Thermoporoelasticity analysis of variable thickness and elastically restrained functionally graded auxetic metamaterial circular plate resting on an auxetic material circular plate

Abstract

The main purpose of this research is to investigate the thermoporoelastic behavior of non-homogeneous circular plate made up of auxetic metamaterial rested on an auxetic material plate. The plate is non-uniform, restrained with flexible support at outer edge and subjected to structure-structure interaction and thermo-mechanical load. The plate material is graded in transverse direction and the Poisson's ratio is constant. Based on the linear thermoporoelasticity theory, the governing state equations in terms of displacements and temperature are acquired. At first, the one-dimensional heat equation including quadratic type heat source is solved to compute the nonlinear distribution of temperature across the thickness. Then, the state equations are solved semi-analytically using state-space (SS) method and differential quadrature (DQ) rule to predict the elastic field quantities. A comprehensive parametric discussion is accomplished to elucidate the effects of key parameters on the steady-state response of the plate to mechanical and thermal loads. The computed results indicate that the auxeticity of the structure and supporting medium, as well as the thermal environment, play a significant role in the thermoporoelastic behavior of the plate.