Bending Behavior of Functionally Graded Plates: Including Surface Effects

In this book, Mindlin plate theory, accounting for the neutral plane position, of functionally graded (FG) plates is formulated for continuums subjected to thermo-mechanical loads with/without incorporating surface energy effects. The mechanical response of ultra-thin FG plates is studied based on Gurtin and Murdoch surface conditions. A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived. The obtained modifications over the classical Mindlin model are involved at both equivalent material stiffnesses and the governing equations. A finite element model is presented to clarify the effects of constituent material properties and surface energies on the behavior of FG plates, whose effective elastic moduli are represented by the simple power law. The proposed finite element model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. A parametric study is also presented to clarify the effects of plate dimensions, mechanical and thermal material properties on the behavior of the FG plate.