Integration of Different Constitutive Models in Multibody System Algorithms
Multibody systems (MBS) in general include two collections of bodies. One collection consists of bulky and compact solids which can be treated as rigid bodies, while the second collection includes bodies that can be treated as flexible bodies that experience small and large deformations and undergo large rotations. Many technological and industrial problems such as liquid sloshing, textile hyper-elastic, biomechanics and vehicle terrain interaction require efficient and accurate modeling of flexible bodies. One of the objectives of this thesis is to develop a low order continuum-based liquid sloshing model that can be successfully integrated with multibody system algorithms. The liquid sloshing model proposed in this thesis allows for capturing the effect of the distributed inertia and the viscosity of the fluid. The fluid viscous forces are defined using the Navier-Stokes equations. In order to demonstrate the use of the approach presented in this study, the assumption of an incompressible Newtonian fluid is considered with a total Lagrangian approach. Fluid properties such as the incompressibility condition are formulated using a penalty method. The low order model that could capture the effect of the distributed fluid inertia on the vehicle dynamics is developed in this thesis using the floating frame reference (FFR) formulation. The use of this approach allows for developing an inertia-variant fluid model that accounts for the dynamic coupling between different modes of the fluid displacements. The matrix of position vector gradients and its derivative are formulated using the FFR kinematic description. The position and velocity gradient tensors are used to define the Navier-Stokes stress forces. The proposed liquid sloshing model is integrated with a MBS railroad vehicle model in which the rail/wheel interaction is formulated using a three-dimensional elastic contact formulation that allows for the wheel/rail separation. Several simulation scenarios are used to examine the effect of the distributed liquid inertia on the motion of the railroad vehicle. The results, obtained using the sloshing model, are compared with the results obtained using a rigid body vehicle model. The comparative numerical study presented in this thesis shows that the effect of the sloshing tends to increase the possibility of wheel/rail separation as the forward velocity increases, thereby increasing the possibility of derailments at these relatively high speeds. Another objective of this thesis is to develop a total Lagrangian non-incremental liquid sloshing solution procedure based on the finite element (FE) absolute nodal coordinate formulation (ANCF). The proposed liquid sloshing modeling approach can be used to avoid the difficulties of integrating most of fluid dynamics formulations, which are based on the Eulerian approach, with MBS dynamics formulations, which are based on a total Lagrangian approach. The proposed total Lagrangian FE fluid dynamics formulation, which can be systematically integrated with computational MBS algorithms, differs significantly from the conventional FE or finite volume methods which are based on an Eulerian representation that employs the velocity field of a fixed control volume in the region of interest. The ANCF fluid equations are expressed in terms of displacement and gradient coordinates of material points, allowing for straight forward implementation of kinematic constraint equations and for the systematic modeling of the interaction of the fluid with the external environment or with rigid and flexible bodies. The fluid incompressibility conditions and surface traction forces are considered and derived directly from the Navier Stokes equations. Two ANCF brick elements, one of which is obtained using an incomplete polynomial representation and the other of which is obtained from a B-spline volume representation, are used. The new approach ensures the continuity of the displacement gradients at the nodal points and allows for imposing higher degree of continuity across the element interface by applying algebraic constraint equations that can be used to eliminate dependent variables and reduce the model dimensionality. Regardless of the magnitude of the fluid displacement, the fluid has a constant mass matrix, leading to zero Coriolis and centrifugal forces. The analysis presented in this thesis demonstrates the feasibility of developing an efficient non-incremental total Lagrangian approach for modeling sloshing problems in MBS system applications in which the bodies can experience large displacements including finite rotations. Several examples are presented in order to shed light on the potential of using the ANCF liquid sloshing formulation developed in this study. This thesis also presents a new flexible MBS approach for modeling textile systems including roll-drafting sets used in chemical textile machinery. The proposed approach can be used in the analysis of textile materials such as lubricated polyester filament bundles (PFB) which have un-common material properties best described by specialized continuum mechanics constitutive models. In this thesis, the ANCF is used to model PFB as a hyper-elastic transversely isotropic material. The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy-Green deformation tensor. Using this energy decomposition, the second Piola-Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. The constitutive equations are used to define the generalized material forces associated with the coordinates of three-dimensional fully-parameterized ANCF finite elements. The proposed approach allows for modeling the dynamic interaction between the rollers polyester filament bundle and allows for using spline functions to describe the PFB forward velocity. The textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain and cross section deformation of the textile material and the relative slip and contact forces between rollers and PFB.
floating frame of reference
absolute nodal coordinate formulation
rail road vehicle systems
multibody system dynamics
transversely isotropic hyperelastic material
total Lagrangian approach