热机电耦合随机参数智能板结构的数值求解  

Randomicity analysis of the piezothermoelasticity intelligent thin plate by appling the numerical method

作　　者：王小兵[1] 陈建军[1] 梁震涛[1] 陈永琴[1] 谢永强[1] 

机构地区：[1]西安电子科技大学机电工程学院,陕西西安710071

出　　处：《西安电子科技大学学报》2008年第4期592-599,共8页Journal of Xidian University

基　　金：国家863项目资助(2006AA04Z402);陕西省自然科学基金资助(2005A009)

摘　　要：针对热机电压电薄板结构,提出了一种包含4个位移节点、2个电势节点和8个温度节点的体单元模型,其位移场按平板壳单元描述,而电势场和温度场则按线性插值方法描述,并基于虚功原理导出了热机电耦合有限元方程.当参数具有随机性而利用矩法求解响应量的数字特征时,为了避开"针对响应量的解析解进行灵敏度求解时运算艰难"这一问题,先将有限元方程转化为状态方程,再对状态方程求导而获得关于灵敏度的微分方程组,进而利用差分法对各个离散时刻的灵敏度进行了数值求解.以压电智能悬臂薄板为例,数值结果表明了所给的数字特征求解过程运算快捷且具有良好的精度.For the piezothermoelasticity intelligent thin plate, a cube finite element model including 4 displacement nodes, 2 electric potential nodes and 8 temperature nodes is presented, its displacement field is defined by means of the plane shell element model, and its electric potential field and temperature field are both defined by means of linear interpolation. The finite element equations are deduced by applying the virtual work principle. When parameters are random and the moment method is used to obtain response＇s numerical characteristics, in order to avoid the difficulty of sensitivities computation on the response＇s analytical solution, the finite element equations are translated to state equations, and the sensitivity differential equations are obtained from the derivative of state equations. Then, the sensitivity at each discrete time is obtained by making use of the deference method. An intelligent cantilever plate is taken as an example, and the numerical results show that the computing process presented has good precision and fast calculation speed.

关 键 词：热机电耦合 有限单元法 差分法 矩法 蒙特卡罗法 数字仿真 

分 类 号：O242.21[理学—计算数学]