准晶数学弹性理论和某些有关研究的进展(上)

范天佑

doi:10.6052/1000-0992-11-168

准晶数学弹性理论和某些有关研究的进展(上)

doi: 10.6052/1000-0992-11-168

范天佑^,

北京理工大学物理学院, 北京 100081

基金项目: 国家自然科学基金项目(10372016,10672022)资助

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通讯作者:
范天佑

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- 文章访问数: 2273
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- PDF下载量: 1660
- 被引次数: 0
出版历程
- 收稿日期: 2011-12-01
- 修回日期: 2012-07-12
- 刊出日期: 2012-09-25

DEVELOPMENT ON MATHEMATICAL THEORY OF ELASTICITY OF QUASICRYSTALS AND SOME RELEVANT TOPICS

FAN Tianyou^,

School of Physics, Beijing Institute of Technology, Beijing 100081, China

Funds: The project was supported by the National Natural Science Foundation of China (10372016, 10672022).

More Information

Corresponding author: FAN Tianyou

摘要

摘要: 本文对固体准晶力学性能和准晶数学弹性, 塑性, 断裂以及有关研究的进展作了评论, 尤其对材料常数和塑性变形行为的测量, 一维、二维、三维准晶弹性理论, 动力学、非线性、缺陷理论、准晶弹性新型偏微分方程的推导和精确分析解, 复分析方法, 变分原理和有限元方法, 有限差分方法这些宏观问题和它们的数学方法进行了分析, 同时对准晶晶格动力学问题的数学理论也作了初步讨论. 近来在软物质中发现了12 次和18次对称准晶, 意义重大, 这里也做了初步介绍. 文中重点讨论此领域最近这些年来中国科学工作者的工作.
- 准晶 /
- 弹性 /
- 塑性 /
- 缺陷 /
- 动力学 /
- 精确解
Abstract: This paper gives an introduction to the development on mathematical theory of elasticity of quasicrystals and some relevant topics, in which the physical framework of elasticity is discussed first, the measuremental data of material constants for quasicrystals in solid phase are one of the most important basis to the theory and applications and are listed in detail. As the fundamental points, the analytic methods and exact solutions for various boundary value or boundary-initial value problems are summarized, the Chinese researchers contributed the effort in this respect. Apart from elasticity, dynamics and plasticity of the novel material are also discussed. At last the paper offers a simple description on a possible theoretical treatment, from the view point of elasticity and hydrodynamics, to quasicrystals in soft matter phase observed very recently.

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参考文献(65)

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准晶数学弹性理论和某些有关研究的进展(上)

doi: 10.6052/1000-0992-11-168

通讯作者:
范天佑

计量

DEVELOPMENT ON MATHEMATICAL THEORY OF ELASTICITY OF QUASICRYSTALS AND SOME RELEVANT TOPICS

Corresponding author: FAN Tianyou

计量

目录

留言板

准晶数学弹性理论和某些有关研究的进展(上)

doi: 10.6052/1000-0992-11-168

通讯作者: 范天佑

计量

出版历程

DEVELOPMENT ON MATHEMATICAL THEORY OF ELASTICITY OF QUASICRYSTALS AND SOME RELEVANT TOPICS

Corresponding author: FAN Tianyou

计量

出版历程

目录

通讯作者:
范天佑