不同理论下广义压电热弹性问题的有限元求解

SOLVING GENERALIZED PIEZOTHERMOELASTIC PROBLEM BY FEM WITH DIFFERENT THEORIES

基于G-L和L-S广义压电热弹性理论研究了无限大厚压电板在上下表面受到条带状热冲击时的广义压电热弹性问题．在时间非常短的情况下,为避免积分变换求解带来的精度丢失,采用有限元方法对问题在时间域进行直接求解,获得压电板在热冲击作用下的温度、位移、应力及电势等,并将结果与经典压电热弹性理论进行比较．结果表明,直接求解方法可以准确描述热在介质中以有限的速度传播．

The generalized piezothermoelastic coupled governing equations are formulated in generalized thermoelasticity theories： G-L theory and L-S theory. For a short time duration, the finite element method is proposed to solve the partial differential equations directly in the time domain. The developed method is applied to a two-dimensional generalized piezothermoelastic problem of a thick piezoelectric plate of infinite extent subjected to thermal shock on its surface. Temperature distributions as well as displacement, stress and electric potential distributions are obtained and represented graphically. Comparisons are macle with the results predicted by the classical piezothermoelastic theories. It is shown that the present method is an effective and exact numerical analysis method for the generalized piezothermoelastic problem.