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

Abstract

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 finer 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 directions'. 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 effective in dealing with reticulated systems whose equilibrium paths are characterized by sharp turns and/or winding loops. Likewise, when dealing with 'perfect' systems, the method provides simpler, more efficient and unambiguous tracing of both the primary and secondary branches in the neighbourhood of bifurcation points. Copyright © 1999 John Wiley & Sons, Ltd.