| When performing dynamical analysis of a constrained mechanical system, a set of index-3 differential algebraic equations, i.e. Euler-Lagrange equations, are often needed to describe the time evolution of the mechanical system. In this thesis, we apply one-leg multi-step methods to integrate the DAEs directly. To overcome some difficulties leading to certain numerical instabilities, a velocity elimination technique is applied to generate a framework that the position and velocity profiles can be obtained in two separate stages: only the position variables and Lagrange multipliers take part in the convergent nonlinear iterations at each time step while the velocity is calculated by the multi-step formula directly without any iteration. The framework is constructed in a manner such that it satisfies all the constraints at the position level and involves variables as few as possible during the iteration. Some convergence analysis are presented and good stability and high efficiency can be seen through the experiments of some benchmark problems.; As the second task of this thesis, we shall propose some mathematical model to simulate the movement of a floating bridge under some moving loadings. The floating bridge system consists of three parts, i.e. river (fluid), floating bridge (multibody system) and vehicles (load) which pass the bridge. Our objective is to find the motion and dynamical responses of the floating bridge with a truck or tracklayer passing on it. The floating bridge is a system of steel rectangular boxes which can be seen as rigid bodies connected by some kinematic joints. In fact, such system is a fluid-structure coupled system and one must treat the governing equations for the floating bridge and fluid, i.e. Euler-Lagrange equations and Navier-Stokes equations, simultaneously. In our work, we apply the one-leg method and operator splitting arbitrary Lagrangian-Eulerian method to solve the coupled system. |
