The Influence of Poisson's Ratio in the Calculus of Functionally Graded Plates: A Recent Study

Abstract

Calculus of functionally graded plates (FGPs) is a current issue of increasing difficulty that is still being developed. Functionally graded materials (FGMs) are a unique class of composite materials that are typically constructed from two materials that have very different properties. As a result, the properties of these materials vary continuously between the material's extreme surfaces, where they are found in their purest form. Metals and ceramic materials are currently the most common materials used in the fabrication of FGMs.  Their volume fractions vary constantly in the thickness direction, according to a material law that applies to all material qualities.  Poisson's ratio is one of the elastic characteristics of any material and consequently, characterizes its behavior. The assumption that the Poisson's ratio will remain constant over the whole plate thickness of the functionally graded plates is a problem that is typically not well supported. This hypothesis does not accurately reflect reality, but it does allow for an analytical solution via direct integration of the plate stiffness.  There are some approaches to calculating functionally graded plates, such as the multilayer plate idea or the equivalent plate concept, that can account for the changing of the Poisson's ratio with plate thickness.  This point is highlighted in the research, which also assesses the impact of Poisson's ratio fluctuation on the estimation of displacements, stresses, and natural vibrations of functionally graded plates. The study provides a novel method for calculating functionally graded plates as well as quantitative support for the hypothesis that the Poisson coefficient has a constant value.