Kinematic and Dynamic Simulation of Rigid and Flexible Systems with Fully Cartesian Coordinates

Abstract

Multibody systems are quite often a complex combination or assembly of mechanical elements with very different mechanical behavior: rigid or flexible, linear or non-linear, etc. Sometimes it can be very difficult to carry out an efficient dynamic simulation with a single software package.

In practical applications, some bodies are so small and rigid that flexibility effects can be neglected safely, with the benefit of an improved numerical efficiency. In some studies, other bodies —such as the main hull of a car or a spacecraft— shall be considered as flexible and, because of their complex geometry and relatively high stiffness, finite elements and modal superposition techniques are the most suitable way to consider small elastic deformations, superimposed to large rigid body rotations and displacements. Finally, some bodies —as spatial booms or other very slender appendages— can be very flexible and experiment large (elastic) deformations and —probably— other second order or coupling effects, that can not be captured with linear methods, such as the standard mode superposition; in this case, large rotation theory of beams and shell finite elements is probably the most suitable solution.

This paper will describe a simple and efficient methodology that, by the use of a common set of variables, allows a unified study of multibody systems, where the three types of mechanical behavior described before coexist. This formulation is independent of the system topology, being able to deal with open and closed loops, and even with variable or changing topologies. The position variables used to simulate all these mechanical behaviors (rigid and elastic bodies, small and large deformations), are Cartesian coordinates of points, Cartesian components of unit vectors, joint coordinates (optionally) and modal coefficients (optionally). The use of a common set of Cartesian and global variables makes very easy the task of formulating the constraint equations. The resulting formulation is then very simple, general and efficient. An example of a complex mechanical system will be presented.