Postbuckling analyses and derivations of Knockdown factors for hybrid-grid stiffened cylinders

Numerical Derivation of Buckling Knockdown Factors for Isogrid-Stiffened Cylinders with Various Shell Thickness Ratios

“…The first is the equivalent thickness (t * ) in the equivalent modeling as shown in Equation (6). The second is the effective thickness (t eff ) which can be defined for the grid-stiffened cylinder such as the orthogrid-and isogrid-stiffened cylinders [28]. In the present modeling, the shell thickness ratio (radius to thickness) of the isogrid-stiffened cylinder is defined based on the equivalent thickness (t * ).…”

“…Therefore, the SPLA is used to represent the geometrically initial imperfection of both the detailed and equivalent models for the isogrid-stiffened cylinders. The SPLA is represented using the following three-step process [28,29], which differs slightly from the original modeling [30].…”

“…Firstly, an assumed perturbation load (Q) in the radial direction is applied to the middle of the cylinder (Figure 6(a), [24][25][26][27][28][29][30]). In the present work, for the detailed model of the isogrid-stiffened cylinder, the radial perturbation load is applied to the intersection point between the axial stiffener of a grid panel and the cylinder's middle line, as shown in Figure 6(b); however, the application point of the radial perturbation load for the equivalent model is considered to be the same point as in the detailed model.…”

“…The geometrically initial imperfection of the cylinder is modeled using the single perturbation load approach (SPLA), which is considered one of the best methods to represent the most realistic and worst initial imperfections of shell structures [24][25][26][27]. In this study, a slightly modified modeling technique for the SPLA [28,29] to the original modeling technique [30] is used.…”

Buckling surrogate-based optimization framework for hierarchical stiffened composite shells by enhanced variance reduction method

“…25 In order to investigate the outstanding load-carrying capacity of hierarchical stiffened panels, numerical and experimental studies have been carried out by Quinn et al, [30][31][32] and corresponding design guidelines of hierarchical stiffened panels were also given by Houston et al 33 Wang et al 21 developed a novel hierarchical stiffened shell reinforced by orthogrid major stiffeners and triangle minor stiffeners and Zhao et al 24 developed a novel one reinforced by triangle major and minor stiffeners, which both improved the bucking loads of stiffened shells significantly. Under the same weight, the hierarchical stiffened shell was verified to have low imperfection sensitivity in comparison to the traditional stiffened shell by Wang et al 22 and Sim et al 34,35 Additionally, the thermal buckling capacity of hierarchical stiffened structures was discussed by Wang et al 36 Although the hierarchical stiffened shell achieves higher load-carrying capacity than the traditional stiffened shell, its optimization problem is more complicated. Generally, the optimization of hierarchical stiffened shells faces two major challenges.…”