PANDA2 - Program for minimum weight design of stiffened, composite, locally buckled panels

PANDA2 finds minimum weight designs of laminated composite fiat or curved cylindrical panels or cylindrical shells with stiffeners in one or two orthogonal directions. The panels or shells can be loaded by as many as five combinations of in-plane loads and normal pressure. The axial load can vary across the panel. Constraints on the design include crippling, local and general buckling, maximum tensile or compressive stress along the fibers and normal to the fibers in each lamina, and maximum in-plane shear stress in each lamina. Local and general buckling loads are calculated with the use of either closed-form expressions or discretized models of panel cross sections. An analysis branch exists in which local post buckling of the panel skin is accounted for. In this branch a constraint condition that prevents stiffener popoff is introduced into the optimization calculations. Much of this paper represents a tutorial run through the PANDA2 processors for a hat-stiffened panel under combined axial compression, in-plane shear and normal pressure. Examples follow in which results from PANDA2 are compared with those in the literature and those obtained with the STAGS and EAL computer programsResults of an extensive study are given for an optimized, blade-stiffened panel design so that it buckles locally at about 10% of the design load. The axially stiffened panel is subjected to pure axial compression. pure normal pressure, combined axial compression and normal pressure, and combined axial compression and residual stresses and deformations that arise from a simulated curing process. An example is provided of a design process applied to a ring and stringer stiffened cylindrical shell similar in geometry and loading to the 2/3 interstage of the ARIANE 4 booster. 1. PURPOSE OF PANDA2 The purpose of PANDA2 is to find the minimum weight design of a stiffened flat or curved panel or complete cylindrical shell made of laminated composite material. Of course, simple isotropic panels and cylindrical shells can also be designed. 1.1 Definition of panel' A panel is defined here as a structure that is either flat or is part of a cylinder. In most cases the user will probably want to analyze a flat panel or a panel that spans less than about 45° of circumference. However, in PANDA2 complete cylindrical shells can be treated by the user's setting up a model of a panel that spans 180°. The buckling loads given by PANDA2 for half of a cylindrical shell are the same as those given in the literature for a complete cylindrical shell because: I. the panel is assumed by PANDA2 to be simply supported along its straight edges; 2. a deep cylindrical panel spanning 1800 of circumference with simple supports along the generators at 0° and at 1800 behaves in the same way as a complete cylindrical shell: the number of circumferential half-waves in the 180° panel in the critical general instability buckling pattern is the same as the number of full circumferential waves in the 3600 cylindrical shell. Later an example is given in which a complete cylindrical shell with a single set of axial and shear loads that vary around the circumference is analyzed as a curved panel spanning 450 and subjected to multiple sets of uniform loads. The panel is optimized for two combinations of in-plane loads: that corresponding to maximum axial compression and that corresponding to maximum in-plane shear. It is usually best to treat complete cylindrical shells in this way rather than try to set up a model for the entire cylinder, because buckling is usually local and concentrated in the areas of maximum load and because PANDA2 was really intended to treat panels, not complete cylindrical shells. Therefore, it is best applied to panels. In PANDA2 the curved edges of a cylindrical panel lie in the plane of the screen (axial coordinate x = 0) and parallel to the plane of the screen (axial coordinate x = L, where L is the length of the panel). The axial coordinate direction x is normal to the plane of the screen and pointing out of the screen. Thus, an axial load on the panel is normal to the screen, with axial tension pointing out of the screen.