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.

除了关注大型工程结构的稳定性和倒塌问题外，屈曲现象在许多其他自然和工程系统中也发挥着关键作用，例如植物对刺激的响应、宏观工程结构的变形、周期性多孔材料的图案化以及从2D纳米结构设计3D形状。更广泛地说，预测从势能井中逃逸是一项普遍的练习，它支配着许多物理系统中的行为，这些系统在面对干扰时无法保持稳定。所有这些情况基本上都是由系统状态的大规模组织主导的，因为系统找到了退出一种状态(即行为)并进入另一种状态的方法。这种转变通常是突然的，这种逃逸行为的后果可能是灾难性的。关注低阶实验屈曲系统是从抽象的理论概念过渡到实用和面向设计的指导方针的关键中间步骤。该奖项支持通过新的理论-计算方法应用新范式的努力，以评估在统计意义上可以通过实验测试逃逸问题的方法，从而为预测、设计和在某些情况下预防提供一个框架，为更复杂的此类系统的设计和控制奠定基础。这个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，但数学还有许多其他潜在的应用：化学反应、纳米结构、地震工程、船舶动力学，仅举几例，甚至可能用于工程以外的用途：某些生物和生态系统。这一研究项目的广泛范围和覆盖范围将为本科生和研究生提供强有力的培训环境。该研究小组还将开发一个积极的推广计划，通过在高中使用3D打印机技术的快速穿透现象和自我引导的探究来激发年轻人对动力学的认识。该奖项将支持理论和应用力学方面的努力，以开发一种创新的统一方法来进行实验的非线性结构屈曲，使用高维圆柱状相空间结构作为理解相空间中势井(平衡态)之间运动的动力学的基本基础。这些管状特征在全局意义上组织了相空间中轨迹的演化。这一观点将被用来理解一些轴向受载的细长机械结构的行为，这些结构的复杂程度各不相同。对于具有时变作用力的单自由度系统，以前已经考虑和确定了从势井中逃生的准则和路线，并与实验合理地吻合。然而，当有两个或更多个自由度时，情况变得更加复杂。然而，即使对于更高维度的情况，最近的工作表明，用于确定即将逃逸(或相当于多井系统中的井之间的过渡)的轨迹的边界的理论计算框架已经开始。对于确定性系统，这些方法本质上是几何的，当噪声和随机效应结合在一起时，它们自然地合并到一个概率框架中。这项研究开发了一种一致的方法来更深入地理解一类重要的结构力学问题，潜在地应用于传统工程结构的屈曲预测，并为设计可以弯曲、折叠和扭转的自适应结构提供了新的机会，即可控制地将结构变形成所需的形状以实现某些目标。