Collaborative Research: Uncertainty Quantification and Model Validation in Thin-Walled Structures: A Probabilistic Paradigm for Advancing Analysis-Based Design

该项目将致力于研究一种先进的薄壁结构非线性稳定性分析框架，同时考虑几何缺陷带来的不确定性。薄壁结构最常见的失效模式是屈曲破坏。这种屈曲是良性的还是灾难性的，在很大程度上取决于结构的细节，最重要的是它的几何缺陷。这项研究旨在通过设计一种使用先进的不确定性量化技术和新的结构分析方法的概率范式，来实现薄壁结构分析中不确定性量化和模型验证的飞跃。提出了几何不确定性的表征和表示方法以及概率缺陷敏感性分析框架，为薄壁结构的完全随机非线性分析铺平了道路。如果成功，这项研究的结果将改变在基于分析的高级薄壁结构设计中处理几何缺陷的方式。由于本项目采用的随机方法具有非常一般性和数学驱动的性质，所开发的方法将适用于各种各样的问题，并将对所有科学和工程学科产生潜在影响。除了研究生指导，本科生研究将是马萨诸塞大学达特茅斯分校(UMD)和约翰·霍普金斯大学(JHU)努力的重点。参与活动的本科生将被要求与当地高中和一所社区大学的学生以及UMD大学新生暑期学院的学生分享他们的经验，希望他们的成功将被其他人效仿。此外，还与专门针对代表性不足群体的项目合作，邀请合格的学生参加这两所大学的研究。除了通过会议和论文传播学术，并将所有开发的工作作为开放源码提供之外，私人投资机构还将利用他们参与工程委员会(如AISC、AISI等)的机会。在学术界之外传播这一发现。

This project will pursue research towards an advanced framework for nonlinear stability analysis of thin-walled structures taking into account the uncertainty associated with geometric imperfections. Thin-walled structures most commonly fail in buckling failure mode. Whether this buckling is benign or catastrophic depends, to a great extent, on the details of the structure, most importantly its geometric imperfections. The research aims at providing a leap towards uncertainty quantification and model validation in the analysis of thin-walled structures by devising a probabilistic paradigm that uses advanced uncertainty quantification techniques along with novel structural analysis methods. Methodologies for the characterization and representation of geometric uncertainties as well as probabilistic imperfection sensitivity analysis frameworks are proposed that have the potential to pave the way for a fully stochastic nonlinear analysis of thin-walled structures. The proposed techniques are complemented by experimental measurements of imperfections with high accuracy, and testing of imperfect members.If successful, the results of this research will transform how geometric imperfections are handled in advanced analysis-based design of thin-walled structures. Because of the very general and mathematics-driven nature of the stochastic approaches adopted in this project, the methodologies developed will be applicable to a wide variety of problems and will have potential impact across all science and engineering disciplines. Alongside graduate student mentoring, undergraduate research will be a focus of the efforts at both University of Massachusetts Dartmouth (UMD) and Johns Hopkins University (JHU). The involved undergraduates will be asked to share their experience with students at local high schools and a community college as well as students attending Freshman Summer Institute at UMD, in hopes that their success will be emulated by others. Also, in collaboration with programs that specifically target underrepresented groups, qualified students are invited to participate in research at both universities. In addition to academic dissemination through conferences and papers and providing all developed work as open source, the PIs will capitalize on their involvement in engineering committees (e.g. AISC, AISI etc.) to disseminate the findings outside of the academic community.