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Optimal bounds from below of the critical load for elastic solids subject to uniaxial compression
Author(s) -
Castellano Anna,
Foti Pilade,
Fraddosio Aguinaldo,
Marzano Salvatore,
Piccioni Mario Daniele
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510136
Subject(s) - compression (physics) , upper and lower bounds , hadamard transform , bifurcation , cylinder , critical load , stability (learning theory) , mathematics , buckling , subject (documents) , computer science , structural engineering , mathematical optimization , materials science , mathematical analysis , physics , engineering , geometry , composite material , nonlinear system , quantum mechanics , machine learning , library science
In the recent papers [1,2] we studied a new procedure based on the Korn inequality for determining sufficient conditions for the Hadamard stability, aimed at determining optimal lower bound estimates for the critical load in bifurcation problems. Here, we discuss the effectiveness of our approach for the classical representative problem of uniaxial compression of a Mooney‐Rivlin circular cylinder. We find that our lower bound estimate is effective and advantageous for applications, since it is easily implementable in numerical codes. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)