Applications of Geometrical Singular Perturbation Theory in Hyperplasticity Accelerated Ratcheting Models

几何奇异摄动理论在超塑性加速棘轮模型中的应用

• 批准号: 2888423
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2888423
• 关键词: Applications; Geometrical; Singular; Perturbation; Theory

EPSRC Project Title: Applications of Geometrical Singular Perturbation Theory in Hyperplasticity Accelerated Ratcheting ModelsAn approach for studying lateral loading for monopile designs is the Hyperplastic Accelerated Racheting Model (HARM) framework developed in collaboration between Orsted and Oxford University [1-3]. Using HARM one can study the loading response of the foundation as a function of stresses. Solving for displacement as a function of lateral loading is a problem in which many cycles of different amplitude are applied during the lifetime of the structure (due to waves etc), and because of a bias in loading from predominant wind directions, ratcheting is often observed [1].The objective of the proposed PhD thesis is to significantly reduce simulation time for modelling cyclic loading such that extended series of unloading/reloading cycles can be introduced in the optimization phase of the pile design. The method used is targeted to be some variation of Geometrical Singular Perturbation Theory (GSPT) [4-6].In my Master Thesis, we utilize the GSPT framework to prove the existence of a relevant slow-fast dynamical system equivalent to a continuous version of the HARM model, where the hyperbolicity of the critical manifold align with unloading and reloading parts of each cycle. This result may address direct solutions to some of the currently faced issues with long-term ratcheting and expected hysteresis analysis [7]. For the 0-D macro modelling approach of HARM two main directions are heavily motivated by the found slow-fast dynamical system in [7]: - First, a study in the performance of GSPT as a standalone tool to obtain integrable (thereby analytical) and non-conservative upper bounds for experienced ratcheting along pile depth. If such results are in alignment with gathered experiments/simulations, they can be used as immediate design parameters. - Secondly, a study on utilizing the knowledge of exactly where the HARM model becomes stiff to current numerical solvers. An idea is to model the fast and slow parts separately & glue them together - avoiding issues with machine number precision. This could lead to not only faster results but also more accurate.In [7] we have only shown existence of a slow-fast system for the 0-D macro model with plasticity surfaces. To align with currently used numerical solutions and improve complexity, a major part of the PhD will also be to extend the theoretical results to higher dimensions (or to new constitutive models such as HySand). As soil modelling is in general complex, it is expected that we reach a boundary point for the theoretical work. The 'until then' reach results are likely to motivate new numerical methods, also expected to be covered within the PhD thesis. Lastly, both the theoretical and numerical work will be validated by comprehensive studies on real-world data from Oxford's test pilings at Yorkshire, Kent and Dunkirk.Areas of investment & support: This project falls within the 'EPSRC Ground Engineering research area'. References[1] G. Houlsby and A. Puzrin, "A thermomechanical framework for constitutive models for rate-independent dissipative materials," International Journal of Plasticity, vol. 16, no. 9, pp. 1017-1047, 2000. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S074964199900073X[2] T. Balaam, "Development and calibration of cyclic loading models for monopile foundations in clays," Ph.D. dissertation, Oxford University, 2020.[3] C. Abadie, "Cyclic lateral loading of monopile foundations in cohesionless soils," Ph.D. dissertation, Oxford University, 01 2015.[4] K. U. Kristiansen, "A review of multiple time scale dynamics: Fundamental phenomena and mathematical methods," 2023, in review.[5] C. Kuehn, "Multiple time scale dynamics with two fast variables and one slow variable," Ph.D. dissertation, Cornell University, 05 2010.[6] C. K. R. T. Jones, Geometric singular perturbation theory.

EPSRC项目标题：几何奇异摄动理论在超塑性加速棘轮模型中的应用一种研究侧向载荷的方法是Orsted和牛津大学合作开发的超塑性加速棘轮模型（HARM）框架[1-3]。使用HARM可以研究地基的荷载响应作为应力的函数。求解位移作为横向载荷的函数是一个问题，其中在结构的寿命期间施加了许多不同幅度的循环（由于波浪等），并且由于载荷偏离主要风向，棘轮效应是经常观察到的[1]。拟议的博士论文的目的是显着减少模拟时间模拟循环加载，这样，扩展系列的卸载/可以在桩设计的优化阶段引入再加载循环。所使用的方法的目标是几何奇异摄动理论（GSPT）的某种变体[4-6]。在我的硕士论文中，我们利用GSPT框架证明了一个相关的慢-快动力系统的存在性，该系统等价于HARM模型的连续版本，其中临界流形的双曲性与每个周期的卸载和重装部分对齐。这一结果可以直接解决目前面临的一些长期棘轮效应和预期滞后分析问题[7]。对于HARM的0-D宏观建模方法，[7]中发现的慢-快动力系统极大地推动了两个主要方向：-首先，研究GSPT作为独立工具的性能，以获得经验棘轮沿着桩深的可积（从而分析）和非保守上限。如果这些结果与收集的实验/模拟一致，则可以将其用作直接设计参数。- 其次，研究了如何利用HARM模型对当前数值求解器变得僵硬的确切位置的知识。一个想法是分别对快部件和慢部件建模并将它们粘在一起-避免机器编号精度的问题。在文献[7]中，我们只证明了具有塑性表面的0维宏观模型存在一个慢-快系统。为了与目前使用的数值解保持一致并提高复杂性，博士学位的主要部分也将是将理论结果扩展到更高的维度（或新的本构模型，如HySand）。由于土壤建模一般是复杂的，预计我们将达到理论工作的边界点。“直到那时”达到的结果可能会激励新的数值方法，也预计将在博士论文中涵盖。最后，无论是理论和数值计算的工作将验证牛津大学的测试桩在约克郡，肯特和敦刻尔克的真实世界的数据进行全面的研究。投资和支持领域：该项目福尔斯属于“EPSRC地面工程研究领域”。参考文献[1] G. Houlsby和A. Puzrin，“一个热机械框架的本构模型的率无关耗散材料，”国际塑性杂志，第16卷，第9期，第17页。1017-1047，2000。[联机]。可用网址：https：//www.sciencedirect.com/science/article/pii/S074964199900073X [2] T. Balaam，“粘土中可压缩地基循环荷载模型的开发和校准”，博士。毕业论文，牛津大学，2020年。[3]C. Abadie，“无粘性土中地基的循环侧向荷载”，博士。毕业论文，牛津大学，2015年1月。[4]K.联合Kristiansen，“多时间尺度动力学的回顾：基本现象和数学方法”，2023年，回顾。[5]C. Kuehn，“具有两个快变量和一个慢变量的多时间尺度动力学”，博士。博士论文，康奈尔大学，2010年5月。[6]C. K. R. T.琼斯，几何奇异摄动理论。