Bending of Super-Elliptical Mindlin Plates by Finite Element Method

Abstract

Bending of shear deformable super-elliptical plates under transverse load was investigated using the Mindlin plate theory by means of the finite element method. Four-noded isoparametric quadrilateral plate bending element with three degrees of freedom per node was used. Parametric results for the maximum deflections were presented via sensitivity analysis for several geometric characteristics such as thickness, aspect ratio, and super-elliptical power. Good agreement with the solutions of elliptical and rectangular plates was obtained using fine mesh. The results revealed that the deflections of clamped and point supported super-elliptical plates lie in the range bounded by elliptical and rectangular plates. However, the bending response of simply supported plates was observed to be entirely different. It was shown that high rate of convergence is required to obtain such a relation and using insufficient number of degrees of freedom results in finding a totally different trend for the clamped case.