Static and dynamic analysis of super-elliptical plates

Abstract

This study reports the static and dynamic analysis of super-elliptical plates ofuniform thickness. There are mainly three distinct boundary conditions (clamped/simplysupportedalong the contour and point supported on the contour) to be examined in the dissertation. In static analysis the plate is subjected to constant lateral load. On the otherhand, in dynamic analysis the undamped free vibration is concerned. The plate perimeteris defined by a super-elliptic function with a power corresponding to the shape rangingfrom an ellipse to a rectangle. The Kirchhoff fourth-order plate theory is employed for the isotropic and the functionally graded elastic plate. Numerical examples for plates withdifferent shapes are solved by the Ritz method and the methods of weighted residuals. Theresults are compared with known ones where possible.