Newton’s method for experimental path-following of nonlinear structures*

Traditional experimental testing of nonlinear structures has not evolved beyond the fundamental techniques of force control (dead loading) and displacement control (rigid loading). These two experimental paradigms face the same issues that computational solvers faced before numerical path-following; namely, limit points in the force-displacement response cannot be traversed by sole force or displacement control. To extend the capabilities of nonlinear testing methods, we have implemented an experimental analogue to numerical path-following. In addition to controlling the displacement at the primary load-introduction points, extra actuators and sensors are attached to control the overall shape of the structure. By perturbing the structure at these control points, and recording the resulting changes in reaction force, an “experimental tangent stiffness” matrix is computed, which is then used in a feedback control system based on Newton’s method. Using an experiment on a shallow arch, we demonstrate the capability of the test setup to path-follow stable and unstable equilibria and traverse limit points.