Absolute nodal coordinate formulation: Elastic forces and application to wheel/rail interaction

The equivalence of the finite element formulations used in flexible multibody dynamics is one of the topics discussed in this investigation. This equivalence is used to address several fundamental issues related to the deformations, flexible body coordinate systems, and the geometric centrifugal stiffening effect. Two conceptually different finite element formulations that lead to exact modeling of the rigid body dynamics are used. These formulations are the absolute nodal coordinate formulation and the floating frame of reference formulation.; The performance of the incremental corotational procedure and the non-incremental absolute nodal coordinate formulation in the analysis of large rotation problems is also investigated. It is demonstrated that the limitation resulting from the use of the nodal rotations in the incremental corotational procedure can lead to simulation problems.; Another objective of this dissertation is to develop simple and accurate elastic force models that can be used in the absolute nodal coordinate formulation for the analysis of two-dimensional beams. These force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach, without the need for introducing a local element coordinate system. Despite the simplicity of the new models, they account for elastic nonlinearity in the strain-displacement relationship. It is demonstrated that the geometric stiffening effects are automatically accounted for by using this new expression for the elastic forces.; An important application for the procedure discussed in this thesis is the railroad wheel/rail interaction. In the multibody formulation of the contact problem, the kinematic contact constraint conditions are formulated in terms of the normal and tangents to the contact surfaces. This leads to the need for evaluating the derivatives up to the third of the functions representing the profile of the wheel and the rail. A multi-layer spline function algorithm is used in order to ensure accurate calculation of these derivatives. The problems of continuity and smoothness of the derivatives are addressed. A new procedure for modeling curved rails using the absolute nodal coordinate formulation is also proposed in this investigation.