circumferentially. The length, L1, of the tank barrel is 300 in, and the radius, r, is 160 in. A half cylindrical tank is considered due to symmetry. The design variables are the isogrid spacing, b, the isogrid blade height, h, and the thicknesses the skin, tl, and the thickness of the isogrid blades, tz. The geometry of the ring is fixed. Following Lamberti et al. (2003) the panel is designed subj ect to two load cases * internal proof pressure of 3 5 psi critical for strength * axial compressive load Nx = 1000 lb/in, with an internal (stabilizing) pressure of 5 psi critical for buckling. Figure 8-1. Isogrid-stiffened cylindrical shell with internal isogrid and external rings with isogrid pattern oriented along circumferential direction for increased bending stiffness in hoop direction The weight W of the panel is minimized subject to the constraint that the probability of failure P of the panel must be lower than a given requirement. The reliability-based optimization of stiffened panels is formulated as minimize W = W(b, h, tz,t,) such that P