Bifurcation Analysis for Large Problems: Algorithms, Software Applications to Micro Electro Mechanical Systems (MEMS)

大问题的分岔分析：微机电系统 (MEMS) 的算法、软件应用

• 批准号: 0209536
• 负责人: Mark Friedman
• 金额: --
• 依托单位: University of Alabama in Huntsville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2006-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0209536&HistoricalAwards=false
• 关键词: Bifurcation; Analysis; Large; Problems; Algorithms

Nonlinear equations depending on parameters are the basis for many scientific and engineering problems. The principal approach of numerical bifurcation analysis is based on continuation of solutions to well-defined operator equations. Such computational results give a deeper understanding of the solution behavior, stability, multiplicity, and bifurcations. This project is concerned with development of new algorithms and software for bifurcation analysis in large nonlinear systems and applications to MicroElectroMechanical Systems (MEMS). Typical MEMS devices lead to multiscale-multiphysics problems. These devices include coupled mechanical, electrical, thermal and other parts. In addition to the bifurcations like beam buckling which involve a single type of physics, MEMS also exhibit bifurcations due to interactions between different energy domains. Bifurcations in MEMS play a variety of roles: (i) bifurcation as a failure mode (lead systems to fail), (ii) bifurcation as a design feature (i.e. bistable systems), (iii) bifurcations to extract material properties.From the engine of an automobile to a hospital operating room, MicroElectroMechanical (MEMS) products are finding applications in every aspect of our lives at an increasing rate. SUGAR is a new system level simulation program in MATLAB for three-dimenisonal MEMS developed at the University of California Berkeley. It is already widely used in academia and industry and is currently under active development, which is a part of the revolution in the MEMS design. SUGAR will be made freely available in source and as a web service. New algorithms for bifurcation analysis in MEMS will be implemented in MATLAB, and then the resulting new code will be incorporated into a MATLAB continuation toolbox, developed at Universiteit Utrecht, to enhance its capabilities for bifurcation analysis of large systems. The upgraded MATLAB continuation toolbox will be integrated into SUGAR and will become a part of the MEMS design loop which includes design, simulation, fabrication, laboratory measurements, and comparison of simulation with measurements.

含参数的非线性方程组是许多科学和工程问题的基础。数值分歧分析的主要方法是基于定义良好的算子方程的解的延拓。这样的计算结果给出了更深入的了解的行为，稳定性，多重性和分歧。本计画主要研究大型非线性系统之分岔分析新演算法与软体，并应用于微机电系统。典型的MEMS器件导致多尺度多物理问题。这些设备包括耦合的机械、电气、热和其他部分。除了像梁屈曲这样涉及单一类型物理的分叉之外，MEMS还表现出由于不同能量域之间的相互作用而导致的分叉。分叉在MEMS中扮演着各种角色：（i）分叉作为一种失效模式（导致系统失效），（ii）分叉作为一种设计特征（即分叉系统），（iii）分叉提取材料特性。从汽车发动机到医院手术室，微机电（MEMS）产品正在以越来越快的速度应用于我们生活的各个方面。SUGAR是美国加州伯克利大学开发的一个新的三维MEMS系统级仿真软件。它已经广泛应用于学术界和工业界，目前正在积极开发中，这是MEMS设计革命的一部分。SUGAR将以源代码和网络服务的形式免费提供。MEMS分叉分析的新算法将在MATLAB中实现，然后产生的新代码将被纳入乌得勒支大学开发的MATLAB延续工具箱中，以增强其大型系统分叉分析的能力。升级后的MATLAB延续工具箱将被集成到SUGAR中，并将成为MEMS设计循环的一部分，包括设计、仿真、制造、实验室测量以及仿真与测量的比较。