Coupled Thermoelasticity of Functionally Graded Plates Based on First-Order Shear Deformation Theory

In this study, an analytical solution is presented for a plate based on the first-order shear deformation theory with functionally graded materials (FGM) subjected to lateral thermal shock loads. Material properties of the plate, except Poisson’s ratio, are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The solution is obtained under classical coupled thermoelastic assumption. A third-order polynomial temperature profile has been considered across the plate thickness with unknown constants. By substituting the profile into equations of motion and energy equation and applying Galerkin method we acquire nine equations for analyzing coupled thermoelasticity of the FGM plate which must be solved simultaneously. The governing partial differential equations are solved using Fourier series expansion method. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inversion method, the solution in time domain is derived. The analytical approach supports us to be able to submit a mathematical expression for classical coupled thermoelastity of the FGM plate. Computed results for the plate with simply supported boundary conditions are presented for different power law indices and various aspect ratios of the plate. Results show that the plate under coupledthermoelasticity assumption vibrates around the steady state situation and vibration amplitude decreases intensively with passing the time. Although, coupled thermoelasticity assumption affects both of temperature and deflection responses, the coupling effect is more apparent in the lateral deflection of the plate. Furthermore validating the process is accomplished by verifying thermomechanical responses and natural frequencies of the FGM plate based on the FSDT with known data reported in the literature.

کلیدواژه ها:

Functionally graded material ، Thermalshock ، First-order shear deformation theory ، Coupled thermoelasticity ، Finite Fourier transformation method