Curved Beam Bridge Structure Curved Bar Grillage Finite Element Analysis Of Internal Force Calculation Method

In the paper,the study of analysis method of internal force for curved-beam bridge structure analyzed by spacial method of curved-bar grillage finite element method is introduced . The concrete contents are as follows:1. Spacial stiffness matrix and equivalent nodal loads matrix for a curved beam element, involving twelve degrees of freedom and taking effect of transverse shearing deformation into account, have been formulated, using Castigliano' s theorem and mechanical method. Lognitudinal and transversal members of grillage, regarded as cuved-beam element and straight-beam element, are analyzed by finite element method, and the module for grillage static analysis is formed, by using table of information of nodal point restraint to assemble stiffness matrix for structure in restraint. The program, which is one of the hard core of forming the influence surface of the internal force for grillage by kinematic method, can deal with principal and subordinate degree of freedom, elaxtic support and constrained displacement rapidly and effectively. It also has application in analyzing structural internal forces under gravity at every construction stage by simulating construction process.2. Based on the Muller-Breslau principle, formulars of equivalent nodal loads for the curved- and straight-beam element while occuring unit relative constrained displacement have been deduced. The influence surface of the internal force for grillage has been analyzed by combining kinematic method with finite element static method, using the superposition principle applied to little deformation. Compared with the static method and kinematic method computing deformation directly, the method presented here bring high efficiency when calculating the influence surface of the internal forcefor curved-bar grillage.3. The fundamental principle of loading of influence surface for straight-bridge is expounded by using the mixed method of dynamic programming and exhautive taking, and which is extended to the loading of influence surface for curved-bridge by quoting the idea of equivalent influence surface. To improve computing precision, the latter applies interpolating function of curved-quadrilateral element containing six npdes to thicking the influence surface of grillage. Compared with lagrangian interpolation for rectangular element and triangle plane interpolation, this way not only improves computing precision but be more suitable for the curved-bar grillage analyzing method introduced this paper.4. Under the integrated development environment of Fortran Powerstation 4.0,the paper has written the above contents into common computing programs with language Fortran77 and finished an integrated module for the calculation of internal forces for the superstructure of curved-beam bridge when analyzed by curved-bar grillage finite element method. Two examples presented have proved the validity of the theory and the arithmetic and the enough precision of the given programs.