耦合均载作用下的电磁热弹性简支圆板

耦合均载作用下的简支空心和实心圆板问题是一个经典问题,对于电磁热弹性材料尚无理论解。构造了5个含有待定常数的单调和函数,将其代入用单调和函数表示的横观各向同性电磁热弹性材料的通解,获得了表面力电磁热耦合均载作用下的简支空心圆板内耦合场的解,再将所得解代入边界条件获得确定待定常数的线性方程组。该解可以退化得到实心圆板对应问题的解。所得各解都是用初等函数表示,非常方便于工程应用。算例比较了在相同热力载荷作用下,具有相同物理常数的热弹性空心圆板、压电热弹性空心圆板和电磁热弹性空心圆板内的弹性场。

MAGNETO-ELECTRO-THERMO-ELASTIC SIMPLY SUPPORTED CIRCULAR PLATE UNDER UNIFORM COUPLED LOADING

Although it is a classical problem for a hollow or solid simply supported circular plate under uniform coupled loading, no theoretic solution for magneto-electro-thermo-elastic media had been obtained. By constructing five mono-harmonic functions containing undetermined constants, the theoretic solution of coupled field in hollow circular plate is obtained by substituting these mono-harmonic functions into the general solution for transversely isotropic magneto-electro-thermo-elastic media. All the undetermined constants are determined by the linear-equation group derived by substituting the theoretic solution into boundary conditions. This solution can be degenerated to the corresponding ones for solid circular plate. All the obtained solutions are expressed in elementary functions and are convenient to apply. Numerical results of a magneto-electro-thermo-elastic hollow circular plate in elastic field are compared with those of thermoelastic and piezothermoelectric hollow circular plates with the same physical constants under the same thermal-mechanical loadings.