On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator
On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator
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关于将 Moreau 扫掠过程简化为 Prandtl-Ishlinskii 算子的几何条件
DOI：
10.3934/dcdsb.2018246
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发表时间：
2016
影响因子：
1.2
通讯作者：
D. Rachinskii
中科院分区：
文献类型：
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作者：
D. Rachinskii
扫掠过程是由J. J. Moreau提出的，作为弹塑性体准静态过程的一般数学形式。这种形式主义处理连接普朗特的弹性理想塑性弹簧，它可以形成一个系统与任意复杂的拓扑结构。该模型将弹簧的应力和伸长之间的复杂关系描述为多维微分包含（变分不等式）。另一方面，Prandtl-Ishlinskii模型假设弹簧的连接非常简单。该模型的结果在一个输入输出算子，它具有许多良好的数学性质，并承认一个显式的解决方案，为任意的输入。结果表明，即使弹簧系统的拓扑结构很复杂，扫描过程也可以约化为Prandtl-Ishlinskii算子。在这项工作中，我们分析的条件，这样的还原。
The sweeping process was proposed by J. J. Moreau as a general mathematical formalism for quasistatic processes in elastoplastic bodies. This formalism deals with connected Prandtl's elastic-ideal plastic springs, which can form a system with an arbitrarily complex topology. The model describes the complex relationship between stresses and elongations of the springs as a multi-dimensional differential inclusion (variational inequality). On the other hand, the Prandtl-Ishlinskii model assumes a very simple connection of springs. This model results in an input-output operator, which has many good mathematical properties and admits an explicit solution for an arbitrary input. It turns out that the sweeping processes can be reducible to the Prandtl-Ishlinskii operator even if the topology of the system of springs is complex. In this work, we analyze the conditions for such reducibility.