Asymptotic limits and wrinkling patterns in a pressurised shallow spherical cap

Ciprian D. Coman, Andrew P. Bassom

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The asymmetric bifurcation problem for a shallow spherical cap is examined. The applied pressure can act either external or internal to the cap and both cases are treated here. Assuming a non-linear axisymmetric basic state, the linearised bifurcation equations for the pressurised shell are investigated in the limit when the thickness of the cap is much less than the maximum rise of the shell mid-surface. Within this regime the wrinkling patterns in both cases are confined to a narrow zone near the edge of the shell, making it possible to solve asymptotically the corresponding equations and derive analytical predictions for both the critical pressure and the corresponding number of wrinkles. Some comparisons with direct numerical simulations are included as well.

Original languageEnglish
Pages (from-to)8-18
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Volume81
Early online date12 Dec 2015
DOIs
Publication statusPublished - May 2016
Externally publishedYes

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Wrinkling
Asymptotic Limit
Shell
Direct numerical simulation
Bifurcation
Internal
Prediction
Cap

Cite this

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Asymptotic limits and wrinkling patterns in a pressurised shallow spherical cap. / Coman, Ciprian D.; Bassom, Andrew P.

In: International Journal of Non-Linear Mechanics, Vol. 81, 05.2016, p. 8-18.

Research output: Contribution to journalArticle

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AB - The asymmetric bifurcation problem for a shallow spherical cap is examined. The applied pressure can act either external or internal to the cap and both cases are treated here. Assuming a non-linear axisymmetric basic state, the linearised bifurcation equations for the pressurised shell are investigated in the limit when the thickness of the cap is much less than the maximum rise of the shell mid-surface. Within this regime the wrinkling patterns in both cases are confined to a narrow zone near the edge of the shell, making it possible to solve asymptotically the corresponding equations and derive analytical predictions for both the critical pressure and the corresponding number of wrinkles. Some comparisons with direct numerical simulations are included as well.

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