Second order shear deformation theory for response analysis on temperature-dependent functionally graded plates due to vibration and mechanical loading

The Second-order Shear Deformation Theory (SSDT) is applied to evaluate the displacement and stress fields included in a functionally graded plate (FGP) by thermo-mechanical loadings. Uniformity, linearity, nonlinearity, heat-flux, and sinusoidal thermal conditions are imposed at the upper and lower surfaces of the FGps. The SSDT is also employed to analyze the free vibration of temperature dependent and independent FGP's. Equilibrium equations and equations of motion of FG square and rectangular plates are derived by employing second order shear deformation theory (SSDT). Navier's method is applied to find the analytical results for the derived equations using an energy method for the case of simply supported boundary conditions. The power law material properties and linear steady-state thermal loads are assumed to be graded between full ceramic at the upper and full metal at the lower surface. In the numerical study, different types of FGPs such as ZrO2/Ti-'6Al-_4V and Si3N4/SUS3O4 are considered. A comparison is made of the non-dimensional results for the temperature-dependent and temperature- independent FGPs and validated using the results published in the literature. By comparing the results with some numerical results, a quantitative agreement is exhibited. This research sWdy used numerical results to quantify the effects of material composition, plate geometry, and temperature fields on vibration characteristics and mode shapes. The effects of the material grading index of a plate on stresses and displacements were investigated to reveal that, the longitudinal stresses in the FGP lie between full-metal and full-ceramic plates. It was found that, the neutral axes for FGP move to the upper surface not to the mid-surface as predicted in homogeneous plates. The SSDT has computed results for in-plane stresses, free vibration and displacement fields, which are acceptable and exhibit very close qualitative behavior and quantitative agreement to other shear deformation theories in existing literature, thus demonstrating its robustness.

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