关键词: 灵敏度, 蒙特卡罗法, 热机电耦合, 数字仿真, 随机参数, 一次二阶矩法, 有限元法

Abstract: An element model including 4 displacement nodes, 2 electric potential nodes and 8 temperature nodes is presented. Its displacement field is defined by means of plane shell element model, and its electric potential field and temperature field are both defined by means of linear interpolation, the detailed element equations are deduced by using virtual work principle. Through the analytic solutions of sensitivities with respect to random parameters and first order second moment method, the numerical characteristics of natural frequencies, mode shapes, temperature field, displacement field and output voltages are solved in turn. Finally , an intelligent cantilever plate is taken as an example. The numerical results are compared with those of Monte Carlo method, the results show that the computing process presented is feasible and has very good precision.

Key words: Finite element method, First order second moment method, Monte Carlo method, Numerical simulation, Piezothermoelasticity, Random parameter, Sensitivity