Development of well-behaved nonlinear structures

  • Bradley Cox

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Historically, the onset of geometric nonlinearity in structural mechanics is viewed as akin to damage or failure. Consequently, the main focus of the practising engineer has been to mitigate any nonlinear response. In preventing nonlinear responses, engineers have inherently limited their useful design space. The motivation behind this thesis pivots around the concept of embracing geometric nonlinearities, including instabilities, and understanding the benefits of considering such phenomena, for designing novel features into structures. In encouraging a paradigm shift to view structural nonlinearities as useful, it is demonstrated that it is possible to design more efficient structures.

A literature search shows that the use of geometric nonlinearities is confined to the development of meta-materials and non-load-bearing structures. This work illustrates that embracing geometric nonlinearities in conventional engineering structures yields significant improvements. In particular, this research focuses on tailoring a structure’s nonlinear response by applying minor alterations to its initial shape or geometry. This enables increases in structural capacity in the form of (i) load-carrying capacity; (ii) compliance; (iii) extended stability. Three distinct structural forms are evaluated, namely arched beams, frames, and shell structures. Case studies are introduced for each of the three structures, and a full exploration of the design space is conducted by employing a nonlinear finite element method coupled with numerical continuation algorithms. The focus is placed on the control and design of the buckling and post-buckling behaviour in these structures, whereby a well-behaved structural response absent of unexpected phenomena is sought.

To this aim the work begins by tackling one of the most common examples of structural nonlinearity, a planar arch exhibiting the textbook ``snap-through'' response. In designing for nonlinearity, the topology of the arch is optimised for maximising the critical buckling load. The findings show that the design of shallow arches using linear kinematic assumptions is antithetical to that of a design accounting for the nonlinear response. These findings illustrate the limitations entailed in optimising the shape of arches using linear assumptions, particularly when the onset of an instability is the target design point. A distinct novelty to the present work is the introduction of modal nudging, a paradigm which can improve the capacity of structures without any significant increase in mass, and convert imperfection-sensitive structures into imperfection-insensitive ones. Herein it is shown that it is applicable to both frame and shell structures. The true complexity of the post-buckled behaviour of axially compressed cylindrical panels, which has often been described as ``chaotic", is shown for the first time. These results not only elucidate the complex nature of post-buckling phenomena, but also highlight the potential of modal nudging into transforming unsafe, unstable post buckling behaviour into safe and stable.

In conclusion, the findings of this thesis bring about new opportunities for the design of efficient structures with greater functionality. Hence, embracing geometric nonlinearity lays the foundation for the development of lighter, safer and multi-functional structures.
Date of Award6 Nov 2018
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorRainer Groh (Supervisor), Alberto Pirrera (Supervisor) & Daniele Avitabile (Supervisor)

Cite this

Development of well-behaved nonlinear structures
Cox, B. (Author). 6 Nov 2018

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)