Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity

Wang, Bo; Tian, Kuo; Zhou, Chuanli; Hao, Peng; Zheng, Yanbing; Ma, Yunlong; Wang, Jiebing

doi:10.1016/j.ast.2016.12.002

Cited by 73 publications

(26 citation statements)

References 31 publications

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“…In this section the WMPLA is applied to the conical shell. For this purpose, a Radial Basis Function (RBF) surrogate-based optimization is performed on the coordinates of multiple perturbation loads [55], [56] in order to implement the WMPLA for a cylindrical shell under pure bending. Through numerical trials, the number of multiple perturbation loads is selected as three, which is a compromise between the optimization convergence and efficiency, the perturbation load is set to 20 N (which can guarantee the convergence of imperfection sensitivity).…”

Section: Worst Multiple Perturbation Load Approach (Wmpla)mentioning

confidence: 99%

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On the development of shell buckling knockdown factors for imperfection sensitive conical shells under pure bending

Wagner

Hühne

Khakimova³

2019

Thin-Walled Structures

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Thin-walled cylindrical shells are used as adapters between cylindrical shells of different diameters in launch-vehicle systems or as tailbooms in helicopters. A major loading scenario for cylindrical shells is bending. The buckling moment of these shells is very sensitive to imperfections (geometry, loading conditions) which results in a critical disagreement between theoretical and experimental results for axially loaded cylindrical shells. The design of these stability critical shells is based on classical buckling loads obtained by a linear analysis which are corrected by a single knockdown factor (0.41-NASA SP-8019) for all cone geometries. This practice is well established among designers and hasn't changed for the past 50 years because the buckling behavior is till today not very well understood. Within this paper a reduced stiffness analysis for cylindrical shells under pure bending is performed. Data of previous experimental testing campaigns are used to validate the new design criteria for different cylindrical shell geometry configurations. The results show that the application of the new design recommendation for cylindrical shell structures results in increased knockdown factors for the buckling moment which in turn may lead to a significant weight reduction potential. All ABAQUS-Python scripts and the results generated for this article are deposited in the Elsevier repository.

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Section: Worst Multiple Perturbation Load Approach (Wmpla)mentioning

confidence: 99%

“…The minimum KDF for the buckling moment of a cylindrical shells equals to 0.41 which is also the proposed Design KDF of the NASA SP-8019 for all cone geometries. The results for cylinders under pure bending (56) from [1] are shown for the purpose of comparison in Fig. 2 (right).…”

Section: Introductionmentioning

confidence: 99%

On the development of shell buckling knockdown factors for imperfection sensitive conical shells under pure bending

Wagner

Hühne

Khakimova³

2019

Thin-Walled Structures

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“…Consequently, an efficient optimization process of the material distribution is required to obtain the desired structural response, usually defined in terms of deflections and load-carrying capacity. Many manufacturing options are also available to fine-tune the stiffness and the onset of buckling: grid stiffeners [ 1 ], multi-layered and variable thickness composites [ 2 ], variable angle tows (VATs) [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of CNT-Nanocomposite Nonlinear Shells

et al. 2020

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Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to accurately describe the point-wise material distribution. The sensitivity to geometrical imperfections is also investigated. The optimization is carried out making use of the Global Convergent Method of Moving Asymptotes. The extensive numerical analyses show that varying the volume fraction distribution as well as the CNTs orientation can lead to significantly enhanced performances towards the loss of elastic stability making these lightweight structures more stable. The most striking result is that for curved shells, the unstable postbuckling response of the baseline material can be turned into a globally stable response maintaining the same amount of nanostructural reinforcement but simply tailoring strategically its distribution.

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“…For example, the dragonfly wing is one typical hierarchical structure with high specific stiffness, including brawny major veins to bear axial load and close-knit minor veins to resist local deformation. 20 Inspired by this, Wang et al 21 developed novel hierarchical stiffened shells with diverse stiffener sizes and patterns, which improved the ability of stiffened shells against buckling and imperfections. Generally, the hierarchical stiffened shell is composed of the skin, major stiffeners (with larger sizes), and minor stiffeners (with smaller sizes).…”

Section: Introductionmentioning

confidence: 99%

“…[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. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Tian

Zhang

et al. 2019

Journal of Reinforced Plastics and Composites

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The surrogate-based optimization of hierarchical stiffened composite shells against buckling is a typical multimodal and multivariables optimization problem. To improve the computational efficiency and global optimizing ability of the surrogate-based optimization of hierarchical stiffened composite shells, an enhanced variance reduction method based on Latinized partially stratified sampling and multifidelity analysis methods is proposed in this paper and then integrated into the surrogate-based optimization framework. In the offline step of the optimization framework, candidate pairing strategies of design variables are generated by Latinized partially stratified sampling and compared by performing priori optimizations based on the low-fidelity analysis method, and the optimal pairing strategy is therefore determined. On the basis of the optimal pairing strategy, the surrogate-based optimization is carried out using the highfidelity analysis method in the online step. With less computational cost in the offline step, the proposed enhanced variance reduction method overcomes the limitation of Latinized partially stratified sampling that the optimal pairing strategy is not obvious in complex problems. Then, extensive optimization examples are carried out to verify the efficiency and effectiveness of the proposed optimization framework. Given an approximate computational cost, the optimal buckling result of the proposed framework using enhanced variance reduction method increases by 18.2% than that of the traditional framework based on Latin hypercube sampling. In particular, the advantage of enhanced variance reduction method in the space-filling ability is highlighted in comparison to Latin hypercube sampling. When achieving an approximate global optimal solution, the proposed framework reduces the total computational cost by 76.3% than the traditional framework. Finally, the numerical implementation of asymptotic homogenization method is used herein for the accurate prediction of effective stiffness coefficients of the initial design and optimal results. Through comparison, it is concluded that the high axial stiffness and bending stiffness are the main mechanism for the high loadcarrying capacity of optimal results.

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Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity

Cited by 73 publications

References 31 publications

On the development of shell buckling knockdown factors for imperfection sensitive conical shells under pure bending

On the development of shell buckling knockdown factors for imperfection sensitive conical shells under pure bending

Optimal Design of CNT-Nanocomposite Nonlinear Shells

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

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