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Analysis and control of stationary inclusions in contact mechanics
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2021-04-14 , DOI: 10.1016/j.nonrwa.2021.103335
Mircea Sofonea

We start with a mathematical model which describes the frictionless contact of an elastic body with an obstacle and prove that it leads to a stationary inclusion for the strain field. Then, inspired by this contact model, we consider a general stationary inclusion in a real Hilbert space, governed by three parameters. We prove the unique solvability of the inclusion as well as the continuous dependence of its solution with respect to the parameters. We use these results in the study of an associated optimal control problem for which we prove existence and convergence results. The proofs are based on arguments of monotonicity, compactness, convex analysis and lower semicontinuity. Then, we apply these abstract results to the mathematical model of contact and provide the corresponding mechanical interpretations.



中文翻译:

接触力学中固定夹杂物的分析与控制

我们从描述弹性体与障碍物的无摩擦接触的数学模型开始,并证明它导致了应变场的平稳包含。然后,受此接触模型的启发,我们考虑由三个参数控制的真实希尔伯特空间中的一般平稳包含。我们证明了夹杂物的独特可溶性以及其溶液相对于参数的连续依赖性。我们将这些结果用于相关的最优控制问题的研究中,以此证明存在性和收敛性结果。证明是基于单调性,紧致性,凸分析和较低半连续性的论据。然后,我们将这些抽象结果应用于接触的数学模型,并提供相应的力学解释。

更新日期:2021-04-14
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