We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The Reduced Basis Method for an Elastic Buckling Problem.
- Authors
Zanon, Lorenzo; Veroy-Grepl, Karen
- Abstract
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)
- Subjects
MECHANICAL buckling; MATHEMATICAL models; ELASTIC structures (Mechanics); NONLINEAR elastic fracture; NONLINEAR theories; EIGENVALUES; COERCIVE fields (Electronics)
- Publication
PAMM: Proceedings in Applied Mathematics & Mechanics, 2013, Vol 13, Issue 1, p439
- ISSN
1617-7061
- Publication type
Article
- DOI
10.1002/pamm.201310213