论文标题
多面体清除过程的有限时间稳定性，并应用于弹性系统
Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems
论文作者
论文摘要
我们使用Adly-Attoych-Cabot的想法[Adv。机械。数学，第12期，施普林格，2006年]。弹性塑料弹簧带有位移控制的负载。我们表明，验证定理的状况最终会导致以下两个问题：（i）识别活动顶点``a'''或active face'a'a'的polyhedron the vector $ c'（t）$ points的``; （ii）计算$ c'（t）$到普通锥到``a''的多面体的距离。在任意弹性系统的情况下，我们提供了一个计算指南，以实现步骤（i） - （ii），并将指南应用于特定示例。由于特定示例的简单性，我们可以通过线性代数和次要组合物的方法来求解（i） - （ii）。
We use the ideas of Adly-Attoych-Cabot [Adv. Mech. Math., 12, Springer, 2006] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form $C+c(t).$ We then employ the ideas of Moreau [New variational techniques in mathematical physics, CIME, 1973] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex ``A'' or the active face ``A'' of the polyhedron that the vector $c'(t)$ points at; (ii) computing the distance from $c'(t)$ to the normal cone to the polyhedron at ``A''. We provide a computational guide to implement steps (i)-(ii) in the case of an arbitrary elastoplastic system and apply the guide to a particular example. Due to the simplicity of the particular example, we can solve (i)-(ii) by the methods of linear algebra and minor combinatorics.
