In functionally graded saturated poroelastic circular plates with immovable simply supported and clamped rims, the axisymmetric nonlinear bending under transverse thermo-mechanical loading has been parametrically studied and compared with the axisymmetric postbuckling and nonlinear bending under thermal loading. Based on the classical plate theory, Love–Kirchhoff hypotheses and Sander’s assumptions, the general coupled nonlinear radial and transverse equilibrium equations, central continuity, symmetry and boundary conditions has been derived in ordinary and state-spatial forms. The corresponding difference equations have been achieved by using the generalized differential quadrature method. The equations have been assembled and numerically solved by using the Newton–Raphson iterative algorithm. The effects of the mechanical and thermal loads, pore distribution type, porosity parameter, Skempton’s coefficient, and thickness and boundary condition type on the behavior of the deflection, whether caused by thermo-mechanical bending, thermal postbuckling, or thermal bending, have been investigated in detail. From the parametric study, a novel quantity determining bending behavior has been found. The axisymmetric themo-mechanical nonlinear bending deflection is inversely and nonlinearly proportional to thermal load when the quantity is greater than a critical value and is nonlinearly proportional to thermal load when the quantity is less than a critical value. It was verified that the plate behavior complies with the general rules known for FG saturated poroelastic circular plates and with those known for metal–ceramic functionally graded circular plates whose governing equations are mathematically analogous to those of the current research.

在具有不可移动简支夹边的功能梯度饱和多孔弹性圆板中，参数化研究了横向热机械载荷下的轴对称非线性弯曲，并与热载荷下的轴对称后屈曲和非线性弯曲进行了比较。基于经典板块理论、Love-Kirchhoff 假设和 Sander 假设，一般耦合的非线性径向和横向平衡方程、中心连续性、对称性和边界条件以普通和状态空间形式导出。利用广义微分求积法得到了相应的差分方程。这些方程已通过使用 Newton-Raphson 迭代算法进行组装和数值求解。机械和热负荷的影响，已经详细研究了孔隙分布类型、孔隙率参数、Skempton 系数、厚度和边界条件类型对挠曲行为的影响，无论是由热机械弯曲、热后屈曲还是热弯曲引起的。从参数研究中，发现了一种确定弯曲行为的新数量。当量大于临界值时，轴对称热-机械非线性弯曲挠度与热负荷成反比和非线性成正比，当量小于临界值时与热负荷非线性成正比。