论文标题
部分可观测时空混沌系统的无模型预测
Homogenization with quasistatic Tresca's friction law: qualitative and quantitative results
论文作者
论文摘要
摩擦接触的建模对于研究不同服务环境下的复合材料的机械性能至关重要。该论文认为具有强烈异质系数和绝对的TRESCA摩擦法的线性弹性系统，并研究了H-Convergence和少量$ε$ - $ - 过时性的均化理论。定性结果是基于H-连接的，它显示原始振荡溶液将弱收敛到均质溶液，而我们的定量结果为定期均质化提供了$ H^1 $ norm中渐近错误的估计值。本文还设计了几个数值实验，以验证定量分析中的收敛速率。
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law, and studies the homogenization theories under the frameworks of H-convergence and small $ε$-periodicity. The qualitative result is based on H-convergence, which shows the original oscillating solutions will converge weakly to the homogenized solution, while our quantitative result provides an estimate of asymptotic errors in $H^1$-norm for the periodic homogenization. This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.
