The influence of Poisson's ratio in the calculus of functionally graded plates

Abstract

A current problem, of increased difficulty, which is still under continuous development, is the calculus of functionally graded plates (FGPs). Functionally graded materials (FGMs) represent a special category of composite materials, usually made on the basis of two materials, with very different properties, so they vary continuously between the extreme surfaces of the material, where the properties are those of the respective materials in their pure state. Today, the most used materials used in the construction of FGMs are ceramic materials and metals. Their volume fractions, in the thickness direction, varies continuously, according to a material law, valid for all material properties. A problem, generally poorly substantiated, is the one related to the assumption of a constant value of the Poisson's ratio over the entire plate thickness of the functionally graded plates. This hypothesis admits an analytical solution, by direct integration, of the stiffness of the plate, but it certainly does not reflect reality. There are some ways of approaching the calculation of functionally graded plates, such as the multilayer plate concept or the equivalent plate concept, which can take into account the variation of the Poisson's ratio on the plate thickness. The paper highlights this aspect and, in addition, evaluates the influence of the variation of Poisson's ratio on the calculation of displacements, stresses and natural vibrations of functionally graded plates. The work represents both an original way of approaching the calculation of functionally graded plates and a quantitative substantiation of the hypothesis of a Poisson coefficient with a constant value.