Statics and dynamics of super elliptical homogeneous and FGM plates

Abstract

In this study super elliptical plates are statically and dynamically analyzed. This class of plates includes a wide range of shapes varying from an ellipse to a rectangle. Although studies on the extreme boundaries of the super elliptical shapes (circle, ellipse, and rectangle) are extensive, contributions on the mid shapes are very limited. The studies are mostly concentrated on dynamics, thermal, and buckling behavior of the plates but not on static behavior. Kirchhoff plate model with isotropic and homogeneous material is studied. The first part of this study is concentrated on static behavior of the super elliptical plates under uniformly distributed surface load. For static analyses clamped boundary is assumed. The partial differential plate equations are solved by Galerkin method. The study is conducted for 10 super elliptical shapes and 14 central plate dimension ratios. The second part of the study deals with the dynamic behavior of super elliptical plates. Free vibration of simply supported plates is investigated and Ritz method is employed for the solution of the governing plate equations. The effect of Poisson’s ratio, which can not be neglected for round edged simply supported plates, is examined in detail. The results of the study are presented in graphical and tabular forms and compared with previously obtained results of the available literature. In the last part of the study, functionally graded material (FGM) Kirchhoff plates have been investigated. For static analysis of the FGM plates, uniformly distributed surface load and clamped boundary is assumed and Galerkin method is employed. In addition to this, free vibration characteristics of simply supported FGM plates are studied by using Ritz method. The Poisson’s ratios of the plates are assumed to be constant, but their Young’s moduli vary in the thickness direction functionally. The objective of this part is to investigate the influence of volume fractions and the component materials on static and dynamic behavior of this class of plates.