Buckling of super ellipsoidal shells under uniform pressure

This paper is concerned with the elastic buckling of super ellipsoidal shells under external uniform pressure. The middle surface of a super ellipsoidal shell is defined by the following equation: ( x / a ) 2 n + ( y / b ) 2 n + ( z / c ) 2 n = 1 , where n is an integer varying from unity to infinity. It is clear from the equation that the range of shell shapes covered sphere (n=1, a=b=c) to cube ( n = ∞ , a = b = c ) and ellipsoid (n=1) to cuboid ( n = ∞ ). By adopting a recently proposed solid shell element for the buckling analysis, the critical buckling pressures of thin to thick super ellipsoidal shells are obtained and tabulated for engineers. The shell element allows for the effect of transverse shear deformation which becomes significant in thick shells. Their buckling shapes are also examined. In addition, a simple approximate formula for predicting the critical buckling pressure of thick spherical shells is proposed.