Critical Load and Postbuckling of Arch Frameworks

Abstract

Symmetrical and asymmetrical buckling and postbuckling behavior of a special type of semi‐rigid, self‐erecting dome (the prestressed dome) is investigated using a nonlinear finite element model. A corotational formulation of a three‐dimensional beam element is used to develop an algorithm for nonlinear stability analysis of space structures, considering large displacement and large rotation. The incremental load technique using the Newton‐Raphson iteration method is utilized to solve the system of nonlinear equilibrium equations. Postbuckling analysis is performed by augmenting the structure with a fictitious elastic spring to have a positive‐definite stiffness matrix in the descending branch of the load‐deflection curve. Buckling of prestressed tapered domes under self‐weight is studied, and special prestressed dome shapes that buckle at higher loads than the equivalent prismatic prestressed dome are determined.