TY - JOUR

T1 - Polarized Hessian covariant

T2 - Contribution to pattern formation in the Föppl-von Kármán shell equations

AU - Guha, Partha

AU - Shipman, Patrick

PY - 2009/9/15

Y1 - 2009/9/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=67649538148&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2008.10.025

DO - 10.1016/j.chaos.2008.10.025

M3 - Article

AN - SCOPUS:67649538148

SN - 0960-0779

VL - 41

SP - 2828

EP - 2837

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 5

ER -