Tracing the equilibrium paths of elastic reticulated systems by means of the 'admissible directions cone' method

Abstract

Standard arc-length methods, which use a constant step-length, may encounter serious difficulties when tracing the equilibrium paths of ‘perfect’ or ‘quasi-perfect’ structural systems. In these cases, in the neighbourhood of bifurcation or sharp turning points, erroneous jumps of the algorithm onto different branches are always possible. These drawbacks can be efficiently overcome by using a self-adapting strategy able to reduce the assigned step-length according to the complexity of the curve. In particular, based on the concept of osculating circle, an inequality constraint is introduced, which forces the secant vector to fall within a prescribed ‘cone of admissible directions’ at each incremental step. The main advantage of this strategy is that it naturally leads to a uniformly accurate sampling of points along the path. The method’s effectiveness is moreover illustrated through its application to the stability analysis of complex reticulated systems, such as Schwedler domes and three-dimensional masts. In particular, the influence of different bracing patterns on their post-critical behaviour is examined