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：几何奇异扰动理论在增生性中的应用加速棘轮模型的方法在研究单型设计的侧向负载方面是增生加速的Racheting模型（HARM）在Orsted和Orsted和Oxford University之间的协作中开发的[1-3]。使用危害可以研究基础的负载响应，这是应力的函数。解决位移作为侧向载荷的函数的求解是一个问题，在该问题中，在结构的生命周期（由于波浪等）的寿命（由于波等）的偏见，在主要的风向上施加了许多不同的振幅周期，因此通常观察到棘轮，因此经常观察到[1] [1]。可以在桩设计的优化阶段引入周期。所使用的方法的目标是几何奇异扰动理论（GSPT）[4-6]。在我的主论文中，我们利用GSPT框架来证明存在相关的慢速动力学系统等于危害模型的连续版本，其中具有较大的流式模型，其中具有统一和相关性的临界表相位。该结果可能会针对某些目前面临的解决方案，并进行了长期棘轮和预期的磁滞分析[7]。对于危害的0-D宏建模方法，在[7]中发现的慢速动力学系统中，两个主要方向的动机很大程度上激发了： - 首先，一项针对GSPT作为独立工具的性能的研究，以获取沿桩深度的经验丰富的Ratchetets的可集成（分析）和非保守的上限。如果这些结果与收集的实验/模拟保持一致，则可以用作即时设计参数。 - 其次，一项有关利用危害模型在何处僵硬到当前数值求解器的知识的研究。一个想法是将快速和放慢的零件分开建模并将它们粘合在一起 - 避免使用机器编号精度的问题。这不仅可能导致更快的结果，而且更准确。为了与当前使用的数值解决方案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，例如hysand）。由于土壤建模是一般复杂的，因此可以预期我们达到理论工作的边界点。 “直到那时”的结果可能会激发新的数值方法，也有望在博士学位论文中涵盖。最后，理论和数值工作将通过对约克郡，肯特和敦刻尔克的牛津测试桩的现实数据的全面研究来验证。投资与支持方面：该项目属于“ EPSRC地面工程研究领域”。参考文献[1] G. Houlsby和A. Puzrin，“用于构成型独立耗散材料的本构模型的热机械框架”，《国际可塑性杂志》，第1卷。 16，不。 9，第1017-1047页，2000年。[在线]。可用：https：//www.sciendirect.com/science/article/pii/s07496419999900073x [2]论文，牛津大学，2020年。[3] C. Abadie，“无内核土壤中单只基础的循环横向负荷”，博士学位。论文，牛津大学，2015年1月1日。[4] K. U. Kristiansen，“对多个时间尺度动态的评论：基本现象和数学方法”，2023年，评论。[5] C. Kuehn，“具有两个快速变量和一个慢变量的多个时间尺度动力学”，博士学位。论文，康奈尔大学，2010年5月5日。[6] C. K. R. T. Jones，几何奇异扰动理论。