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Minimum weight design by GENOPT/BIGBOSOR4 of an externally pressurized circumferentially corrugated cylindrical shell and verification by STAGS, by David Bushnell, Retired, accepted for the 56th AIAA Structures, Structural Dynamics and Materials Meeting, Kissammee, Florida, January 5 – 9, 2015 (paper withdrawn because of lack of ability to speak clearly due to oro-mandibular dystonia).
ABSTRACT: The results reported here are analogous to those reported in a previous paper on minimum weight design of elastic axially compressed prismatic complexly corrugated panels and shells in which the corrugations, each of which is a little cylindrical segment, run in the longitudinal direction. Here the corrugations, each of which is a little toroidal segment, run in the circumferential direction. The complexly corrugated shell of revolution is loaded by uniform external lateral normal pressure. There is no axial load component equal to pr/2, and the shell of revolution is free to expand or contract in the axial direction as the external pressure is applied. As before, the GENOPT/BIGBOSOR4 system is used to build the model and to perform the optimization. The minimum weight of the circumferentially corrugated shell is determined in the presence of the following behavioral constraints: 1. The shell shall not buckle locally, 2. The shell shall not buckle in a general mode that is symmetric at the plane of symmetry, 3. The shell shall not buckle in a general mode that is anti-symmetric at the plane of symmetry, 4. The maximum effective stress in the wall of the shell shall be less than a specified value. “Corners” at junctions between adjacent toroidal segments are eliminated by the automatic insertion of small “smoothing” toroidal segments. The circumferentially corrugated shells are optimized with and without the inclusion of nonlinear geometric effects, and it is found that these nonlinear effects are significant. Optimized designs are extremely sensitive to small changes in certain of the decision variables, making it difficult to find “global” optimum designs, especially when nonlinear theory is used. Several optimized designs determined with GENOPT/BIGBOSOR4 are verified by comparison with predictions from the general-purpose computer program STAGS. The agreement between the predictions of GENOPT/BIGBOSOR4 and STAGS is always good when linear theory is used, good for local buckling when either linear or nonlinear theory is used and fair for general buckling when nonlinear theory is used. There is always good agreement between BIGBOSOR4 and STAGS for the prediction of axisymmetric pre-buckling maximum effective stress.
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