Finite element analysis of buckling and post-buckling behaviors of arches with geometric imperfections

Abstract

The buckling and post-buckling behavior of arches is very sensitive to their geometric imperfections. The purpose of this paper is to develop a refined curved finite element that might accurately represent the actual geometry of arches so that the imperfection effects on their buckling behavior could be properly investigated. For an arch with known geometric imperfections, the element stiffness matrix is precisely formulated in terms of Lagrangian variables for a perfect arch from a general incremental variational principle. In general, the element stiffness matrix contains Lagrangian strain, first and second order incremental strain and imperfection terms. For any general planar imperfect arch with a variable curvature, the element stiffness matrix is evaluated by numerical integration; however, for a nominally circular arch, it can be represented in closed form. Numerical results in terms of load-deformation curves are presented for a number of circular arches with and without imperfections and compared with existing solutions.