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首页> 外文会议>American Society of Mechanical Engineers(ASME)/Society of Tribologists and Lubrication Engineers(STLE) International Joint Tribology Conference 2004(IJTC 2004) vol.1 pt.A; 20041024-27; Long Beach,CA(US) >NON-UNIQUENESS, EIGENVALUE SOLUTIONS AND WEDGED CONFIGURATIONS INVOLVING COULOMB FRICTION
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NON-UNIQUENESS, EIGENVALUE SOLUTIONS AND WEDGED CONFIGURATIONS INVOLVING COULOMB FRICTION

机译：涉及库仑摩擦的非唯一性，特征值解决方案和楔形构造

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摘要

It is well known that the conventional Coulomb friction condition can lead to non-uniqueness of solution in elastostatic solutions if the friction coefficient is sufficiently high. Interest in this field has centered on discrete formulations, particularly with reference to the finite element method. More recently Hild has demonstrated the existence of a multiplicity of non-unique solutions to a simple problem in two-dimensional continuum elasticity and showed how to determine the conditions for such states to exist by formulating an eigenvalue problem. Both the discrete and continuum examples of non-uniqueness seem to be related to the well known physical phenomenon whereby a frictional system can become locked or 'wedged' in a state of stress even when no external loads are applied (the homogeneous problem), but the equivalence is not complete because of the influence of unilateral inequalities in the physical problem. We shall discuss the relations between these concepts in the context of simple continuum and discrete problems in two-dimensional linear elasticity.
机译：众所周知，如果摩擦系数足够高，常规的库仑摩擦条件会导致弹性体溶液中溶液的不唯一性。该领域的兴趣集中在离散公式上，尤其是在有限元方法方面。最近，希尔德（Hild）证明了二维连续弹性中一个简单问题的多个非唯一解的存在，并展示了如何通过表述特征值问题来确定此类状态存在的条件。非唯一性的离散实例和连续实例都似乎与众所周知的物理现象有关，通过这种现象，即使没有施加外部载​​荷（均匀问题），摩擦系统也可以在应力状态下锁定或“楔入”，但是由于物理问题中单方面不平等的影响，等价不完全。我们将在简单连续体和二维线性弹性离散问题的背景下讨论这些概念之间的关系。

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