Optimum design of hierarchical stiffened shells for low imperfection sensitivity

Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint

“…The computational parameters, such as geometric dimensions, boundary conditions and material properties, etc., are exactly identical to those in Ref. [36]. Such a benchmark example is representative of fuel tanks in current launch vehicles.…”

Generatrix shape optimization of stiffened shells for low imperfection sensitivity

“…An optimization procedure for thin-walled structures was formulated by Reitinger and Ramm [13], which included buckling behavior and imperfection sensitivity. Motivated by research in the field of biology [14], Wang et al [15] proposed a concept of hierarchical stiffened shells to restrict the developments of out-of-plane deformations caused by imperfections. Hrinda [16] found that a cylindrical shell with a concave hyperbolic imperfection has a larger buckling load than that for the perfect cylinder, and stiffened shells with a convex hyperbolic generatrix shape were proven to be less sensitive to eigenmode-shape imperfections by Hao et al [17].…”

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

“…Generally, the hierarchical stiffened shell is composed of the skin, major stiffeners (with larger sizes), and minor stiffeners (with smaller sizes). [22][23][24][25][26][27][28][29] The typical buckling modes for hierarchical stiffened shells are the global buckling mode, the partial global buckling mode (happens between the adjacent major stiffeners), skin local buckling mode, stiffener local buckling mode, and plastic buckling mode. 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.…”

“…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.…”

“…[37][38][39] The explicit dynamic method has been extensively used to evaluate the collapse load for stiffened panels, 40 stiffened shells, [41][42][43] and hierarchical stiffened shells. 21,22 However, the computational time of the explicit dynamic method heavily relies on the element number and size, which results in the low computational efficiency of the buckling analysis of hierarchical stiffened shells. In this case, Wang et al 21 smeared the minor stiffeners by means of asymptotic homogenization method, which reduced the post-buckling analysis time of hierarchical stiffened shells based on the detailed finite element method (FEM) by 84%.…”