A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

Yang, Licai; Luo, Ying; Qiu, Tian; Zheng, Hao; Zeng, Peng

doi:10.1016/j.euromechsol.2021.104406

Cited by 14 publications

(7 citation statements)

References 18 publications

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“…Referring to present literatures 21,25,26 for thin-walled cylindrical shells and taking combined non-uniform loads of equations ( 1) and ( 3) into consideration, we can derive the following governing differential equations:…”

Section: Governing Differential Equationsmentioning

confidence: 99%

“…Wang et al 24 experimentally studied nonlinear postbuckling behaviors of stiffened circular shells by constructing an advanced loading system, which were under uniform axial compression and stepped non-uniform external pressure. Recently, Yang et al 25,26 developed a one-parameter regular perturbation method to study the stability of circular shells under distributed lateral pressure or local axial compressive load. Using the presented formulas, common load conditions in practical engineering were considered.…”

Section: Introductionmentioning

confidence: 99%

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Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

Yang

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper focuses on the buckling problem of cylindrical shells under combined non-uniform axial compression and external pressure. To obtain buckling loads, a completely new method called two-parameter perturbation method is established. Using this method, governing differential equations are solved and buckling loads expressed by load functions, load parameters, and shell dimensions are derived for the first time. Comparative studies show that buckling loads by the analytical formulas coincide with those for combined uniform loads or single wind load in literatures. Buckling of a cylinder subjected to combined bending and wind loads is analyzed, and confirmed by the Galerkin method for the case of small load variations. Therefore, the presented formulas are adequately validated. The numerical calculations are carried out to analyze the effects of non-uniform load parameters on buckling load coefficient. The obtained results in this paper can be applied to evaluate buckling loads for cylinders subjected to combined non-uniform loads in actual engineering.

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Section: Governing Differential Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

Yang

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…The typical locking treatment approaches, which may not be restricted to solid-shell elements, include assumed natural strains (ANS), 18,19 enhanced assumed strain (EAS), 20 discrete strain gap (DSG), 21 B-method, [22][23][24][25] mixed formulations, 22,[26][27][28] selective/reduced integration, 26,[29][30][31] and projection techniques based on the moving least square (MLS). 32 Extensive literatures have reported that shells are studied by kinds of numerical methods: the finite element method (FEM), [33][34][35] the meshfree method, [36][37][38][39] and analytical 40,41 or semianalytical 42,43 methods and so forth. Apart from these, the approach of isogeometric analysis (IGA) introduced by Hughes et al 44 has also been frequently adopted in the analysis of laminated shells.…”

Section: Introductionmentioning

confidence: 99%

“…Extensive literatures have reported that shells are studied by kinds of numerical methods: the finite element method (FEM), 33–35 the meshfree method, 36–39 and analytical 40,41 or semianalytical 42,43 methods and so forth. Apart from these, the approach of isogeometric analysis (IGA) introduced by Hughes et al 44 has also been frequently adopted in the analysis of laminated shells 9,15,45–47 .…”

Section: Introductionmentioning

confidence: 99%

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Fan

Huang

Zeng

et al. 2022

Numerical Meth Engineering

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The computation cost of matrix formation in isogeometric analysis can be drastically reduced by employing tensor decomposition, but the performance like accuracy and robustness still depends on the approach used to realize the low‐rank approximation for the nonpolynomial integral kernels. In the buckling analysis of laminated shells with solid‐shell model, the integral kernels are not smooth in the thickness direction due to their material and stress distribution and have a high complexity because the curvilinear coordinate systems are involved in the representation of anisotropic constitutive relations, which makes it more difficult to guarantee the decomposition accuracy. This paper proposes a robust high‐fidelity tensor‐decomposition based matrix formation method for stiffness matrix and geometric stiffness matrix of the isogeometric buckling analysis problem. The proposed method avoids using a spline approximation and employs the hierarchical block‐wise decomposition approach (HBD) to obtain a determinate decomposition result, which saves more time without loss of accuracy and produces less canonical ranks with a reliable procedure. Besides, the matrix calculation is partly independent of the number of layers, showing a higher efficiency when the number of layers is larger. Finally, several experiments with various Gaussian curvatures are implemented to validate the proposed method.

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“…Wang et al [20] experimentally investigated post-buckling of a stiffened cylinder which was loaded by a combination of axial load and variable external pressure produced by airbags. Yang et al [21] also conducted an analytical investigation on buckling of cylinders under non-uniform lateral pressure loads, which was accomplished by a single perturbation procedure.…”

Section: Introductionmentioning

confidence: 99%

Analytical buckling load formulas for cylindrical shell structures with variable thickness under non-uniform external pressure

Yang

2022

Mathematics and Mechanics of Solids

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The novel contribution of this paper is to develop a quadratic perturbation method to derive general analytical buckling load formulas for cylindrical shell structures with varying wall thickness under non-uniform lateral pressure loads for the first time. Arbitrary thickness and lateral pressure loads are skillfully described and governing differential equations are derived. A quadratic perturbation method is developed to derive buckling load formulas, which establishes the relation among buckling loads, thickness, and load functions. The presented formulas are adequately validated by comparing with recent results for variable wall thickness or non-uniform external pressure, and exhibit a great advantage in determining buckling loads. For the purpose of engineering application, buckling of a cylinder with linear thickness under linear liquid pressure and wind load is deeply studied by the presented formulas. This study can provide a highly efficient method for buckling load computation, and a guide to design the thickness of the shell under non-uniform lateral loads.

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A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

Cited by 14 publications

References 18 publications

Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Analytical buckling load formulas for cylindrical shell structures with variable thickness under non-uniform external pressure

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