Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads

In the present study, a displacement based nonlinear finite element model for functionally graded porous micro-plates is developed based on the general third-order shear deformation plate theory and the modified couple stress theory. The developed finite element model accounts for von Karman nonlinear strains, a power-law variation of two material constituents through the plate thickness, and different distributions of porosity with a constant volume of voids on static bending of micro-plates are analyzed. The length scale dependency is captured using a single parameter of the modified couple stress theory. A power-law distribution is assumed to model the variation of the two material constituents, while the porosity distributions vary according to cosine functions. The temperature-dependent properties are obtained using a cubic-spline interpolation from experimental data. A one-dimensional steady-state heat conduction problem is solved using the effective thermal conductivity of the porous material based on the Maxwell-Eucken model to obtain temperature distribution through the plate thickness. The Newton-Raphson iteration scheme is used to solve the nonlinear system of equations. A parametric study is conducted to demonstrate the effects of material and porosity parameters, temperature and length scale dependencies, and boundary conditions on the deflections and stress distributions.

Automated summary

In this study, a nonlinear finite element model for functionally graded porous micro-plates is developed based on the general third-order shear deformation plate theory and the modified couple stress theory. The model accounts for von Karman nonlinear strains, power-law variation of material constituents, porosity distributions, temperature-dependent properties, and length scale dependency. A parametric study demonstrates the effects of material and porosity parameters, temperature and length scale dependencies, and boundary conditions on deflections and stress distributions.