Abstract Modern numerical path-following techniques provide a comprehensive suite of computational tools to study the bifurcation behaviour of engineering structures. In contrast, experimental testing of load-bearing nonlinear structures is still performed using simple force control (dead loading) or displacement control (rigid loading). This means that established experimental methods cannot trace equilibrium manifolds in their entirety because structures snap to alternative equilibria at limit points in the forcing parameter and because branch switching to alternative equilibria cannot be controlled and performed reliably. To extend current testing methods, in Part I of this paper, we implement an experimental path-following method that uses tangent quantities (stiffness and residual forces) and Newton’s method to continue along stable and unstable equilibrium paths and traverse limit points. In addition to enforcing the displacement at primary load-introduction points, the overall shape of the structure is controlled via secondary actuators and sensors. Small perturbations of the structure using the secondary actuators allow an experimental tangent stiffness to be computed, which is then used in a control algorithm. As a pertinent test case, the experimental method is applied to a transversely loaded shallow circular arch. Due to the complexity of the test setup, the experiment is first designed using a virtual testing environment based on a surrogate finite element model. Experimental results demonstrate the robustness of the proposed experimental method and the usefulness of virtual testing as a surrogate, but also highlight that experimental efficiency and the effects of noise and sensor uncertainty is of particular concern. In Part II, we present perspectives on future research directions and novel testing capabilities that are enabled by extending the methodology to pinpointing of critical points, tracing of critical boundaries, and branch switching.

中文翻译：

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使用牛顿法进行平衡的实验路径跟踪。第一部分：理论、建模、实验

摘要 现代数值路径跟踪技术为研究工程结构的分岔行为提供了一套全面的计算工具。相比之下，承载非线性结构的实验测试仍然使用简单的力控制（恒载）或位移控制（刚性加载）进行。这意味着已建立的实验方法不能完整地追踪平衡流形，因为结构在强制参数的极限点处捕捉到替代平衡，并且因为无法可靠地控制和执行到替代平衡的分支切换。为了扩展当前的测试方法，在本文的第一部分，我们实施了一种实验路径跟踪方法，该方法使用切线量（刚度和残余力）和牛顿方法沿着稳定和不稳定的平衡路径继续并遍历极限点。除了在主要载荷引入点强制位移外，结构的整体形状还通过辅助执行器和传感器进行控制。使用辅助致动器的结构的小扰动允许计算实验切线刚度，然后将其用于控制​​算法。作为相关的测试案例，该实验方法应用于横向加载的浅圆拱。由于测试设置的复杂性，实验首先使用基于代理有限元模型的虚拟测试环境进行设计。实验结果证明了所提出的实验方法的稳健性和虚拟测试作为替代品的有用性，但也强调了实验效率以及噪声和传感器不确定性的影响是特别值得关注的。在第二部分，我们提出了未来研究方向和新测试能力的观点，这些能力通过将方法扩展到关键点的精确定位、关键边界的跟踪和分支切换来实现。