Motion formalism in flexible multibody dynamics

Abstract

A multibody system is characterized by two distinguishing features: system components undergo finite relative rotations and these components are connected by mechanical joints that impose restrictions on their relative motion. Being able to accurately simulate flexible multibody systems is crutial for predicting dynamic properties of a system. For the purpose of simulation and design, Finite Element Method (FEM) is becoming an integral part of the simulation process. In the thesis, we propose a faster and more accurate FEM of simulating flexible multibody systems that can meet the increasing demands of industry compared with traditional methods. The traditional process requires long computational time and is not sufficiently accurate. The reason is that the analysis of flexible multibody systems is complex because describing the motion of fundamental elements such as beams and shells requires both the displacement and rotation fields. Many researchers prefer to treat rotation and displacement fields separately to reduce the computation complexity, resulting in deficiencies of motion nature and the locking phenomenon although they all consider the co-rotational screw theory can best describe the body motion. In the thesis, we generalize the screw theory and describe all kinematic expressions in a novel manner-dual numbers for dealing with complex algebra to reduce the mathematical manipulations. Within the framework of multibody dynamics, the governing equations for beam structures based on Hamilton’s principle are nonlinear differential equations. The crucial difficulty is selecting a proper method of solving equations. We propose a generalized-α scheme to deal with the problem. Interpolation of displacements and motion are the heart of the FEM. The ”slerp interpolation of rotation” is generalized to the interpolation of motion for the reason of a requirement for convergence of the FEM by Zienkiewicz. Interestingly, the novel interpolation can be reduced to a linear interpolation if the strain is very small. This illustrates why many commercial softwares still prefer to use the classical polynomial interpolation. And then, the FEM is formulated and implemented to the flexible beam element undergoing a large displacement based on the generalized screw theory. A numerical example is also presented to validate the FEM implementation regarding the flexible beam motion.

Date of Award	2016
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology