## Experimental continuation of nonlinear load-bearing structures

### Rainer Groh

University of Bristol

The drive for lightweighting in structural engineering leads to ever thinner structures that deform in nonlinear ways and that are prone to sudden instabilities. Simultaneously, a renewed interest in structural instability revolves around purposefully embedding instabilities in structures to add functionality beyond structural load-carrying capability (e.g. dynamic shape adaptivity). To date, the design of nonlinear structures is guided almost entirely by computational modelling, in particular the use of numerical continuation tools.

Advances in experimental testing of nonlinear structures, on the other hand, are significantly lagging behind numerical methods. While numerical continuation principles such as path-following, calculation of bifurcations, branch-switching, and bifurcation tracking are now well established, nonlinear experimental methods of structures have not advanced beyond simple displacement and force control. This means that the nonlinear response of even simple nonlinear structures cannot be fully characterised, as established techniques induce dynamic snaps at limit points and subcritical bifurcations. There is thus huge potential for devising novel and non-destructive ways of testing nonlinear structures by applying concepts from the field of continuation to experimental mechanics.

At the University of Bristol, we have developed a testing method based on adding control points with auxiliary sensors and actuators to a structure to: (i) stabilise otherwise unstable equilibria; (ii) control the shape of the structure to transition between different stable equilibria; and (iii) compute an experimental “tangential” stiffness matrix (the Jacobian), which ultimately allows Newton's root-finding algorithm to be implemented experimentally. With this approach all the features of the numerical techniques mentioned above can (theoretically) be replicated. The testing method has been applied to laboratory scale test specimens such as the snap-through of a shallow arch, and this seminar will provide an overview of the mathematical background to experimental continuation, its application, and outlook to future experiments.