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The Reduced Basis Method for an Elastic Buckling Problem
Author(s) -
Za Lorenzo,
VeroyGrepl Karen
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310213
Subject(s) - buckling , eigenvalues and eigenvectors , nonlinear system , mathematics , a priori and a posteriori , constraint (computer aided design) , estimator , uniqueness , basis (linear algebra) , mathematical optimization , linear elasticity , mathematical analysis , finite element method , structural engineering , geometry , physics , statistics , philosophy , epistemology , quantum mechanics , engineering
In this work, we apply the Reduced Basis (RB) Method to the field of nonlinear elasticity. In this first stage of research, we analyze a buckling problem for a compressed 2D column: Here, the trivial linear solution is computed for an arbitrary load; the critical load, marking the transition to nonlinearity, is then identified through an eigenvalue problem. The linear problem satisfies the Lax‐Milgram conditions, allowing the implementation of both a Successive Constraint Method for an inexpensive lower bound of the coercivity constant and of a rigorous and efficient a posteriori error estimator for the RB approximation. Even though only a non‐rigorous estimator is available for the buckling problem, the actual RB approximation of the output is more than satisfactory, and the gain in computational efficiency significant. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)