General analysis and application to redundant arches under static loading

The aim of this paper is to define an exact formulation of a curved beam finite element for static analysis. The basic equations are combined in the coupled fundamental system in terms of radial displacement v, tangential displacement u and rotation ϕ. An original procedure for solving the fundamental system of equations is used. A finite element formulation based on shape functions that satisfy the homogeneous form of the fundamental system of differential equations is developed. The effects of bending moment, axial extension and transverse shear are taken into account. The exact elastic solution renders the element obtained free of shear and membrane locking. An efficient numerical procedure is presented for determining the pressure curve in the case of circular arches under static loading and arbitrary bonding conditions. The solution obtained is applicable to the analysis of both thin and thick curved beams. Several examples of arches with various loading and boundary conditions are investigated to illustrate the validity and the accuracy of the method. Finally, the effect of the arch rise on the structural response is pointed out.