一类Signorini问题的边界变分不等式

本文讨论了一类简化的Signorini问题。首先将原问题和一个边值问题建立联系，其次将原问题的解分解为不带不等边界条件的变分方程的解和一个变分不等式的解。然后利用边值问题的边界积分方程将变分不等式等价地化解为边界变分不等式。这样原求区域上的第一类椭圆变分不等式问题化解为求一个区域上的变分方程和一个边界变分不等式。最后说明了边界变分不等式解的存在唯一性。文末计算了柱面和半无限刚性基础的摩擦接触问题。结论表明文中方法具有较好的精度。

Boundary Variational Inequality for a Kind of Signorini Problem

A kind of simplified Signorini problem was discussed. First, the equivalent boundary value problem was yielded. Next, the original solution as two ones was separated, one is the solution of variational equation on region, which has no inequality boundary condition; another is the solution of a variational inequality. Using the boundary integration equation for the equivalent boundary value problem, the variational inequality was reduced as a boundary variational inequality. By this way the elliptic variational inequality of first kind on a certain region was transformed into a variational equation and a boundary variational inequality. The existence and uniqueness for the solution of boundary variational equality was also shown. Finally the frictional contact of an elastic cylinder with rigid foundation was discussed. It reveals that our result is more accurate than those predicted by other method.