Mathematical Sciences: Global Continuation Methods in Nonlinear Elasticity

数学科学：非线性弹性中的全局延拓方法

• 批准号: 9625830
• 负责人: Timothy Healey
• 金额: $ 2.13万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625830&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Global; Continuation; Methods

6/3/96 Dear Dr. Hariharan: Our Department Financial Assistant is now working up a new budget in accordance with your recommendations from today. She will mail it out sometime tomorrow for your non-official approval, before we sign it, etc. Is a Text format OK for this, or would it be better to fax it to you? I am prepared to make a best effort attempt to meet the original scope of the work, given the reduced budget. Here is the abstract that you requested: ************* DMS-9625830: Global Continuation Methods in Nonlinear Elasticity P.I.: T.J.Healey Abstract. We plan to carry out research in global nonlinear analysis of partial differential equations of nonlinear elasticity. A major thrust of the proposed work will be focused on problems involving phase change (weak solutions and loss of ellipticity). The analysis of such models at a very general level is fundamental to the understanding of martensitic transformations and shape-memory effects, which are observed in many advanced engineering alloys. Some interesting problems of classical nonlinear elasticity will also be considered. The work has two major goals: (i) To obtain new qualitative results and detect new phenomena - of both mathematical and physical significance; (ii) To obtain new global-continuation (existence) results in problems of 2 and 3-dimensional elasticity - including problems involving phase transformations. In classical problems (rubber elasticity), tools developed by Healey and co-workers in previous NSF-sponsored work will play an important role. For phase-change problems, an entirely new approach based upon higher-gradient regularization, global continuation and singular limits is being proposed. Broadly speaking,the proposed work will provide important mathematical underpinnings to difficult nonlinear problems arising in traditional engineering fields like structural & mechanical engineering and also in more modern areas like materials scien ce. The work has the potential to: (i) provide new mathematical tools for the analysis of hard problems of engineering practice,leading ultimately to safer and more optimal design of structures; (ii) lead to a better understanding of the nonlinear material behavior of certain engineering alloys, with potential applications to manufacturing engineering and the design of non-passive or "smart" structures. ********* Let me know if this is not acceptable - I'll be happy to make changes. Thanks, Tim Healey

6/3/96亲爱的Hariharan博士：我们的部门财务助理现在根据您今天的建议制定新的预算。 她明天某个时候将其邮寄出您的非官方批准，在我们签署之前等等。 鉴于预算减少，我准备尽力实现最初的工作范围。 这是您要求的摘要：*********** DMS-9625830：非线性弹性中的全局延续方法P.I。：T.J.Healey摘要。 我们计划在非线性弹性的部分微分方程的全球非线性分析中进行研究。 拟议工作的主要力量将集中在涉及相变的问题上（弱解决方案和椭圆度丢失）。 对此类模型在非常一般的层面上的分析是对马氏体转换和形状内存效应的理解，这在许多高级工程合金中都可以观察到。 还将考虑一些古典非线性弹性的有趣问题。 这项工作有两个主要目标：（i）获得新的定性结果并检测到数学和身体意义的新现象； （ii）获得新的全球范围（存在）会导致2和3维弹性的问题 - 包括涉及相变的问题。 在经典问题（橡胶弹性）中，Healey和同事在以前的NSF赞助工作中开发的工具将发挥重要作用。 对于相变问题，正在提出一种基于较高梯度正则化，全球延续和奇异限制的全新方法。 从广义上讲，拟议的工作将为在结构和机械工程等传统工程领域以及在更现代的材料等领域等传统工程领域产生的困难非线性问题提供重要的数学基础。这项工作有可能：（i）提供新的数学工具来分析工程实践的严重问题，最终导致结构的更安全，更最佳的设计； （ii）可以更好地理解某些工程合金的非线性物质行为，并在制造工程中使用了潜在的应用以及非帕斯或“智能”结构的设计。 *********让我知道这是否是不可接受的 - 我很乐意进行更改。 谢谢，蒂姆·希利