关于Hill-Ogden通用菌株的注意事项
1Department of Mechanical & Manufacturing Engineering, University of Calgary, Calgary, AB, Canada.
概括
本研究回顾了Hill-Ogden通用应变张量及其在曲线坐标中的表示. 它探讨了特定的几何上下文的协变和反变元件.
科学领域:
- 连续力学 连续力学
- 不同几何学微分几何学
背景情况:
- 一般化的应变张器对于描述材料变形至关重要.
- 在曲线坐标中表示这些张量具有独特的挑战.
研究的目的:
- 为了提供希尔-奥格登通用应变张器的概述.
- 以共变形式主义来讨论它们在通用 (曲线) 坐标中的表示.
- 探索这种形式主义对里曼的多样性的适应性.
主要方法:
- 对希尔-奥格登通用应变张量公式的审查.
- 在一般化 (曲线) 坐标中对张量表示的分析.
- 完全共变形式主义的应用.
主要成果:
- 希尔-奥格登通用应变张器可以自然地用共变量或对变量组件定义.
- 每个组件类型 (共变/对变) 最适合特定的几何环境.
- 协变形式主义可以适应关于里曼的多样性的更一般的理论.
结论:
- 了解共变和反变组件的双重性质是选择适当表示的关键.
- 协变形式主义为曲空间上的高级连续力学提供了一个灵活的框架.
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