Bending, Buckling, and Vibration of Equilateral Simply Supported or Clamped Triangular Plates with Rounded Corners

AbstractThe pb2-Ritz method and the homotopy shape function are used for bending, buckling, and vibration analyses of equilateral triangular plates with rounded corners. On the basis of the comprehensive results obtained, it is found that the deflection shape, buckling load, and fundamental frequency vary nonlinearly with respect to the corner roundedness parameter α and Poisson’s ratio for simply supported plates, whereas these aforementioned results vary nonlinearly with respect to α only for clamped plates. The use of the pb2-Ritz method facilitates the development of approximate formulas for the accurate prediction of deflection shapes, buckling loads, and fundamental frequencies for simply supported and clamped rounded-corner equilateral triangular plates. These formulas presented in this paper should be useful for designers working on such plates.