Closed-Form Solution for In-plane Nonlinear Elastic Buckling of Parabolic Three-Pinned Arches

Abstract

The parabolic three-pinned arches are commonly used in structural engineering; however, its in-plane nonlinear buckling is not explored in the available publications. This paper investigates the closed-form solutions of in-plane nonlinear elastic buckling of the parabolic three-pinned arches. The equilibrium differential equations of in-plane nonlinear elastic buckling are derived based on the membrane and bending strain in the Cartesian coordinate system and the virtual work principle, and the equilibrium equation of nonlinear buckling are obtained by the integration of the membrane strain along the span. Comparisons with finite element results show that the nonlinear elastic buckling predictions of proposed method have sufficient accuracy in a large parameter range.