Citation

Sio JAC. Int. J. Crashworthiness 1999; 4(1): 39-58.

Copyright

(Copyright © 1999, Informa - Taylor and Francis Group)

DOI

unavailable

PMID

unavailable

Abstract

The methods of multibody system dynamics provide most of the numerical tools required to construct models of vehicles and to describe biomechanical models of occupants with accuracy. Some of the most recent developments in this area of applied mechanics extended the basic capabilities of the multibody formulations to include the description of the system components deformation. For a given model of a vehicle each moving part is represented as a rigid body or as a flexible body experiencing linear elastic or fully nonlinear deformations. The relative motion of the system components is described by imposing kinematic constraints between them. the interactions among the system components, with other objects and multibody systems or even the coupling with the equations of other disciplines to describe aerodynamics effects or contact-impact conditions are efficiently modeled in this numerical environment. These characteristics suggest that the multibody methodologies provide appropriate ingredients to develop not only the simple conceptual models used in the early phases of the design process but also the more elaborate models of complex systems required for analysis. In this work, the position and orientation of each body of the system is described by a set of Cartesian coordinates or by natural coordinates, which consist in a set of points and vectors representing each body. For flexible bodies. the linear or nonlinear deformations are described with reference to a body fixed coordinate system using an updated Lagrangean formulation and the finite element method. In this form the equations of motion of the flexible bodies exhibit the coupling between the gross rigid body motion and the component flexibility. The relative motion between each of the multibody, components is assured by imposing kinematic constraints in the form of algebraic equations that relate the coordinates used to describe the system. The contact and impact between the system components and other bodies, internal or external to the system. is described using a continuous contact force model. Alternatively, unilateral constraints representing motion restrictions for a particular body in contact, are used. For situations where the deformed region of the component in contact is much smaller than the region of the same body that behaves in a rigid manner a kinetostatic formulation is used. Here, the inertial coupling between the body deformations and its gross motion is neglected. Finally, the formulations reviewed are applied to the description of a biomechanical model and several vehicle models that are simulated in different scenarios, including vehicle rollovers with and without occupants and pedestrian impact. Based on these applications the advantages of using a unified formulation to describe all systems are discussed.