标题： 分布应力平衡条件的一些后果 显示英文标题

标题： Some Consequences of the Distributional Stress Equilibrium Condition

摘要： 我们推导了应力平衡条件的分布形式的两个结果，同时结合了分段光滑的应力和体力场以及在界面上的奇异集中。 首先，我们得到了体内的局部平衡条件和界面上的平衡条件，后者包括界面上的应力和应力偶极子的条件。 其次，我们得到了非光滑无散度应力场的必要条件和充分条件，以使得存在一个应力函数场，从而使平衡条件被显然满足。 在此过程中，我们允许区域是不可收缩的，并且具有互不相连的边界组成部分。 这两个推导展示了分布理论在处理奇异应力场中的实用性。 显示英文摘要

摘要： We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First we obtain the local equilibrium conditions in the bulk and at the interface, the latter including conditions on the interfacial stress and stress dipole. Second we obtain the necessary and the sufficient conditions on the divergence-free non-smooth stress field for there to exist a stress function field such that the equilibrium is trivially satisfied. In doing so we allow the domain to be non-contractible with mutually disjoint connected boundary components. Both derivations illustrate the utility of the theory of distributions in dealing with singular stress fields.