Gene

Engineering

Buckling

Spherical shell

Materials science

Bending

Computer security

Robustness (evolution)

RADIUS

Apoptosis

Biochemistry

Computer science

Mechanical engineering

Physics

Development (topology)

Upper and lower bounds

Mathematics

Shell (structure)

Gene knockdown

Mathematical analysis

Composite material

Bend radius

Structural engineering

Chemistry

Mechanics

International Journal of Mechanical Sciences

In this paper a physically based and deterministic design procedure for spherical shells under external pressure is introduced. Within the new design concept the membrane energy of a sphere is incrementally reduced by means of perturbation cutouts, until a bending energy dominate state is identified. The threshold between membrane energy state and bending energy state represents a robust plateau for the buckling pressure. A comprehensive numerical investigation was performed in order to study the influence of radius-to-thickness ratio (R/t) as well as the dome height-to-base radius ratio (H/r). The results verify that both geometric properties ratios significantly influence the lower-bound buckling pressure, especially if plastic buckling occurs. Improved shell buckling design factors are given in the form of an simple analytic equation. The corresponding threshold KDFs were validated with a large number of buckling experiments and deliver much higher KDFs than currently used empirical guidelines. Based on the new design criterion lower-bound estimation for the buckling pressure of a tori-spherical bulkhead and the inner dome of the cryogenic upper stage ESC-A from the European space launch-vehicle Ariane 5 are determined.

Robust knockdown factors for the design of spherical shells under external pressure: Development and validation