering, such as to design the morphing aircraft. However, the modeling and numerical solution for the dynamic response of this type of rigid-flexible mixture multibody system still exists problem. This paper focuses on the numerical solution of the dynamic responses of a class of system composed by spatial multi rigid bodies and shell structure with large deformation. Based on the numerical methods, modeling and numerical solution of three categories of issues are included:(1) spatial rigid multibody dynamic system;(2) geometrical nonlinear dynamics of shell structures with large deformation;(3) rigid-flexible coupling dynamics of a class of multi rigid bodies and structure mixture system.Firstly, the modified schemes of the physical orthogonal projection method for suppressing the constraint violation in solving spatial rigid multibody dynamics is proposed, where the mass matrix singular problem leading by using the quaternions to describe the orientation coordinates is avoided. The existence and uniqueness of the solution of spatial rigid multibody dynamic system with singular mass matrix are also proved.Secondly, the degenerated shell element for geometric nonlinear analysis based on the principle of virtual power is developed. The nonlinear shell element formulation derived in rate form is accurate under the shell assumptions, which enables the convergence for a large loading step or a large time step, and no shear locking appeared.Thirdly, the convergence accuracy analysis for the generalized composite implicit time integration method is proposed. An accuracy condition which enables the displacement, velocity and acceleration achieving second order simultaneously is presented and proved. The accuracy characteristics of time integration method under various frequencies are clarified. It is revealed that the Bathe composite implicit integration scheme is an optimal method in the generalized two sub-steps composite implicit time integration method family. The numerical damping decreasing phenomenon in high frequencies is also found.Fourthly, a computational method for solving dynamic response of geometric nonlinear shell structures is developed by embedding the composite implicit time integration scheme into the degenerated shell element. The developed approach not only can lead to a symmetrical stiffness matrix, but also can keep the energy and(angular) momentum conservation and/or decay, i.e., it is unconditionally stable. It can accurately and effectively solve the shell structures undergoing free vibration with large deformation and undergoing spatial large overall motion with large deformation, even by using large time step.Finally, an explicit-implicit time integration scheme for a class of rigid-flexible coupling dynamics of multi rigid bodies and structure(flexible body) mixture system is proposed. It can successfully and effectively solve the system dynamic responses of the spatial single rigid body with large deformable shell structure, the spatial multi rigid bodies with large deformable structure, and the subsystem contained spatial multi rigid bodies with large deformable shell structure(including large overall motion). This method keeps the energy conservation and/or decay, and is stable.The modeling and numerical solution proposed for solving spatial multi rigid bodies and large deformable shell structure can provide an effective numerical approach and analysis tool for deformable mechanism analysis and control strategies design for the deformable mechanism and structure.