小周期孔洞区域中一类压电问题的均匀化分析

压电复合材料在传感器、航空航天和半导体材料等领域的应用越来越广泛，对这些材料的研究引起了很多学者的关注．文章利用双尺度渐近展开的方法和均匀化方法，对一类具有小周期孔洞结构区域中的压电耦合问题，进行了其对应的均匀化力学及电学常数的正则性的分析，讨论了均匀化解的存在唯一性．在理论研究中为对应材料的等效力学、电学常数计算提供了理论与计算依据，刻画了材料的等效物理行为；在数值计算中，为进一步得到高精度的数值解提供了理论支持与算法依据．

Homogenization analysis for one new kind of piezoelectric problem in periodic perforated domain

Piezoelectric composite materials have been widely used in sensors, aeronautics and semiconductor materials. The analysis of effective mechanic and electric behaviors for piezoelectric composites in periodic perforated domain has been developed to a new research field. Based on the two-scale method and homogenization method, the ellipticities and symmetries of homogenization constants of piezoelectric problem in perforated do- main are analyzed and the xistence and uniqueness of homogenization equations are proved. In theoretic research, the result could be taken as the scientific basis, and in numerical simulation the result could be applied to construct the high effective numerical solutions for these problems.