A comprehensive study on the size-dependent hygrothermal analysis of exponentially graded microplates on elastic foundations

Abstract

In this paper, the effects of hygrothermal conditions on various behaviors, such as bending, free vibration, mechanical and thermal buckling, of exponentially graded microplates lying on two-parameter elastic foundations are investigated. The trigonometric four-variable plate theory incorporated to the modified couple stress theory (MCST) is employed to derive the equations of motion. The present MCST contains an internal material length scale parameter, thus it can capture the size effect. The microplate is assumed to be subjected to a temperature rise and moisture concentration which are varied linearly through the thickness of the plate. Based on an exponential law, the material properties of the microplate are graded only in z direction. The equations of motion are solved analytically to obtain the displacements, stresses, eigenfrequencies and critical buckling load and temperature of the microplates. The present results are validated by comparing them with those previously published. The numerical examples reveal that considering the size effect and/or the elastic foundations leads to an increment in plate stiffness and thereby leads to a decrement in the deflection and an increment in eigenfrequency and buckling loads. It is also shown that the size effect is negligible for the thicker plate.