## Fully Coupled Analysis of Large Scale Tracked Vehicle Systems with Flexible Link Chains

##### Abstract

This thesis examines multiple multibody dynamic formulations and their effects in the large displacement analysis of flexible bodies. The second chapter will examine the effect of using independent finite rotation fields in the large displacement analysis of flexible beams first formulated 30 years ago. This finite rotation description is at the core of the large rotation vector formulation (LRVF), which has been used in the dynamic analysis of bodies experiencing large rotation and deformation. The LRVF employs two independently interpolated meshes for describing the flexible body dynamics: the position mesh and the rotation mesh. The use of these two geometrically independent meshes can lead to coordinate and geometric invariant redundancy that can be the source of fundamental problems in the analysis of large deformations. It is demonstrated in this thesis that the two geometry meshes can define different space curves, which can differ by arbitrary rigid body displacements. The material points of the two meshes occupy different positions in the deformed configuration, and as a consequence, the geometries of the two meshes can differ significantly. Other issues including energy conservation and the inextensibility of the rotation mesh will also be discussed. Simple examples are presented in order to shed light on these fundamental issues.
The third chapter of this thesis focuses on the dynamic formulation of mechanical joints using different approaches that lead to different models with different numbers of degrees of freedom. Some of these formulations allow for capturing the joint deformations using discrete elastic model while the others are continuum-based and capture joint deformation modes that cannot be captured using the discrete elastic joint models. Specifically, four types of joint formulations are considered in this chapter; the ideal, penalty, compliant discrete element, and compliant continuum-based joint models. The ideal joint formulation, or constrained dynamics approach, which does not allow for deformation degrees of freedom in the case of rigid body or small deformation analysis, requires introducing a set of algebraic constraint equations that can be handled in computational multibody system (MBS). When the constrained dynamics approach is used, the constraint equations must be satisfied at the position, velocity, and acceleration levels. The penalty method, on the other hand, ensures that the same algebraic equations are satisfied at the position level only with a force-based approach. In the compliant discrete element joint formulation, no constraint conditions are used; instead the connectivity conditions between bodies are enforced using forces that can be defined in their most general form in MBS algorithms using bushing elements that allow for the definition of general nonlinear forces and moments. The new compliant continuum-based joint formulation, which is based on the finite element (FE) absolute nodal coordinate formulation (ANCF), has several advantages: (1) It captures modes of joint deformations that cannot be captured using the compliant discrete joint models; (2) It leads to linear connectivity conditions, thereby allowing for the elimination of the dependent variables at a preprocessing stage; (3) It leads to a constant inertia matrix in the case of chain like structure; and (4) It automatically captures the deformation of the bodies using distributed inertia and elasticity. The formulations of these three different joint models are compared in order to shed light on the fundamental differences between them. Numerical results of a detailed tracked vehicle model are presented in order to demonstrate the implementation of some of the formulations discussed in this chapter.
Because of the lack of computational methods that can be used for the direct calculation of the stresses of complex multibody systems such as tracked vehicles, the dynamic stresses of such systems are often evaluated at a post-processing stage using forces obtained from a rigid body analysis. With the recent developments in MBS dynamics, detailed flexible body models of vehicle systems can be developed and used to evaluate, for the first time, the accuracy of the stress prediction based on the rigid body force calculations. It is, therefore, the objective of this chapter to use the finite element absolute nodal coordinate formulation, which automatically accounts for the dynamic coupling between the rigid body motion and the elastic deformation, to obtain the stress results. These results are then used to evaluate the accuracy of the stresses calculated at a post-processing stage using forces determined from a rigid body analysis. ANCF finite elements are used to perform the coupled dynamic analysis and obtain the stresses based on a fully nonlinear flexible body analysis. In order to obtain an accurate representation of the stresses in the case of the rigid body analysis, the floating frame of reference (FFR) formulation dynamic equations are used to define the inertia and joint reaction forces that must be used in the post-processing stress calculations. To this end, the rigid body accelerations, including the angular accelerations, as well as the joint reaction forces are first predicted using a rigid body analysis. The solution of the rigid body problem is then used to formulate the FFR equations associated with the elastic coordinates. These equations include the effect of the inertia, centrifugal, and Coriolis forces resulting from the rigid body displacements. The resulting linear second order ordinary differential equations associated with the FFR elastic coordinates are solved for the elastic accelerations which are integrated to determine the elastic coordinates and velocities. The obtained elastic coordinates are used to determine the stresses which are compared with the stresses obtained using the fully coupled ANCF analysis. The two approaches described are explained in detail and used in the stress analysis of the track links in a complex three-dimensional tracked vehicle model. One of the most common areas of failure for such tracked vehicles is attributed to the failure of the track link chains, and therefore, performing a detailed fully coupled stress analysis, as the one described in this chapter, is necessary in order to obtain more accurate stress results and avoid failure of such complex vehicle systems.

##### Subject

Multibody system dynamicsjoint formulations

tracked vehicles

ANCF finite elements

flexible multibody dynamics

large rotation vector formulation

floating frame of reference

##### Type

thesistext