Starred Polyhedral Shell Reinforced with Internal Pockets Considering an Internal Vacuum

The concept of vacuum lighter-than-air vehicles is a generalization of the idea behind floating vehicles, which enclose a volume of gas that is lighter than air. In particular, the enclosed volume is completely evacuated. From a pure geometrical perspective, the sphere is appealing because of the symmetry properties and the best surface-area-to-volume ratio. However, the pressure differential between the external fluid and the internal vacuum imposes significant compressive forces, which put the structure at risk of instability due to buckling. At the present technology level, no available material can be used to create a shelled sphere with a relatively large radius-to-thickness ratio and an internal vacuum without buckling. This work explored the concept of a star polyhedron obtained from the pentakis icosidodecahedron by adding pockets on the triangular surfaces. Under the assumption of elastic linear isotropic material and using commercial software ABAQUS version 2016, it was demonstrated that the stability performance, postbuckling response, type of buckling and its location, and mesh convergence properties are significantly affected by the ratio of the radius of the circumscribed sphere to the shell thickness. The structure exhibits sensitivity to the geometric imperfections, as assessed by using different amplitudes and types of imperfections. However, it was demonstrated that the proposed shape presents a true buckling load approximately twice that of a sphere, indicating that the adopted geometry is less sensitive to manufacturing imperfections than is a circumscribed sphere. Using the Buckingham $\mathrm{\Pi }$ theorem, an empirical formula predicting the buckling load (eigenvalue analysis of the perfect structure) was derived and related to the corresponding relationship valid for spherical shells.