Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free sh...Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.展开更多
Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations ...Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.展开更多
Contact-impact processes occur at most cases in multibody systems. Sub-periods and sub-regional methods are frequently used recently, and different coordinates are introduced in both of the approaches. However, the su...Contact-impact processes occur at most cases in multibody systems. Sub-periods and sub-regional methods are frequently used recently, and different coordinates are introduced in both of the approaches. However, the sub-regional method seems to be more effective. Floating frame of reference formulation is widely used for contact treatment, which describes displacements by the rigid body motion and a small superposed deformation, and the coordinates depicting the deformation include finite element nodal coordinates and modal coordinates, the former deals with the contact/impact region, and the later describes the non-contact region. In this paper, free interface substructure method is used in modeling, and the dynamic equation of a single body is derived. Then, using the Lagrange equation of the first kind, the dynamic equations of multibody systems are established. Furthermore, contact-impact areas are treated through additional constraint equations and Lagrange multipliers. Using such approach, the number of system coordinates and the dimensions of mass matrix are significantly reduced with the modal truncation, therefore both of the efficiency and accuracy are guaranteed. Finite element method in the local contact region can deal with contact/impact between arbitrarily complex interfaces, whereas, additional contact constraints used in the nodal description region can avoid the customized parameters that are used in the continuous force model. C 2013 The Chinese Society of Theoretical and Applied Mechanics.[doi： 10.1063/2.1301307]展开更多
基金supported by the National Natural Science Foundation of China (Grants 11772188, 11132007)
文摘Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.
基金supported by the National Natural Science Foundation of China (11132007)
文摘Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.
基金supported by the National Natural Science Foundation of China(11132007)
文摘Contact-impact processes occur at most cases in multibody systems. Sub-periods and sub-regional methods are frequently used recently, and different coordinates are introduced in both of the approaches. However, the sub-regional method seems to be more effective. Floating frame of reference formulation is widely used for contact treatment, which describes displacements by the rigid body motion and a small superposed deformation, and the coordinates depicting the deformation include finite element nodal coordinates and modal coordinates, the former deals with the contact/impact region, and the later describes the non-contact region. In this paper, free interface substructure method is used in modeling, and the dynamic equation of a single body is derived. Then, using the Lagrange equation of the first kind, the dynamic equations of multibody systems are established. Furthermore, contact-impact areas are treated through additional constraint equations and Lagrange multipliers. Using such approach, the number of system coordinates and the dimensions of mass matrix are significantly reduced with the modal truncation, therefore both of the efficiency and accuracy are guaranteed. Finite element method in the local contact region can deal with contact/impact between arbitrarily complex interfaces, whereas, additional contact constraints used in the nodal description region can avoid the customized parameters that are used in the continuous force model. C 2013 The Chinese Society of Theoretical and Applied Mechanics.[doi： 10.1063/2.1301307]
