Virtual Testing of Experimental Continuation

TL;DR

This paper introduces a novel experimental continuation method that enables the path-following of unstable equilibria in nonlinear structures, overcoming limitations of traditional testing methods and allowing validation of structures exploiting instabilities.

Contribution

The paper presents a new virtual testing approach capable of traversing limit points and unstable equilibria, advancing experimental validation of nonlinear structures.

Findings

Enables experimental validation of unstable equilibria.

Supports testing of structures exploiting instabilities.

Provides a theoretical foundation linking shape control to analysis concepts.

Abstract

We present a critical advance in experimental testing of nonlinear structures. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points on a structure. This approach is unable to traverse limit points in the control parameter, as the immediate equilibrium beyond these points is statically unstable, causing the structure to snap to another equilibrium. As a result, unstable equilibria---observed numerically---are yet to be verified experimentally. Based on previous experimental work, and a virtual testing environment developed herein, we propose a new experimental continuation method that can path-follow along unstable equilibria and traverse limit points. To support these developments, we provide insightful analogies between a fundamental building block of our technique---shape control---and analysis concepts such as the principle of virtual work and Galerkin's method. The proposed testing method will enable the validation of an emerging class of nonlinear structures that exploit instabilities for novel functionality.