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This and the next two slides are from the paper: "Optimum design of stiffened panels with substiffeners" by David Bushnell and Charles Rankin, AIAA 46th Structures, Structural Dynamics, and Materials Conference, Paper no. AIAA-2005-1932, 2005, called "2005 PANDA2 paper" in the next two slides.
The curved panel (cylindrical shell) was first optimized by PANDA2, then the optimized cylindrical shell and sub-domains of it were analyzed with the use of the STAGS computer program. The optimum design shown here and in the next two slides is for a complete cylindrical shell with no imperfections (a perfect cylindrical shell). The design load corresponds to load factor, Pcr = 1.0.
This is Fig. 1 from the 2005 PANDA2 paper. This slide shows a STAGS model for local and for inter-ring buckling: This sub-domain model includes 1 major ring bay x 3 major stringer bays; case name = testax4p; bifurcation buckling mode 1, buckling load factor from STAGS, Pcr = 0.98903. (Pcr = 1.0 is the design load.) The PANDA2 model predicts buckling at the load factor, Pcr = 1.0 (the design load factor).
Loading used for the examples shown here and in the next two slides:
Axial Resultant (lb/in), Nx(1) Load Set A = -100000 lb/in
Hoop Resultant (lb/in), Ny(1) Load Set A = -20000 lb/in
In-plane shear (lb/in), Nxy(1) Load Set A = 20000 lb/in
Uniform pressure, (psi),p(1) Load Set A = -200 psi
Zero loading in Load Set B
ABSTRACT OF THE 2005 PANDA2 PAPER:
The capability of the computer program PANDA2 to generate minimum-weight designs of stiffened panels and cylindrical shells is enhanced to permit the adding of substiffeners with rectangular cross sections between adjacent major stringers and major rings. As a result many new buckling margins exist that govern buckling over various domains and sub-domains of the doubly stiffened panel or shell. These generally influence the evolution of the design during optimization cycles. The substiffeners may be stringers and/or rings or may form an isogrid pattern. The effects of local, inter-ring, and general buckling modal imperfections can be accounted for during optimization. Perfect and imperfect cylindrical shells with external T-shaped stringers and T-shaped rings and with and without substringers and subrings and under combined axial compression, external pressure, and in-plane shear are optimized by multiple executions of a "global" optimizer called SUPEROPT. It is found that from the point of view of minimum weight there is little advantage of adding substiffeners. However, with substiffeners present the major stringers and rings are spaced farther apart at the optimum design than is so when there are no substiffeners. The weight of a cylindrical shell with substiffeners is much less sensitive to the spacing of the major T-shaped stringers than is the case for a cylindrical shell without substiffeners. The optimum designs obtained by PANDA2 are evaluated by comparisons with buckling loads obtained from a general-purpose finite element program called STAGS. Predictions from STAGS agree well with those from PANDA2.
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