A new three dimensional absolute coordinate based beam element with application to wheel/rail interaction.

摘要

In this thesis, the following three main topics are discussed: (1) Efficient implementation of the absolute nodal coordinate formulation that leads to an optimum sparse matrix structure for multibody applications; (2) Development of a new three dimensional beam element based on the absolute nodal coordinate formulation that account for shear, torsion and rotary inertia; (3) Application of the absolute nodal coordinate formulation to the dynamics of multibody railroad vehicle systems.; The efficient implementation of the absolute nodal coordinate formulation is accomplished by utilizing the fact that this formulation leads to a constant mass matrix. A Cholesky decomposition of the mass matrix is then used in order to obtain a constant velocity transformation matrix. This velocity transformation is used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. The inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motion. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this investigation. Numerical examples are presented in order to demonstrate the use of Cholesky coordinates in the simulation of the large deformations in flexible multibody applications.; The second objective of this investigation is to develop an absolute nodal coordinate formulation for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this investigation takes into account the effect of rotary inertia, torsion and shear effects, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. A general continuum mechanics approach is used to develop the elastic forces of the proposed beam elements. The results obtained using the two elements are compared with the results obtained using existing incremental methods.; An important application for the procedure discussed in this thesis is the railroad wheel/rail interaction. A simplified form of the developed two-noded isoparametric beam element is used in the geometric description of curved tracks. The dynamic behavior of a single wheelset travelling on a curved track is investigated and the hunting motion of atypical North American three-piece truck is analyzed using a general nonlinear multibody approach. The nonlinearities due to the wheel and the rail surface profiles are considered in the constraint contact model used in the multibody methodology.