Axisymmetric nonlinear behavior of functionally graded saturated poroelastic circular plates under thermo-mechanical loading

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.