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This and the next several slides are from the 2012 GENOPT paper, "Use of GENOPT and BIGBOSOR4 to obtain optimum designs of multi-walled inflatable spherical and cylindrical vacuum chambers", by David Bushnell and Charles Rankin, AIAA 53rd Structures, Structural Dynamics, and Materials Conference, 2012, AIAA Paper 2012-1416, referred to as "2012 GENOPT paper" in the next several slides.
ABSTRACT of the 2012 GENOPT paper:
GENOPT/BIGBOSOR4 is applied to the problem of perfect elastic spherical or cylindrical “shells” the complex inflatable wall of which is a webbed sandwich. The spherical or cylindrical “shell” is stabilized by uniform pressure applied between its inner and outer walls and subjected to uniform pressure applied to its outermost wall.
The distance between the inner and outer walls of the optimized spherical balloons is smaller than that for the optimized cylindrical balloons. The pre-buckling behavior of the spherical balloons is “crankier” (more nonlinear) than that of the cylindrical balloons with the result that certain special strategies have to be introduced in order to permit the generation of optimum designs via the GENOPT processor called SUPEROPT.
General buckling modes of the type observed in optimized cylindrical balloons have so far not been observed in any spherical balloons, optimized or not. Local buckling modes include both axisymmetric modes and non-axisymmetric modes with many circumferential waves. Since [1] was written ([1] is about an early version of this software applicable only to cylindrical balloons) new versions of the “balloon” software, behavior.balloon and bosdec.balloon, have been created by means of which both cylindrical and spherical balloons and balloons with either radial webs or truss-like (slanted) webs can all be optimized and analyzed with use of the same “balloon” software.
Since Ref. [1] (listed in the References section of the 2012 GENOPT paper) was produced a new behavioral constraint has been added that involves a load factor corresponding to the initial loss of tension in any of the segments of the balloon wall. This new behavioral constraint is related to initial wrinkling of the balloon, which is a type of buckling that pertains to both cylindrical and spherical balloons.
Optimum designs are found for balloons made of polyethylene terephthalate, which has a maximum allowable stress of 10000 psi and weight density, 0.1 lb/in3, and for balloons made of a much stronger and lighter fictitious carbon fiber cloth, which has much higher maximum allowable tensile and compressive stresses, 75600 psi and 59600 psi, respectively, and lower weight density, 0.057 lb/in^3.
The optimized weights of the balloons made of the much stronger and lighter fictitious carbon fiber cloth are 15 to 20 times lighter than those made of polyethylene terephthalate.
A section is included showing optimized designs of cylindrical balloons made of the fictitious carbon fiber cloth, which is not included as a material option in Ref. [1] (listed in the References section of the 2012 GENOPT paper).
Some peculiarities of the pre-buckling deformations and general buckling modes of optimized spherical and cylindrical balloons made of fictitious carbon fiber cloth are displayed. These optimized balloons, which have much thinner walls than the optimized balloons made of polyethylene terephthalate, exhibit significant spurious local “zig-zag” components of pre-buckling and bifurcation buckling modal displacements.
Convergence studies with respect to the number of nodal points used for each segment of the balloons indicate that this spurious local “zig-zag” characteristic does not have a major influence on the prediction of the overall behavior of the balloons. Therefore, it appears that the optimized designs are valid despite the spurious local “zig-zag” characteristic, which disappears with increasing numbers of nodal points used in each segment of a balloon wall.
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