3D Geometric Nonlinear Analysis Of Flexible Suspension Bridges

As a kind of flexible structure, suspension bridge has strong geometrical nonlinearity. This thesis focuses on the calculation of cable curve for suspension bridge under dead load and the geometric nonlinear analysis of suspension bridge.The accurate cable curve for suspension bridge under dead load is needed both in the design and construction stage. It is necessary to establish appropriate calculation method of cable curve for suspension bridge under dead load complying with the actual situation. Firstly, parabola theory, a traditional calculation theory of linetype for suspension bridge, is introduced. Secondly, according to the behavior of suspension bridge, two kinds of segmental catenary theory of the cable curve for suspension bridge are deduced, respectively ignoring and considering the change of dead-weight distribution after the elastic extension of cable. Finally, dynamic relaxation method is a theory widely used in the analysis of space cable-membrane structures, changing static problem into a dynamic problem in the application of dynamics theory. In this paper, dynamic relaxation method is applied to the calculation of cable curve for suspension bridge.The main contents about geometric nonlinear analysis of suspension bridges are as follows:First of all, the basic principle of geometric nonlinear finite element method for structures is introduced. After that, T.L formulation and U.L formulation are deduced. According to the strong geometric nonlinear characteristics of suspension bridges, CR formulation is presented to accurately deduct the rigid displacement and rotation of the elements bringing no internal force increment, by introducing the co-rotating coordinate system of the elements. CR formulation can get the real deformation of elements, transferring large displacement and rotation in the global coordinate system into small displacement and rotation in the co-rotating coordinate system of the elements.Then, based on the CR formulation, the internal force vector and tangent stiffness matrix of large rotation and small strain space bar and plane beam element are deduced.The transformation between cross-section coordinate system and co-rotating coordinate system of the space beam elements can be realized by introducing the Euler-Rodrigues finite rotation formulation. According to the basic assumptions of cable member element and catenary equation, the iterative format of internal force and tangent stiffness matrix of small strain elastic catenary cable elements can be deduced, by using cable segment analysis method. At last, the CR formulation verifies to be correct and reliable in the treatment of geometrical nonlinearity through several examples, it can be used in the geometric nonlinear analysis of flexible suspension bridges.