Collaborative Research: A New Framework for Prediction of Buckling and Other Critical Transitions in Nonlinear Structural Mechanics

协作研究：预测非线性结构力学中屈曲和其他关键转变的新框架

• 批准号: 1537425
• 负责人: Lawrence Virgin
• 金额: $ 28万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1537425&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Framework; Prediction

In addition to the conventional concern of stability and collapse in large-scale engineering structures, buckling phenomena play a key role in many other natural and engineered systems, e.g., plants responding to stimuli, deformations of macro-scale engineering structures, patterning of periodic porous materials, and design of 3D shapes from 2D nanostructures. More generally, predicting the escape from a potential energy well is a universal exercise, and governs behavior in many physical systems that are unable to maintain stability in the face of disturbances. All these situations are essentially dominated by the large-scale organization of system states, as the system finds a way to exit one state (i.e., behavior) and get to another. Often this transition is sudden, and the consequences of this escaping behavior may be catastrophic. Focusing attention on low-order experimental buckling systems is the key intermediate step in transitioning from an abstract theoretical concept to practical and design-oriented guidelines. This award supports an effort to apply a new paradigm, by way of a fresh theoretical-computational approach, to assess the ways in which the problem of escape can be tested experimentally, in a statistical sense, and hence provide a framework for prediction, design, and in some cases prevention, laying the groundwork for more sophisticated design and control of such systems. This project brings together two researchers from complementary backgrounds. Although the framework will be developed within the realm of nonlinear structural dynamics, there are many other potential applications of the mathematics: chemical reactions, nanostructures, earthquake engineering, ship dynamics, to name a few, and even possible utility beyond engineering: certain biological and ecological systems. The broad range and reach of this research project will provide a strong training environment for undergraduate and graduate students. The research team will also develop an active outreach program to excite young minds about dynamics through snap-through phenomena and self-guided inquiry using 3D printer technology at high schools.This award will support an effort in theoretical and applied mechanics to develop an innovative unified approach to experimental nonlinear structural buckling, using high dimensional cylinder-like phase space structures as the fundamental basis for understanding the dynamics governing motion between potential wells (equilibrium states) in phase space. These tube features organize the evolution of trajectories in phase space in a global sense. This point-of-view will be applied to understand the behavior of a number of axially loaded slender mechanical structures, of varying degrees of complexity. Criteria and routes of escape from a potential well have previously been considered and determined for one degree of freedom systems with time-varying forcing, with reasonable agreement with experiments. However, when there are two or more degrees of freedom, the situation becomes more complicated. Yet, even for the higher dimensional case, recent work suggests the beginnings of a theoretical-computational framework for determining the boundary of those trajectories which will soon escape (or equivalently, transition between wells in multi-well systems). These methods are geometric in nature for deterministic systems, merging naturally into a probabilistic framework when noise and stochastic effects are incorporated. The research develops a consistent approach to a deeper understanding of an important class of structural mechanics problems, with potential applications to buckling prediction for traditional engineered structures, and emerging opportunities to design adaptive structures that can bend, fold, and twist, i.e., controllably morphing structures into a desired shape to achieve some objective.

除了对大规模工程结构中稳定性和崩溃的常规关注外，屈曲现象在许多其他天然和工程系统中都起着关键作用，例如，植物对刺激的反应，宏观规模工程结构的变形，周期性多孔材料的模式以及来自2D纳米结构的3D形状的设计。更一般而言，预测势能井的逃脱是一种普遍的练习，并且控制着许多在面对干扰时无法保持稳定性的物理系统的行为。所有这些情况基本上都由系统状态的大规模组织主导，因为该系统找到了一种退出一个状态（即行为）并进入另一种状态的方法。这种过渡通常是突然的，这种逃避行为的后果可能是灾难性的。将注意力集中在低阶实验屈曲系统上是从抽象的理论概念转变为实用和面向设计的指南的关键中间步骤。该奖项支持通过一种新的理论计算方法来应用新范式，以评估可以从统计意义上对逃生问题进行实验测试的方式，从而为预测，设计和预防提供了一个框架，为预防的框架提供了对此类系统进行更复杂的设计和控制的基础工作的框架。该项目汇集了来自互补背景的两名研究人员。尽管该框架将在非线性结构动力学领域内开发，但数学的其他潜在应用：化学反应，纳米结构，地震工程，船舶动力学，仅举几例，甚至是工程以外的可能实用程序：某些生物学和生态系统。该研究项目的广泛范围和范围将为本科生和研究生提供强大的培训环境。研究团队还将制定一项积极的宣传计划，通过使用3D打印机技术在高中时使用3D打印机技术来激发年轻人关于动态的思想。这项奖项将支持理论和应用机制中的努力，以开发创新的统一方法，以实验性的非线性结构屈曲，使用较大的运动层依赖于较高的运动型固定型，以使基本型号的依然依然固定为动力学，这是基本型的基础式的，作为基础式的依风，作为基本的依赖性的基础，以此为基础式的依风， （平衡状态）在相空间中。这些管特征在全球意义上组织了相空间中轨迹的演变。该观点将应用于了解多个复杂程度的许多轴向加载细长的机械结构的行为。 以前已经考虑并确定了一个自由系统的标准和逃脱途径，并确定了随着时间变化的强迫，并与实验合理地一致。但是，当有两个或以上的自由度时，情况就会变得更加复杂。然而，即使对于较高维度的情况，最近的工作也表明了一个理论计算框架的开始，用于确定这些轨迹的边界，这些轨迹很快就会逃脱（或等效地，多孔系统中的井之间的过渡）。这些方法本质上是确定性系统的几何形状，当噪声和随机效应纳入时，自然将其合并为概率框架。该研究开发了一种一致的方法，可以深入了解一类重要类别的结构力学问题，并潜在地应用于传统工程结构的屈曲预测，以及设计自适应结构的新兴机会，这些结构可以弯曲，折叠和扭曲，即，即可控制地将其变形结构变成所需的形状，以实现一些目标。