中文摘要：

功能梯度压电材料（FGPM）是一类材料特性连续变化的力电耦合材料.由于材料性能的不均匀性,相应的力学分析具有很大挑战.基于混合扩展多尺度有限元法（MEMsFEM）建立了FGPM力电耦合问题的分析模型.采用传统多尺度有限元法构造电势多尺度基函数,用扩展多尺度有限元法在不同坐标方向构造位移多尺度基函数,并通过引入耦合附加项考虑各坐标方向位移场间的耦合作用.多尺度基函数的构造可以有效捕捉材料的非均质性,由此可以在粗尺度上对问题进行求解,明显减少了计算量.最后通过数值算例验证了MEMs FEM的有效性和高效性.文中模型为功能梯度材料力学行为的数值模拟提供了有效途径.

英文摘要：

Functionally graded piezoelectric material （FGPM） is an electromechanical coupling material of conti- nuous property variation. Due to the heterogeneity of the FGPM property, investigating the mechanics of this mate- rial has posed a great challenge. In this paper, an analytical model describing the electromechanical coupling of the FGPM is constructed based on the mixed extended multi-scale finite element method （MEMsFEM）. In the model, the multi-scale base functions of electrical fields are set up by using the traditional multi-scale finite element method, and the muhi-scale base functions of displacement fields in different directions are set up by using the ex- tended multi-scale finite element method. Moreover, the coupling terms are introduced to model the coupling a- mong the displacement fields in different directions. Since constructing multi-scale base functions helps capture the material heterogeneity effectively, it is feasible to solve the problem in a coarse grid scale, which can significantly reduce the computation amount. Finally, the proposed method is proved to be effective and efficient by numerical examples. It is thus concluded that the proposed method provides an effective approach to simulating the mechani- cal behaviors of functionally graded materials.