A self-adaptive strategy for uniformly accurate tracing of the equilibrium paths of elastic reticulated structures

The paper describes an incremental procedure for tracing with uniform accuracy the equilibrium paths of elastic reticulated structures subject to conservative proportional loads. Like most traditional arc-length methods, the length of the secant vector is chosen as the increment of the representation parameter, but in contrast to them, here, in order to obtain "ner sampling along arcs of greater curvature, its initial assigned value is susceptible to stepwise reduction along the path. This is accomplished by requiring the secant vector at each step to lie inside a prescribed &cone of admissible directionsʹ. As a consequence, where the path is almost rectilinear, the description of curves remains identical to that furnished by conventional procedures, while for increasing curvature the tracing becomes more and more detailed. This strategy proves to be very e!ective in dealing with reticulated systems whose equilibrium paths are characterized by sharp turns and/or winding loops. Likewise, when dealing with &perfectʹ systems, the method provides simpler, more e$cient and unambiguous tracing of both the primary and secondary branches in the neighbourhood of bifurcation points