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Chapter 7 Frictional Contact Problems for Thin Elastic Structures and Weak Solutions of Sweeping Process

机译:第7章薄弹性结构的摩擦接触问题和清扫过程的弱解

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摘要

The linearized equilibrium equations for straight elastic strings, beams, membranes or plates do not couple tangential and normal components. In the quasi-static evolution occurring above a fixed rigid obstacle with Coulomb dry friction, the normal displacement is governed by a variational inequality whereas the tangential displacement is seen to obey a sweeping process, the theory of which was extensively developed by Moreau in the 70s. In some cases, the underlying moving convex set has bounded retraction and, in these cases, the sweeping process can be solved by directly applying Moreau's results. However, in many other cases, the bounded retraction condition is not fulfilled and this is seen to be connected to the possible event of moving velocity discontinuities. In such a case, there are no strong solutions and we have to cope with weak solutions of the underlying sweeping process.
机译:直线弹性线,梁,膜或板的线性平衡方程不耦合切向分量和法向分量。在库仑干摩擦作用下,在固定刚性障碍物上方发生的准静态演化中,法向位移受变分不等式的控制,而切向位移服从扫掠过程,该理论在20世纪70年代由摩尔(Moreau)广泛发展。 。在某些情况下,基础移动凸集具有一定的缩回,在这些情况下,可以通过直接应用Moreau的结果来解决扫掠过程。但是,在许多其他情况下,没有满足有限的缩回条件,这被认为与运动速度不连续的可能事件有关。在这种情况下,就没有强大的解决方案,而我们必须应对潜在的席卷过程的弱解。

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  • 来源
  • 会议地点 Chania(GR)
  • 作者

    Patrick Ballard;

  • 作者单位

    Laboratoire de Mecanique et d'Acoustique, 31 Chemin Joseph Aiguier,13402 Marseille Cedex 20, France;

  • 会议组织
  • 原文格式 PDF
  • 正文语种 eng
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