中文摘要：

利用渐近展开的方法对具有一般周期结构的复合材料中描述压电现象的电势与位移建立了二阶双尺度渐近展开式及边界层解,得到了局部单胞内电场与位移场的相互耦合关系,并给出了复合材料中电势与位移的双尺度结合边界层的有限元计算方法。数值算例表明了该方法的可行性与高效性。

英文摘要：

By means of the asymptotic method,the two-order two-scale asymptotic expansions coupled with boundary layer of the electrical potential and the displacement were built for the structures of general periodic composites under piezoelectric condition,the coupled relation between the displacement field and the electric field within basic cell is given,and the finite element method and the algorithm of two-scale coupled with boundary layer of the displacement and the electrical potential are presented.The effectiveness and high efficiency is shown by some simple numerical examples.