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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

基本信息

批准号：
1537349
负责人：
Shane Ross
金额：
$ 25万
依托单位：
Virginia Polytechnic Institute and State 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=1537349&HistoricalAwards=false
关键词：
Collaborative Research New Framework Prediction

项目摘要

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.

除了传统上对大型工程结构稳定性和倒塌的关注之外，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。更一般地说，预测势能井的逃逸是一种普遍的练习，它控制着许多在面临干扰时无法保持稳定的物理系统的行为。所有这些情况本质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。通常这种转变是突然的，这种逃避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理论概念过渡到实用和设计导向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通过实验测试逃逸问题的方法，从而为预测、设计以及在某些情况下的预防提供框架，为此类系统的更复杂的设计和控制奠定基础。该项目汇集了两位背景互补的研究人员。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应用：化学反应、纳米结构、地震工程、船舶动力学等等，甚至可能超出工程范围：某些生物和生态系统。该研究项目的广泛范围和影响力将为本科生和研究生提供强大的培训环境。研究团队还将开发一个积极的外展计划，通过高中使用 3D 打印机技术的快速现象和自我引导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领域的努力，开发一种创新的统一方法来实验非线性结构屈曲，使用高维圆柱状相空间结构作为理解势井之间动态控制运动的基础（平衡态）在相空间中。这些管特征在全局意义上组织了相空间中轨迹的演化。这种观点将用于理解许多不同复杂程度的轴向加载细长机械结构的行为。先前已经考虑并确定了具有时变强迫的单自由度系统的势井逃逸标准和路线，与实验具有合理的一致性。然而，当有两个或更多自由度时，情况就变得更加复杂。然而，即使对于更高维度的情况，最近的工作也表明了理论计算框架的开始，用于确定那些很快就会逃逸的轨迹（或者等效地，多井系统中的井之间的过渡）的边界。这些方法本质上是确定性系统的几何方法，当噪声和随机效应合并时，它们自然地合并到概率框架中。该研究开发了一种一致的方法，可以更深入地理解一类重要的结构力学问题，具有对传统工程结构的屈曲预测的潜在应用，以及设计可弯曲、折叠和扭曲的自适应结构的新机会，即将结构可控地变形为所需形状以实现某些目标。