论文标题
周期性域中的变性罗宾型牵引力问题
A degenerating Robin-type traction problem in a periodic domain
论文作者
论文摘要
我们考虑具有周期性空隙的线性弹性材料。在空隙的边界上，我们设置了罗宾型牵引条件。然后，当罗宾条件变成纯牵引力时，我们研究了位移溶液的渐近行为。对机智而言，将有一个矩阵函数{$ b [k]（\ cdot）$在分析上取决于真实参数$ k $，而以$ k = 0 $的形式消失，我们将类似于Robin条件的Dirichlet部分乘以$ b [k]（\ cdot）$}。我们表明，可以用$ k $的功率系列来编写排量解决方案，该$ k $在整个社区中以$ 0 $ $ 0 $ 0的价格汇合。为了进行分析，我们使用功能分析方法。
We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then we investigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function {$b[k](\cdot)$ that depends analytically on a real parameter $k$ and vanishes for $k=0$ and we multiply the Dirichlet-like part of the Robin condition by $b[k](\cdot)$}. We show that the displacement solution can be written in terms of power series of $k$ that converge for $k$ in a whole neighborhood of $0$. For our analysis we use the Functional Analytic Approach.
