论文标题
具有周期性高对比度的线性弹性系统的均匀收敛性
Uniform convergence for linear elastostatic systems with periodic high contrast inclusions
论文作者
论文摘要
我们考虑了与背景介质相比，弹性参数的line弹性弹性系统具有定期分布的夹杂物的对比度很高。当将弹性夹杂物的某些参数发送到极端值时，我们基于层电位技术开发了一种统一的方法来量化三个收敛结果。更准确地说，我们研究了不可压缩的包含物限制，其中包含物的大量模量趋于无穷大，软包裹物限制了块状模量和剪切模量均趋于零，而硬夹杂物却限制了剪切模量趋于无穷大。我们的方法产生的收敛速率与夹杂物阵列的周期性无关，并且比这种类型的一些早期结果更加明显。证明的一个关键要素是，与与周期性无关的周期性夹杂物相关的弹性neumann-Poincare操作员建立了统一的光谱差距。
We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a unified method based on layer potential techniques to quantify three convergence results when some parameters of the elastic inclusions are sent to extreme values. More precisely, we study the incompressible inclusions limit where the bulk modulus of the inclusions tends to infinity, the soft inclusions limit where both the bulk modulus and the shear modulus tend to zero, and the hard inclusions limit where the shear modulus tends to infinity. Our method yields convergence rates that are independent of the periodicity of the inclusions array, and are sharper than some earlier results of this type. A key ingredient of the proof is the establishment of uniform spectra gaps for the elastic Neumann-Poincare operator associated to the collection of periodic inclusions that are independent of the periodicity.
