Polarized Hessian covariant: Contribution to pattern formation in the Föppl-von Kármán shell equations

Partha Guha, Patrick Shipman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We analyze the structure of the Föppl-von Kármán shell equations of linear elastic shell theory using surface geometry and classical invariant theory. This equation describes the buckling of a thin shell subjected to a compressive load. In particular, we analyze the role of polarized Hessian covariant, also known as second transvectant, in linear elastic shell theory and its connection to minimal surfaces. We show how the terms of the Föppl-von Kármán equations related to in-plane stretching can be linearized using the hodograph transform and relate this result to the integrability of the classical membrane equations. Finally, we study the effect of the nonlinear second transvectant term in the Föppl-von Kármán equations on the buckling configurations of cylinders.

Original languageBritish English
Pages (from-to)2828-2837
Number of pages10
JournalChaos, Solitons and Fractals
Volume41
Issue number5
DOIs
StatePublished - 15 Sep 2009

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