Experimental Continuation of Nonlinear Structures

Numerical continuation techniques provide a comprehensive suite of computational tools to study the behaviour of nonlinear systems. However, load-bearing structures undergoing nonlinear deflections are still tested experimentally using force controlled (dead) loading or displacement controlled (rigid) loading. As a result, the existing experimental methods cannot traverse limit points in the loading parameter without inducing snaps to alternative equilibria, and are restricted to measuring exclusively stable equilibria. Identifying unstable equilibria is important for buckling-sensitive structures, as unstable states form the stabilising energy barriers around stable equilibria, and unstable states can be connecting branches between different stable states that can be exploited for shape morphing applications.

To map numerical techniques that address the above-mentioned limitations into the experimental domain, the computation of an `experimental tangential stiffness matrix' is an essential pre-requisite. Additional actuators/sensors are introduced to control the shape of the structure and compute the experimental tangential stiffness matrix. A quasi-static experimental continuation method was developed, which can continue along stable and unstable equilibria and traverse limit points using Newton's method. We demonstrate these capabilities in an experiment on a pinned, shallow arch loaded transversely by a mid-span point load, and traverse two limit points in the load-displacement equilibrium manifold. This novel experimental method facilitates extended testing of soft, extremely deformable and generally nonlinear structures, and allows other techniques used in the numerical continuation community to be directly applied in experimental testing of geometrically nonlinear structures.