表面热力耦合均载作用下的简支圆板

针对表面热力耦合均载作用下的简支空心和实心圆板,构造了3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热弹性材料的通解，获得了表面热力耦合均载作用下的简支空心圆板内热弹性场的解，再将所得解代入边界条件获得了确定待定常数和组合待定常数的线性方程组.经过合理退化进一步得到了实心圆板对应问题的解，所得各解都是用初等函数表示，非常方便工程应用.算例给出了在热力耦合载荷作用下的简支空心圆板内热弹性场的分布.应力分布图显示正应力峰值分布在上下表面的中部，剪应力峰值分布在中面的两侧.

Simply supported circular plate under uniform thermo-mechanical coupling loading

The thermo-elastic field in a simply supported hollow or solid circular plate under thermo-mechanical coupling loading was investigated.For this object,three mono-harmonic functions were constructed,which included undetermined constants.The theoretical solution of thermo-elastic field in hollow circular plate was obtained by substituting three mono-harmonic functions into the general solution for transversely isotropic thermo-elastic materials.All the undetermined constants were determined by the linear-equation group derived by substituting the theoretical solution into boundary conditions.This solution can be degenerated to the corresponding ones for solid circular plate.All obtained solutions are expressed in elementary functions and are convenient to use.Numerical results of coupled fields in hollow circular plate were presented in detail.The figures show that the normal stress peak value is at the middle of the upper and lower surfaces,and that the shear stress peak value is at the two sides of the middle plane.