This is the cover figure from the unpublished 1990 GENOPT report, "SPHERE - Program for minimum-weight design of isogrid-stiffened spherical shells under uniform external pressure", by David Bushnell.
The decision variables are d, h, ts, and t.
ABSTRACT from the "SPHERE" report:
A system pf programs called "SPHERE" has been developed for optimization of stiffened spherical shells under uniform external pressure. The stiffeners are assumed to be blades (rectangular cross section) and are arranged in an isogrid pattern in order to maintain isotropy of the stiffened wall. In this way formulas and tables applicable to buckling of monocoque isotropic spherical shells can be applied, with proper definition of effective modulus and wall thickness, to buckling of stiffened spherical shells.
Both the skin of the shell and the stiffeners are assumed to be of isotropic material, with different material properties in skin and stiffeners. Only membrane prebuckling states are considered.
The theory used follows, for the most part, that given in Ref. 1 (Meyer, et al,, "Isogrid Design Handbook", 1972), with the exception that skin and stiffeners may be of different material. The effect of transverse shear deformation is ignored. The effect of initial imperfections is included. An example is provided.
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