对于粘性弹性中的爬行模型的前向和反向问题.
H Itou1, V A Kovtunenko2,3, G Nakamura4,5
1Department of Mathematics, Tokyo University of Science , Tokyo 162-8601, Japan.
概括
本研究证明了使用固定点定理对准静态粘弹性问题的解决方案的存在,并为准线性情况构建了半分析解决方案. 它还通过使用提霍诺夫规则化从测量中识别设计变量来解决反向问题.
科学领域:
- 固体机械学 固体机械学
- 材料科学 材料科学 材料科学
- 应用数学 应用数学 应用数学
背景情况:
- 粘弹性材料在压力下表现出时间依赖的机械行为.
- 非线性弹性描述了使用隐性,多值函数的应变反应.
- 了解粘性弹性对于设计结构和材料至关重要.
研究的目的:
- 分析依赖于时间的构成方程,用于在爬行过程中的粘弹性材料.
- 证明存在并构建准静态和准线性粘弹性问题的解决方案.
- 为了解决从测量中识别材料属性的反粘弹性问题.
主要方法:
- 对于强制和最大单调图的布劳德-明蒂定点定理的应用.
- 准线性粘弹性问题的半分析公式的构建.
- 提霍诺夫规则化在有界尺度和变形的空间中的反向问题.
主要成果:
- 已经证明了准静态粘弹性问题的解决方案的存在.
- 半分析解决方案是为准线性粘弹性问题构建的.
- 对于反向问题,可以得到一个非空的最佳变量集,以同otropic 核识别为例.
结论:
- 这项研究为分析粘弹性行为提供了严格的数学框架.
- 开发的方法适用于前向和反向粘弹性问题.
- 这项工作有助于理解力学中的非平滑变量问题.
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