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

Jiajia Shen*, Rainer Groh, Mark Schenk, Alberto Pirrera

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

65 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)25-40
Number of pages16
JournalInternational Journal of Solids and Structures
Early online date11 Dec 2021
Publication statusE-pub ahead of print - 11 Dec 2021

Bibliographical note

Funding Information:
R.M.J.G. is funded by the Royal Academy of Engineering under the Research Fellowship scheme [Grant No. RF\201718\17178]. J.S. and A.P. are funded by the UK Engineering and Physical Sciences Research Council [Grant No. EP/M013170/1].

Publisher Copyright:
© 2020 The Author(s)


  • experimental Newton's method
  • nonlinear structures
  • virtual testing
  • stability
  • bifurcations


Dive into the research topics of 'Experimental Path-Following of Equilibria Using Newton's Method, Part II: Applications and Outlook'. Together they form a unique fingerprint.

Cite this