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...     

一类小周期椭圆方程的三重尺度渐近分析

利用三重尺度方法对一类小周期椭圆方程进行了三重尺度渐近展开分析,构造了对应的三重尺度形式渐近展开式,得到了均匀化常数和均匀化方程.在形式渐近展开的基础上,构造了对应边值问题解的三重尺度渐近近似解,并分析了对应三重尺度形式渐近误差估计.     

Multi-scale analysis for the structure of composite materials with small periodic configuration under condition of coupled thermoelasticity

The two-scale asymptotic expression of the solution for the increment of temperature in a structure with a small periodic configuration is presented first, and the two-scale asymptotic expression of the displacement for the structure under the coupled thermoelasticity condition is then derived in this paper. In the asymptotic expressions the two-scale coupled relation between the increment of temperature and displacement is included. The approximate solutions and its error estimations are given. The project supported by the National Natural Science Foundation of China (19932030) and Special Funds for Major State Basic Research Projects     

微结构片外弯曲测试装置及试样设计

硅是微电子机械系统（简称微机电系统）中最常见的功能结构材料,可靠性是制约硅微构件小尺度加工和大规模制造的瓶颈问题．为研究硅微构件的力学特性,本文开发了一套以压电驱动、微力测量、位移检测为核心组件的片外测试系统．设计了一种将四个弯曲测试梁集于一体的微结构,借助有限元方法确定其尺寸,并用理论方法验证有限元分析的合理性．本文着重确保了四个关键设计目标：一、每根测试梁最大应力应位于其与外框架结合处;二、未断裂测试梁的最大应力受其他梁的断裂的影响应足够小;三、各个测试梁的最大应力的差别应足够小;四、支撑梁的最大应力应明显小于测试梁．最后测试了试样的弯曲强度,实验加载曲线和有限元分析基本吻合,表明测试装置和试样设计是合理的,为后续的硅微构件可靠性测试奠定了基础．     

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.     

Multi-scale FE computation for the structures of composite materials with small periodic configuration under condition of coupled thermoelasticity

In this paper, the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic (TSA) expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first, then the multi-scale finite element algorithms based on TSA are discussed. Finally the numerical results evaluated by the multi-scale computational method are shown. It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell. The project supported by the National Natural Science Foundation of China (19932030) and Special Funds for Major State Basic Research Projects     

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     

一种微构件拉伸测试系统及测试结构设计

微机电系统(Micro-Electro-Mechanical Systems,MEMS)的力学性能是研究MEMS可靠性的一个重要部分。目前,微结构片外拉伸测试的难点在于如何在实现较高精度的夹持和测试的同时能够较好地控制成本,这是本文着重解决的问题。首先,针对单晶硅各向异性湿法体硅工艺的特点,设计了一种新颖而经济的试样结构,利用力学分析确定其结构尺寸,通过有限元分析验证其合理性;其次,设计了一种简单经济的微结构片外拉伸测试系统;最后,加工出样本并进行准静载拉伸强度测试。结果表明:微梁尺寸增大,拉伸强度降低,同时验证了本装置在微结构拉伸准静载测试中的适用性。     

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．