A Special Finite Element for Static and Dynamic Study of Mechanical Systems under Large Motion, Part 1

Abstract

In this work the 3D dynamics of mechanical systems, structures and mechanisms, are studied. These systems are divided into so-called macro-elements. Because of large rotations involved by the motion of each macro-element the Euler-Rodrigues parameters are used to describe the global motion of the system. The paper presents in details the study of one macro-element behaviour using a special finite element type for beam system. The stiffness and mass matrices are found starting from the variational formulation of the movement equations expressed only in Euler-Rodrigues parameters. The most important aspect of the proposed approach is that the exact equations, written for the deformed configuration, are solved. Therefore an extremely accurate and very fast convergent method results. This method is non-incremental which means that in static analysis the accuracy does not depend on the number or of the load steps, in many cases only one load step is sufficient.