Analysis and tailoring of stiffened panels with asymmetries via extended modal nudging

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Lightweight structures are inherently prone to instabilities and the usual effort to suppress such effects and limit operation to the linear regime can lead to unnecessarily stiff structures. Consider stiffened panels, for instance, the classical example of load-carrying structures in the aerospace industry. They are generally not allowed to operate in the postbuckling regime and, when they are, there is barely any change from the pre- to the postbuckling response stiffness. This means that the postbuckling response is stiffener dominated. Hence, the final design is made of bulky stringers and the structure is not as light as it could potentially be if the structure was allowed to operate more compliantly. Nonetheless, the reluctance to embrace nonlinearities can be largely attributed to the perceived unpredictable and uncontrollable nature of instabilities and the ensuing structural behaviour beyond critical points. For this reason, this thesis considers that exploiting nonlinearities in load-carrying structures depends on a two-step process that consists of (1) navigating and understanding the postbuckling equilibrium landscape; and, based on this information, (2) tailoring or tuning the resulting response such that it remains predictable and robustly controllable upon load application.

Previous studies have shown that it is indeed possible to design well-behaved nonlinear structures that fulfil the requirements in (2) using modal nudging, a recently developed response tailoring technique. Modal nudging harvests information from the stable regions of the postbuckling regime that inform small changes in the original geometry and ultimately force the structure to follow a certain preferential path. Depending on the target path, an improved structure can be achieved (e.g. with higher load-carrying capacity, stiffness/compliance) and thus the technique can be used as a lightweighting methodology. It is clear, however, that to take advantage of the postbuckling regime in full, step (1) first needs to be adequately satisfied. This is not a trivial task, as past the onset of instability, the resulting equilibrium landscape is significantly more complex, and an advanced path-following method is required for exploration. This complexity increases even further for postbuckling of realistic structures that often behave in a non-symmetric manner due to a plethora of factors, e.g. geometrical imperfections or less obvious coupling behaviour from composite laminates. As a result, perfect pitchfork bifurcations cease to exist, giving space to disconnected paths that are not easily identified by even the most advanced solvers.

In this thesis, a novel navigation procedure is proposed to navigate the equilibrium landscape of non-symmetric responses using generalised path-following methods. This modification allows the exploration of the non-symmetric case in a systematic way and effectively extends the scope of the modal nudging tailoring methodology to complex problems with inherent broken symmetries. Thus, for the first time it is possible to apply the methodology to a composite stiffened panel with elastic coupling behaviour and an increase in load-carrying capacity is obtained. Because this work relies heavily on design by numerical modelling, guidelines are also provided for exploring the postbuckling regime in a reliable and robust manner that minimises numerical noise that otherwise can inadvertently change the observed response. Collectively, this work contributes to the exploration, design and control of well-behaved nonlinear structures that could pave the way to a new generation of functionally optimised and lightweight aerospace structures.
Date of Award21 Mar 2023
Original languageEnglish
Awarding Institution
  • University of Bristol
SponsorsNational Council of Scientific and Technological Development
SupervisorAlberto Pirrera (Supervisor), Rainer Groh (Supervisor) & Paul M Weaver (Supervisor)

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