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The shell has been optimized by PANDA2. Notice that there are several local buckling modes that occur at essentially the same load factor (close to unity) but with very different numbers of circumferential waves, n:
(a) local buckling of rings and shell skin that is antisymmetric about the ring-web-shell-skin intersections with considerable deformation of both the shell skin and the ring-web-ring-flange cross sections. n=3 circumferential waves.
(b) “semi” local buckling in which some ring-web-shell-skin intersections are displaced in the buckling mode, and there is some deformation of the ring cross sections.
(c) local buckling antisymmetric about the ring-web-shell-skin intersections with a lot of deformation of the ring cross section and shell skin between adjacent rings. There is almost no displacement of the ring-web-ring-flange intersections.
(d) local buckling of the ring webs and ring flanges with no participation of the shell skin the the buckling mode.
(e) In this particular (overly conservative) model that represnts (inaccurately) general buckling, the general buckling mode is associated with a much lower load factor (about 0.58) than the design load factor (1.0). The general buckling load factor is too low because symmetry conditions are imposed at both ends of the cylindrical shell. Hence the shell can buckle in a manner analogous to buckling of a big cirumferentially stiffened ring rather than buckling of a simply-supported ring-stiffened shell.
FROM:
Bushnell, David (1), Jiang, Hao (2) and Knight, Norm F., Jr. (2)
(1) Lockheed Martin Advanced Technology Center, Palo Alto, CA
(2) Old Dominion Univ., Norfolk, VA
“Additional buckling solutions in PANDA2”, AIAA-1999-1233, 40th AIAA Structures, Structural Dynamics and Materials Conference, April 1999
ABSTRACT: Three new buckling models have been incorporated into PANDA2, a program for minimum weight design of stiffened composite panels and shells: (1) buckling of unstiffened panels or unstiffened portions of panels with use of double-trigonometric series expansions for buckling modal displacement components, u, v, w; (2) general buckling of cylindrical stiffened panels with both rings and stringers treated as discrete beams; and (3) inter-ring buckling of cylindrical panels based on a discretized single module model containing discretized ring segments and a discretized skin-smeared-stringer cylindrical surface to which the ring is attached. Examples are provided of buckling of certain isotropic and laminated composite flat and cylindrical unstiffened and stiffened panels and shells for which the predictions from the modified PANDA2, formerly unacceptably inaccurate, are compared with predictions from STAGS, a general-purpose finite element code. The new comparisons demonstrate that the modified PANDA2 is now well qualified for preliminary design in particular cases for which it previously yielded unreliable designs and designs that were overly conservative. The optimum design of a composite ring and stringer-stiffened cylindrical shell derived by PANDA2 is evaluated with the use of STAGS. The optimum design of an isotropic hydrostatically compressed internally T-ring stiffened cylindrical shell optimized by PANDA2 is evaluated with the use of the shell-of-revolution code BOSOR4. There is good agreement between PANDA2 predictions and STAGS and BOSOR4 predictions for buckling of the optimized designs.
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