Flexible Multibody Dynamics

In this paper the evolution of a dynamic model for flexible multibody systems is presented. This model is based on an equivalent rigid-link system (ERLS) and, in the first formulation, has been exploited together with a FEM approach for the modeling of planar flexible-link mechanisms. Subsequently, the model has been linearized in order to be applied for control purposes and then it has been extended to the three-dimensional case. In the last years, a modal approach has been developed and the ERLS concept has been applied in order to formulate the dynamics of spatial flexible mechanisms with a component mode synthesis (CMS) technique.

Virtual Product Development (VPD) is a key enabler in CAE and depends upon accurate implementation of multibody dynamics. This paper discusses the formulation and implementation of a large-scale multibody dynamics simulation code.  In the presented formulation, the joint variables are used as the generalized coordinates and spatial algebra is used to formulate the system equations of motion.  Although the presented formulation utilizes the joint variables as the generalized coordinates, closed-loop mechanisms can be easily modeled using impeded constraints.  Baumgart stabilization approach is used to eliminate the constraint violations without using the expensive Newton-Raphson iterations.  Integrated rigid and flexible body dynamic simulation allows accurate prediction of structural loads, stress, and strains.  Both modal and nodal flexible body approaches are discussed in the paper.  In the presented formulation, the vehicle-terrain interaction can be easily modeled and integrated in the multibody code.

The paper presents the formulation of dynamic equations of motion of the closed-loop rigid-flexible multibody system using the Decoupled Natural Orthogonal Complement (DeNOC) matrices, introduced elsewhere for rigid multibody systems. The flexible link is discretized using assumed mode method to represent the link deflection. The closed-loop rigid-flexible system was analyzed by first cutting it at an appropriate joint to form an open-loop serial-chain system or a tree-type system. The opened joint was substituted with suitable constraint forces denoted with λ's, which are known as Lagrange multipliers. These multipliers were treated as external forces to the resulting open-loop subsystems. The Lagrange multipliers are then calculated at its subsystem level to reduce the complexity of overall formulation and hence the recursive and computationally efficient formulation for closed-loop rigid-flexible multibody systems is introduced which gives the analytical expressions for the matrices and vectors associated with the dynamics equations of motion. The formulation is illustrated with a rigid-flexible four-bar mechanism.

The paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non-linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.

In this paper, the design of a cam and follower mechanism 1 as a mean to simulate the action of a force is shown. The
mechanism causes a variation of the distance between two optical elements, and this is detected by an optoelectronic system which is used in the development of a load cell. As the cam profile can be designed according to the expected displacement, and the movement of the last one produces a variation in the distance between the transmitter and receiver of optical signal, it is pretended to establish the comprobation fundamentals prove that the operating principle applied in the construction of the load cell is correct, this is, the follower displacement must coincide –with a scaling factor- with the data obtained by the transducer

A technique for representing large finite rotations in terms of only three independent parameters, the conformal rotation vector, is described and applied to the finite element formulation of 3-D mechanisms problems. A beam finite element that takes into account large finite rotations and various types of rigid joints have been developed. Some test examples which demonstrate the applicability of the proposed technique are presented.

Passenger cars, transit buses, railroad vehicles, off-highway trucks, earth moving equipment and construction machinery contain structural and light-fabrications (SALF) components that are prone to excessive vibration due to rough terrains and work-cycle loads’ excitations. SALF components are typically modeled as flexible components in the multibody system allowing the analysts to predict elastic deformation and hence the stress levels under different loading conditions. Including SALF component in the multibody system typically generates closed-kinematic loops. This paper presents an approach for integrating SALF modeling capabilities as a flexible body in a general-purpose multibody dynamics solver that is based on joint-coordinates formulation with the ability to handle closed-kinematic loops. The spatial algebra notation is employed in deriving the spatial multibody dynamics equations of motion. The system kinematic topology matrix is used to project the Cartesian quantities into the joint subspace, leading to a condensed set of nonlinear equations with minimum number of generalized coordinates. The proposed flexible body formulation utilizes the component mode synthesis approach to reduce the large number of finite element degrees of freedom to a small set of generalized modal coordinates. The resulting reduced flexible body model has two main characteristics: the stiffness matrix is constant while the mass matrix depends on the elastic modal coordinates. A consistent set of pre-computed inertia shape integrals are identified and used to update the modal mass matrix at each time step. The implementation of the component mode synthesis approach in a closed-loop recursive multibody formulation is presented. The kinematic equations are modified to include the effect of the flexible body modal elastic coordinates. Also, modified constraint equations that include the effect of flexibility at the joint connections and the necessary details of the Jacobian matrix are presented. Baumgarte stabilization approach is used to stabilize the constraint equations without using iterative schemes. A sample results for flexible body impeded in a closed system will be presented to demonstrate the above mentioned approach.