在分数非局部中等中直线偏斜
Tamara Kyrylych1, Yuriy Povstenko1
1Department of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
Materials (Basel, Switzerland)
|May 7, 2025
概括
这项研究引入了一个新的非局部弹性理论,使用分数扩散绿色函数内核. 它成功地将压力场模拟在没有奇点的偏离周围,推进了连续力学.
科学领域:
- 连续力学 连续力学
- 非局部弹性理论 非局部弹性理论
- 数学物理 数学物理
背景情况:
- 经典弹性理论面临的挑战是小规模的材料行为.
- 非局部应力张量对于捕捉尺寸效应和奇点至关重要.
- 完整的表述对于非局部的构成关系是必不可少的.
研究的目的:
- 开发一种新的非局部弹性理论.
- 为了在直和扭曲偏斜线周围建模应力场.
- 消除应力场中的非物理奇点.
主要方法:
- 使用分数扩散方程的绿色函数作为非局部性内核.
- 应用拉普拉斯积分变换与非局部性参数相关.
- 在无限的介质中分析离谱的解决方案.
主要成果:
- 衍生应力场用于直和扭曲偏斜.
- 证明了当非局部性参数接近零时,从非局部向局部行为的过渡.
- 证实了在离谱线上没有非物理奇点的存在.
结论:
- 提出的非局部弹性理论有效地模拟了离线应力场.
- 使用分数扩散绿色函数内核提供了一个物理上有意义的方法.
- 这个框架提供了压力度的无奇点描述.
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