Non-Standard Plate and Shell Models in Solid Mechanics

固体力学中的非标准板壳模型

• 批准号: 1538228
• 负责人: David Steigmann
• 金额: $ 40万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1538228&HistoricalAwards=false
• 关键词: Non; Standard; Plate; Shell; Models

Plate and shell theories are fundamental to the field of structural mechanics. They are essentially two dimensional representations of thin structures and afford a convenient and effective means for engineers to analyze the strength and safety of diverse types of components, ranging from the domes of buildings to aircraft fuselages, ship hulls and automobile bodies. Thin shells also constitute the basic components of an enormous range of biological structures, including cells, bones and parts of the eye, to name just a few. Thin structures are ubiquitous in nature and technology because they afford by far the most efficient arrangements for sustaining loads while minimizing weight. Current engineering theories for plate and shell structures are based on plausible assumptions about how the material of the plate deforms in three dimensions, to aid in the formulation of a tractable two-dimensional model. However, it is known that these assumptions are sometimes not realized in practice. This award supports fundamental advances in these theories that do not rely on such assumptions, while taking into account the effects of plasticity and fiber reinforcement in the constituent materials. Results from this research will enable the analysis of more efficient aerospace, automotive and civil structures, and will therefore benefit the U.S. economy and society in general. The techniques established here will provide engineers with improved analysis tools and will also benefit emerging fields such as biomechanics. These methods and results will be disseminated in the form of a monograph currently in progress, and through course lectures and specialized short courses.Modern work on theories of plates and shells emphasizes rigorous dimension reduction procedures such as asymptotic expansions or gamma convergence. These are invariably based on the underlying assumption that the plate or shell behaves elastically. In contrast, in the older literature one finds models that account for more general material behavior, such as plasticity and the anisotropy induced by fiber reinforcement, albeit based on ad hoc assumptions about the underlying kinematics which may not be realized in general applications. The present research is designed to fill the gap between existing models that address such effects in ad-hoc approaches, and modern models that are confined to purely elastic behavior but are overall more rigorous. The research therefore has the potential to significantly expand the reach of structural and solid mechanics. The research team will define new models for the inelastic behavior in shells, based on dimension reduction approaches, to include plasticity and diffusion of species within the shell material. The team will also establish models that account for the effects of intrinsic flexural and torsional stiffness of the fibers in fiber-reinforced plates and shells. This is expected to yield a substantial improvement over existing theories that account only for the anisotropy conferred by the fibers. These theoretical advances will be supported by extensive numerical simulations.

板壳理论是结构力学的基础.它们本质上是薄结构的二维表示，为工程师提供了一种方便有效的手段来分析各种类型的组件的强度和安全性，从建筑物的圆顶到飞机机身，船体和汽车车身。薄壳也构成了大量生物结构的基本组成部分，包括细胞，骨骼和眼睛的部分，仅举几例。薄结构在自然界和技术中无处不在，因为它们提供了迄今为止最有效的结构，可以在最小化重量的同时承受载荷。当前板壳结构的工程理论是基于关于板的材料如何在三维中变形的合理假设，以帮助制定易于处理的二维模型。然而，众所周知，这些假设在实践中有时并不现实。该奖项支持这些理论的根本性进展，这些理论不依赖于这些假设，同时考虑到构成材料中塑性和纤维增强的影响。这项研究的结果将使更有效的航空航天，汽车和民用结构的分析，因此将有利于美国经济和社会的整体。这里建立的技术将为工程师提供改进的分析工具，也将有利于新兴领域，如生物力学。这些方法和结果将以目前正在编写的专著的形式，并通过课程讲座和专门的短期课程加以传播。现代工作的板壳理论强调严格的降维程序，如渐近展开或伽玛收敛。这些都是基于板或壳的弹性行为的基本假设。相比之下，在旧的文献中，人们发现模型，占更一般的材料行为，如塑性和纤维增强引起的各向异性，尽管基于特设的假设，可能无法实现在一般应用程序的基础运动学。本研究旨在填补现有模型之间的差距，解决这种影响的特设的方法，现代模型，仅限于纯弹性行为，但总体上更严格的差距。因此，这项研究有可能显着扩大结构和固体力学的范围。研究小组将根据降维方法定义壳体非弹性行为的新模型，以包括壳体材料内的塑性和物种扩散。该团队还将建立模型，解释纤维增强板和壳中纤维的固有弯曲和扭转刚度的影响。预计这将产生一个实质性的改进，现有的理论，只占各向异性赋予的纤维。这些理论进展将得到广泛的数值模拟的支持。