Tracing complex equilibrium paths of elastic structures by an improved 'Admissible Directions Cone' method

The post-critical behaviour of a slender elastic structure under an assigned system of proportional loads is wholly disclosed by means of its equilibrium path. To achieve a uniformly accurate tracing of the path, incremental-iterative strategies use a variable step-length to adapt the sampling of points to the complexity of the curve. This paper illustrates a revised formulation of the ‘Admissible Directions Cone’ method, a particular arc-length procedure, in which an inequality constraint is added to the standard set of governing equations to limit the change in angle experienced by the tangent to the path in a step. The effectiveness of the method is demonstrated in severe circumstances, such as the examples presented here, concerning simple kinematically indeterminate truss structures, whose equilibrium paths are nevertheless characterised by bifurcation points at the origin and zero-load secondary branches.