The Application Of Distributed Transfer Function Method To Girders And Beams Analysis

In this thesis, the Distributed Transfer Function Method (DTFM) is applied to the analysis of different kinds of girders and beams, including vertical and horizontal bending beam, Timoshenko beam and curved beam. The solution model of DTFM, which is applicable to various kinds of boundary conditions, constraints and complicate outside forces, has been figured out .The work of the thesis is as following:1. The differential control equations and the boundary conditions of vertical and horizontal bending beam have been cast into a state space form by defining a state vector. And using the DTFM, the closed-form solution of the displacement is gained. The complicate system is divided into sub-systems according to the outside forces and constraints. Using the DTFM and FEM, the equilibrium equations can be solved. The numerical DTFM is used in non-uniformed system to gain approximation.2. The DTFM solution of uniformed and non-uniformed Timoshenko beam is figured out. Combining the sub-systems according to the continuum of nodes displacement and equilibrium force condition, the complicate system with various outside forces and constraints has been solved by DTFM.3. Based on the deflection curve of curved-beam differential equation which take radian as element, the distribute transfer function which has either cycle-curve axes or normal curve axes has been built. Special treatment has been put in practice for the situation where unites are not smoothly connected. The system equilibrium equations are given after the coordinate transformation.There are several innovations in the application of DTFM in this thesis. In general, this method can be widely used in the analysis of girder and beam, and it has the advantages such as convenient for computer programme, uniform solution, high precision etc.