In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. In numerical section, are comprehensively investigate the effects of grading index, hygrothermal environmental conditions, rotating speed, and temperature- and moisture-dependency of elastic constant of FGMEE.

在本文中，我们研究了承受轴对称湿热磁机电负载的功能梯度磁电弹性 (FGMEE) 空心圆柱体的径向位移、应力、电势和磁势的历史。平面应变条件。材料特性被视为半径的幂律函数。使用应力-位移关系、平衡方程、静电和静磁方程，我们找到了一个包含蠕变应变的微分方程。最初，消除蠕变应变，我们获得原始应力和电势和磁势的解析解。在下一步中，考虑蠕变应变，我们通过应用诺顿定律和 Prandtl-Reuss 方程来计算稳态湿热边界条件的蠕变应力率。最后，使用迭代方法，我们可以随时找到随时间变化的蠕变应力、径向位移以及磁场和势场的重新分布。在数值部分，综合考察了分级指数、湿热环境条件、转速以及FGMEE弹性常数对温度和水分的依赖性的影响。