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Technical Brief

Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects

[+] Author and Article Information
Francisco López Jiménez, Joel Marthelot

Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

Anna Lee

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

John W. Hutchinson

School of Engineering and Applied Sciences,
Harvard University,
Cambridge, MA 02138

Pedro M. Reis

Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139;
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 28, 2016; final manuscript received December 26, 2016; published online January 24, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(3), 034501 (Jan 24, 2017) (4 pages) Paper No: JAM-16-1580; doi: 10.1115/1.4035665 History: Received November 28, 2016; Revised December 26, 2016

We explore the effect of precisely defined geometric imperfections on the buckling load of spherical shells under external pressure loading, using finite-element analysis that was previously validated through precision experiments. Our numerical simulations focus on the limit of large amplitude defects and reveal a lower bound that depends solely on the shell radius to thickness ratio and the angular width of the defect. It is shown that, in the large amplitude limit, the buckling load depends on an single geometric parameter, even for shells of moderate radius to thickness ratio. Moreover, numerical results on the knockdown factor are fitted to an empirical, albeit general, functional form that may be used as a robust design guideline for the critical buckling conditions of pressurized spherical shells.

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Figures

Grahic Jump Location
Fig. 1

(a) Contour plot of the knockdown factor, κd, for different values of the normalized radius, η, and defect angle, β0. The solid, dashed, and dashed-dotted lines correspond to instances of constant geometric parameter λ (see legend). (b) Knockdown factor, κd, versus normalized radius, η, normalized by κd (η = 1000), for different values of λ and δ¯.

Grahic Jump Location
Fig. 2

(a) Plateau knockdown factor, 〈κd〉plateau, as a function of the geometric parameter, λ, for different values of the dimensionless radius, η. The solid line corresponds to the fit of the data to Eq. (4), using the numerical values for η = 1000. Inset: representative example of κd versus δ¯, for λ = 2.5 and η = 100. (b) Plateau knockdown factor, 〈κd〉plateau, as a function of the defect angle, β0, for different values of the dimensionless radius, η.

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