AbstractsEngineering

Use of Non-inertial Coordinates and Implicit Integration for Efficient Solution of Multibody Systems

by Ahmed K. Aboubakr




Institution: University of Illinois – Chicago
Department:
Year: 2015
Keywords: Non-inertial Coordinates; longitudinal train forces; coupler geometric nonlinearities; railroad vehicle dynamics; multibody systems. TLISMNI implicit numerical integration; multibody system differential /algebraic equations; sparse matrix implementation; Jacobian-free Newton-Krylov, stiff equations.
Record ID: 2058861
Full text PDF: http://hdl.handle.net/10027/19332


Abstract

Development of computational methods, formulations, and algorithms to study interconnected bodies that undergo large deformation, translational, and rotational displacements is the main focus for this thesis. This thesis discusses the use of the concept of non-inertial coordinates and implicit numerical integrations methods to solve stiff MBS differential/algebraic equations. Complex MBS examples that consist of rigid and flexible bodies are used as examples in order to demonstrate the use of these developed algorithms. One of the main contributions of this thesis is to employ the concept of the inertial and non-inertial coordinates to obtain an efficient solution for practical MBS applications. Inertial coordinates have generalized inertia forces associated with them, while the non-inertial coordinates have no generalized inertia forces. In order to avoid having a singular inertia matrix and/or high frequency oscillations, the second derivatives of the non-inertial coordinates are not used when formulating the system equations of motion in this study. In this case, the system coordinates are partitioned into two distinct sets; inertial and non-inertial coordinates. The use of the principle of virtual work leads to a coupled system of differential and algebraic equations expressed in terms of the inertial and non-inertial coordinates. The differential equations are used to determine the inertial accelerations which can be integrated to determine the inertial coordinates and velocities. The non-inertial coordinates are determined by using an iterative algorithm to solve a set of nonlinear algebraic force equations obtained using quasi-static equilibrium conditions. The non-inertial velocities are determined by solving these algebraic force equations at the velocity level. The non-inertial coordinates and velocities enter into the formulation of the generalized forces associated with the inertial coordinates. Using the concept of non-inertial coordinates and the resulting differential/algebraic equations obtained in this thesis leads to significant reduction in the numbers of state equations, system inertial coordinates, and constraint equations; and allows avoiding a system of stiff differential equations that can arise because of the relatively small mass. The development of accurate nonlinear longitudinal train force models is necessary in order to better understand railroad vehicle dynamic scenarios that include braking, traction, and derailments. Car coupler forces have significant effects on the longitudinal train dynamics and stability. Using the concept of non-inertial coordinate developed in this thesis allows developing of a more detailed coupler model that captures the coupler kinematics without significantly increasing the number of state equations and the dimension of the problem. The coupler model proposed in this thesis allows for the car bodies to have arbitrary displacements, also avoids having a stiff system of differential equations that can result from the use of relatively small masses. In order to…