Experimental Path-Following of Equilibria Using Newton's Method, Part II: Applications and Outlook

Abstract In Part I of this paper, a quasi-static experimental path-following method was developed that uses tangent quantities in a feedback controller, based on Newton’s method. The ability to compute an experimental tangent stiffness opens the door to more advanced path-following techniques. Here, we extend the experimental path-following method to: (i) pinpointing of critical points (limit and branching points); (ii) branch switching to alternate equilibrium paths; and (iii) tracing of critical points with respect to a secondary parameter. We initially explore these more advanced concepts via the virtual testing environment introduced and validated in Part I. Ultimately, the objective is to demonstrate novel testing procedures and protocols made possible by these advanced experimental path-following procedures. In particular, three pertinent examples are discussed: (i) design sensitivity plots for shape-adaptive morphing structures; (ii) validation of nonlinear FE benchmark models; and (iii) non-destructive testing of subcritical (unstable) buckling of thin-walled shells.