Spline Kantorovich method and analysis of general slab bridge deck

Abstract

In this paper, the spline Kantorovich method is developed and applied to the analysis and design of bridge decks. First, the bridge deck is mapped into a unit square in the Xi - eta plane. The governing partial differential equation of the plate is reduced to the ordinary differential equation in the longitudinal direction of the bridge by the routine Kantorovich method. Spline point collocation method is then used to solve the derived ordinary differential equation to obtain the displacements and internal forces of the bridge deck. Mindlin plate theory is incorporated into the differential equation and, as a result, the effect of shear deformation of the plate is also considered. Possible shear locking is avoided by the reduced integration technique. Numerical examples show that the proposed new numerical model is versatile, efficient, and reliable.Key words: Kantorovich method, spline function, partial differential equations, ordinary differential equations, point collocation method, bridge deck.