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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.

除了大型工程结构中的稳定性和倒塌的传统关注之外，屈曲现象在许多其他自然和工程系统中起着关键作用，例如，植物对刺激的反应，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，预测从势能阱中逃逸是一种普遍的练习，并且支配着许多在面对扰动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所主导的，因为系统找到了退出一个状态的方法（即，行为），并得到另一个。这种转变通常是突然的，这种逃避行为的后果可能是灾难性的。把注意力集中在低阶的实验屈曲系统是从抽象的理论概念过渡到实际的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的范式，以评估逃逸问题可以在统计意义上进行实验测试的方式，从而为预测，设计和在某些情况下预防提供框架，为更复杂的设计和控制奠定基础。该项目汇集了两名来自互补背景的研究人员。虽然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，甚至可能超越工程：某些生物和生态系统。这个研究项目的广泛范围和范围将为本科生和研究生提供一个强大的培训环境。该研究团队还将开发一个积极的推广计划，通过在高中使用3D打印技术的快速通过现象和自我引导探究来激发年轻人对动力学的兴趣。该奖项将支持理论和应用力学方面的努力，以开发实验非线性结构屈曲的创新统一方法，使用高维圆柱状相空间结构作为理解相空间中势威尔斯（平衡态）之间的动力学控制运动的基本基础。这些管状特征在全局意义上组织了相空间中轨迹的演化。这个观点将被应用于理解一些轴向加载的细长机械结构的行为，不同程度的复杂性。标准和路线的逃逸从一个潜在的井以前被认为是和确定的一个自由度系统随时间变化的强迫，与实验的合理协议。然而，当存在两个或更多个自由度时，情况变得更加复杂。然而，即使对于更高维的情况下，最近的工作表明，开始的理论计算框架，用于确定这些轨迹的边界，很快就会逃脱（或等效地，过渡之间的威尔斯多井系统）。这些方法是几何性质的确定性系统，自然合并成一个概率框架时，噪声和随机效应。该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，具有传统工程结构屈曲预测的潜在应用，以及设计可以弯曲，折叠和扭曲的自适应结构的新机会，即，可控制地将结构变形为期望的形状以实现某些目的。