Static analysis of point-supported super-elliptical plates

Abstract

This paper reports the static analysis of point-supported super-elliptical plates of uniform thickness subjected to a uniformly distributed lateral load. The plate perimeter was defined by a super-elliptic function with a power, corresponding to shapes ranging from an ellipse to a rectangle. The analysis was based on the Kirchhoff-Love plate theory and the computations were carried out by the Ritz method. Lagrange multipliers were used to satisfy the boundary conditions. Isotropic and homogeneous plates with 20 different shapes were examined for two distinct aspect ratios. Convergence studies were performed for the central deflection and the central bending moments. The results were checked against those of a corner-supported square plate and good agreement was obtained.

Bending of Super-Elliptical Mindlin Plates by Finite Element Method

“…Despite the recently published papers, the studies on the analysis of super-elliptical plates have mostly been made for the dynamic behavior, and generally thin plates have been investigated [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. To the best of the author's knowledge, there are only nine published papers on the bending of superelliptical plates all of which focused on thin plates only [60][61][62][63][64][65][66][67][68]. Thus, the current work was motivated by the lack of contributions on the bending analysis of shear deformable superelliptical plates.…”

Generalization of the super ellipsoid concept and its application in mechanics

“…and Altay [7] conducted static analysis of point-supported super-elliptical plates of uniform thickness subjected to uniformly distributed load, and authors noted: "Studies on rectangular plates with rounded corners are rather scarce, although they are used extensively in industrial applications as structural and machine elements". Static analysis of super-elliptical clamped plates was dealt with by Çeribaşı et al [8], by the Bubnov-Galerkin method.…”