Two-scale finite element method for piezoelectric problem in periodicstructure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element...     

特殊二元生成t-半群

主要考虑了满足生成关系xy=x^2=yx，或者yx=y=yx的二元生成t-半群，给出了它的三个等价条件，并且定义了局部循环半群，可分半群，不可分半群，及条件P^*，条件A^*。从而给出循环半群的等价刻画。这些都可看作文[2]关于循环t-半群结论的推广。为使某些引理，命题或定理的作用更为明朗。本文还举出相应的例题来体现所述目的。     

周期孔洞区域中热力耦合问题的双尺度有限元计算

复合材料的研究中经常遇到具有周期孔洞结构的材料,由于区域的小周期性及剧烈振荡性,用传统的有限元计算方法来计算这些材料对应的问题时需要大量的计算机存储空间及计算时间.对这类材料的热力耦合问题给出了一种新型的高阶双尺度渐近解,得到了对应的均匀化常数、均匀化方程及对应的有限元算法.数值算例表明,周期单胞的局部结构对局部应力与应变有较大的影响.算法对数值模拟这类材料的力学行为是高效和可行的. 关键词： 双尺度方法 热力耦合 周期孔洞区域 有限元方法     

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic structure under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.     

周期结构区域中压电问题的双尺度有限元方法

近年来纤维压电复合材料的力电性能预测已发展为一个重要的研究领域．对力电耦合周期结构的复合材料问题,通过引入匹配的边界层得到了电势与位移解的新型双尺度有限元计算方法,建立了电势与位移的双尺度耦合关系,分析了双尺度有限元解的误差.数值算例验证了方法的有效性．