VIBRATION OF PERFORATED DOUBLY-CURVED SHALLOW SHELLS WITH ROUNDED CORNERS

This study examines the natural frequency and vibratory characteristic s of doubly-curved shallow shells having an outer super-elliptical per iphery and an inner super-elliptical cutout. A super-elliptical bounda ry in this context is defined as (2x/a)2n + (2y/b)2n = 1, where n = 1, 2, 3, ..., infinity. This class of shells with rounded outer and inne r comers has a great advantage over shells with a rectangular planform as stress concentration at the comers is greatly diffused. As a resul t, the high stress durability of such shells has a great potential for use in practical engineering applications, especially in aerospace, m echanical and marine structures. The doubly-curved shells investigated possess variable positive (spherical), zero (cylindrical) and negativ e (hyperbolic paraboloidal) Gaussian curvatures. A global energy appro ach is proposed to the study of such shell problems. The Ritz minimiza tion procedure with a set of orthogonally generated two-dimensional po lynomial functions is employed in the current formulation. This method is shown to yield better versatility, efficiency and less computation al execution than the discretization methods.