Free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports on the diagonals

Nonlinear Bending and Thermal Post-buckling Analysis of FGM Super Elliptical Thin Plates

“…The maximum dimensionless deflections of Si 3 N 4 /SUS304 FGM super elliptical plates with immovable simply supported edge and immovable clamped edge subjected to transverse uniformly distributed loads in different temperature fields are calculated. It can be concluded that the deflections increase with increasing value of mechanical loads in Figures 2-7 , and subjected to the same mechanical loads, the deflections increase with increasing value of volume fraction index N in Figure 2 and 5 and increasing value of temperature rise in Figure 3 [ 5,6] . Without mechanical loads, downward initial Figure 3 and the upward initial deflections in Figure 4 can be observed for the plates with immovable simply supported edge, while no initial deflections can be observed for the plates with immovable clamped edge in Figures 6 and 7.…”

“…Super elliptical plates which are defined by shapes between an ellipse and a rectangle have a wide range of use in engineering applications. Some studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for linear behaviors of super elliptical plates are available in the literature. Wang et al [1] presented accurate frequency and buckling factors for super elliptical plates with either simply supported or clamped edges by using Rayleigh-Ritz method.…”

“…Zhou et al [5] analysed three-dimensional free vibration of super elliptical plates based on linear elasticity theory using Chebyshev-Ritz method. Altekin [6] gave out free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports, Altekin and Altay [7] calculated static analysis of point-supported super-elliptical plates, then Altekin [8,9] discussed free vibration and bending of orthotropic super elliptical plates on intermediate supports. Çeribaşı et al [10] gave out static linear analysis of super elliptical clamped plates based on the classical plate theory by Galerkin's method, Çeribaşı and Altay [11] investigated free vibration of super elliptical plates with constant and variable thickness by Ritz method, then Çeribaşı [12] investigated static and dynamic linear analyses of thin uniformly loaded super elliptical clamped functionally graded plates.…”

Bending of Super-Elliptical Mindlin Plates by Finite Element Method

“…Unlike plates with sharp corners, rectangular plates with rounded corners enable to diffuse and dilute stress concentrations [40]. 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].…”

Characterizing the vibration of an elastically point supported rectangular plate using eigensensitivity analysis

“…A brief overview of recent contributions is presented. Altekin [1] consider both bucking and free vibration of elliptical plates which have point supports along the symmetric diagonals. A Ritz approach is used to solve for the fundamental frequency and critical buckling load.…”