Buckling of Externally Pressurized Shallow Spherical Caps from Composites

Abstract

Buckling of shallow spherical shells subjected to external pressure has been exploited, for example, in pressure safety devices. Shallow spherical caps have also been used as mirrors and more recently they have been considered as energy concentrators in space applications. Hence there is a renewed interest in their static stability performance. This paper addresses two issues: (1) buckling performance of caps, with shallowness parameter, lambda, varying from 3.5 to 7.5, and (2) the effect of boundary conditions on the buckling strength. In the first case, for elastic buckling of caps, there is a sudden drop in the buckling strength for small magnitude of cap’s geometrical parameter lambda, i.e., for lambda ≈ 4.0. This has recently been re-confirmed for steel caps. However, it is not clear whether this drop can be eliminated or reduced in caps made from composites mainly through the lamination sequence and also by appropriate supporting of the caps perimeter—as typically used in inflatable space antenna. The current paper examines spherical caps made from composites subjected to quasi-static external pressure. The effect of different lamination sequences on the buckling strength is examined for a range of the shallowness parameter. In the second part, it is proposed to use a closed toroidal shell as means of supporting the cap’s perimeter. The supporting toroidal shells can be of different cross-section, i.e., circular or elliptical. The toroids can also be internally pressurized, differently laminated, etc. Additionally the point of attachment can be chosen in such a way that buckling load is as large as possible. The effect of some of these parameters on the buckling pressures is quantified. This is an entirely numerical study.