Finite element approach for transient analysis of multibody systems

A three-dimensio nal, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequen- tial transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code. ANY recently proposed space structures are large and complex. To reduce packing volume, these structures may be delivered to orbit by the Space Shuttle and then de- ployed/assembled on orbit. To reduce weight, efficient designs of such systems tend to lead to flexible, low-frequency, and often joint-dominated structures. Consequently, interaction between rigid-body motion and structural deformation will likely occur. For efficient operation of structural systems re- quiring component articulation, it is desirable to maneuver components as rapidly as possible. However, operational speed is limited by excessive dynamic deformation if vibrations are not suppressed. In order to suppress excessive vibration responses, active controls may be utilized with the control design usually based on linear methods. This represents a sig- nificant design simplification since the articulation is governed by nonlinear equations. Moreover, another simplification is the use of reduced structural models. To assess the impact of these simplifications, analytical simulations are usually per- formed to examine design performance as well as stability. Simulation codes for multibody systems such as DADS, 1 DISCOS,2 and TREETOPS3 use an assumed mode approach to describe the structural deformations of components. In other words, this approach requires users to select a set of deformation modes to represent flexibility for each flexible component. In general, deformation modes are obtained by solving an eigenvalue problem using general finite element programs. This requires that the question of what boundary conditions of the components shall be specified be answered. A flexible bar with pin joint at its ends may behave like a cantilever beam or simply supported beam, depending on the total equivalent mass and constraints at its ends. Note, also, that the equivalent masses and constraints are time varying. A second question requiring an answer is how many modes are needed and/or which modes shall be kept to represent flex-