The computer-oriented Kantorovich - finite difference method and its application on bridge engineering.

摘要

The Kantorovich-finite difference method has been developed and applied for analysis and design of bridge structures in this thesis. Firstly, the bridge deck is mapped into an unit square in the {dollar}xi{dollar}-{dollar}eta{dollar} plane. Secondly, the governing partial differential equation of the deck is reduced to the ordinary differential equation in the longitudinal direction of the bridge by the routine Kantorovich method. Finally, the finite difference method is employed to solve the above-derived ordinary differential equation to get the displacements and internal forces. The present method has been examined on right, skewed or general slab bridge decks and box-girder bridges. Mindlin plate theory and Kirchhoff plate theory are incorporated into the differential equation and, as a result, the designer has the option of either including or excluding the effect of shear deformation of the plate in the analysis. Possible shear locking is avoided by the reduced integration technique. Numerical examples show that the proposed new numerical model is versatile, efficient and reliable.