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On the mathematical structure of Eigen-deformations in a Föppl-von Kàrmàn Bifurcation system


Coman, CD and Bassom, AP, On the mathematical structure of Eigen-deformations in a Föppl-von Kàrmàn Bifurcation system, Journal of Elasticity, 131, (2) pp. 183-205. ISSN 0374-3535 (2018) [Refereed Article]

DOI: doi:10.1007/s10659-017-9652-3


Bifurcations of thin circular elastic plates subjected to uniform normal pressure are explored by taking into account the flexural compliance of the edge restraint. This effect is accounted for by formally reinforcing the outer rim of the plate with a curved beam element, whose net effect is akin to a Hookean spring relating the inclination of the median surface of the plate (with respect to a horizontal plane) and the radial edge moment. The new added feature reflects the imperfect nature of the boundary restraints achieved under realistic physical conditions, and includes as particular cases the usual boundary conditions associated with flexurally simply-supported and clamped plates. It is shown here that in the limit of eigen-deformations with very short wavelengths in the azimuthal direction the two equations in the Föppl-von Kármán bifurcation system remain coupled. However, for edge restraints close to the former type the asymptotic limit of the bifurcation system is described by an Airy-like equation, whereas when the outer rim of the plate is flexurally clamped the Airy-like structure morphs into a standard equation for parabolic cylinder functions. Our singular perturbation arguments are complemented by direct numerical simulations that shed further light on the aforementioned results.

Item Details

Item Type:Refereed Article
Keywords:plate equations, wrinkling, bifurcations
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:124766
Year Published:2018
Deposited By:Mathematics and Physics
Deposited On:2018-03-08
Last Modified:2019-02-27

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