Vibration of perforated doubly-curved shallow shells with rounded corners

This study examines the natural frequency and vibratory characteristics of doubly-curved shallow shells having an outer super-elliptical periphery and an inner super-elliptical cutout. A superelliptical boundary in this context is defined as (2x/a)²ⁿ + (2y/b)²ⁿ = 1, where n = 1, 2, 3, ..., ∞. This class of shells with rounded outer and inner corners has a great advantage over shells with a rectangular planform as stress concentration at the corners is greatly diffused. As a result, the high stress durability of such shells has a great potential for use in practical engineering applications, especially in aerospace, mechanical and marine structures. The doubly-curved shells investigated possess variable positive (spherical), zero (cylindrical) and negative (hyperbolic paraboloidal) Gaussian curvatures. A global energy approach is proposed to the study of such shell problems. The Ritz minimization procedure with a set of orthogonally generated two-dimensional polynomial functions is employed in the current formulation. This method is shown to yield better versatility, efficiency and less computational execution than the discretization methods. © 1994.