Nonlinear bifurcation analysis of statically loaded free-form curved beams using isogeometric framework and pseudo-arclength continuation

Abstract

This paper presents an isogeometric analysis (IGA) integrated with pseudo-arclength continuation technique in order to predict the elastic bifurcation behavior of geometrically nonlinear free-form curved beams under static loading. The presented formulation is based on the Timoshenko beam theory and accounts for shear deformations in the large-displacement analysis of curved beams. The full equilibrium path of the buckled structures including common types of static instabilities (e.g., the saddle–node and pitchfork bifurcations) can be tracked by the presented approach. Thanks to the exact geometry representation of the IGA framework, the objective of this paper is to extend the current literature of the nonlinear buckling analysis of curved beams to a broader range of free-form geometries with engineering applications. Some practical case studies with different loading scenarios are investigated and the results are validated against the commercial finite element software and well-established benchmark examples.