New static and dynamic analyses of macro and nano FGM plates using exact three-dimensional elasticity in thermal environment

In this article, the static and dynamic behaviors of macro and nano inhomogeneous plates made of functionally graded materials (FGMs) have been investigated based on three-dimensional elasticity theory in combination with the nonlocal theory of Eringen. Variation of deflection along the thickness has been considered as the result of three-dimensional analysis. The governing equations have been derived and developed considering the nonlocal theory for nano-scale plates. Conveniently, the results of macro-sized plates were concluded by neglecting the small scale effects. The results were compared with the some related papers available in the literature. Since the three-dimensional elasticity has been applied, the obtained results are more accurate than other plate theories. In addition, if the plate is subjected to thermal loading, only the results of three-dimensional analysis will be correct. Since the nonlocal analysis has been assumed, the small-scale effects and related parameters have been studied for the nano-scale plates. Finally, the effects of some other important parameters have been surveyed on the results, such as the size of plate, loading, FGM parameters, and boundary conditions.