In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both threedimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other threedimensional element used in this investigation is a cable element obtained from a more general threedimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.

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Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, new three-dimensional nonlinear dynamic rubber chains and belt drives models are developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates, and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drive mechanisms is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

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