Static analysis of superelliptical clamped plates by Galerkin's method

In this study, clamped superelliptical plates under uniformly distributed surface load are statically analyzed. Linearly elastic, homogeneous, and isotropic material is considered. The classical thin plate model (Kirchhoff) is employed. The lack of contributions on the static behavior of this sort of plate shapes is the fundamental motivation of the current study. Galerkin's method is used to obtain solutions. The method is conducted for polynomial series at powers ranging from 2 to 8 in order to get converging solutions. Maximum deflections of the plates and mid-point moments are obtained and the results are arranged in tabular form. For purpose of understanding, the behavior trend of the structure with respect to the parameters, some of the solutions are organized in graphical form. The study is performed for a wide range of superelliptical plates. The results are also examined with respect to the parameters a/b ratios and n, which are the plate aspect ratio and the superelliptical power, respectively.