Vol. 5, No. 6, 2010

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An enhanced asymptotic expansion for the stability of nonlinear elastic structures

Claus Dencker Christensen and Esben Byskov

Vol. 5 (2010), No. 6, 925–961

A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions.

The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions, such as inextensibility. Membrane locking and similar problems are also handled by the method.

elastic stability, full nonlinearity, asymptotic expansion
Received: 19 March 2010
Revised: 24 August 2010
Accepted: 30 August 2010
Published: 1 January 2011
Claus Dencker Christensen
NKT Flexibles I/S
Priorparken 510
DK-2605 Brøndby
Esben Byskov
Department of Civil Engineering
Aalborg University
Sohngaardsholmsvej 57
DK-9000 Aalborg