- Title
- Canonical finite element method for solving nonconvex variational problems to post buckling beam problem
- Creator
- Ali, Elaf; Gao, David
- Date
- 2016
- Type
- Text; Conference proceedings
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154175
- Identifier
- vital:11055
- Identifier
-
https://doi.org/10.1063/1.4965409
- Identifier
- ISSN:0094243X ISBN:9780735414389
- Abstract
- The goal of this paper is to solve the post buckling phenomena of a large deformed elastic beam by a canonical dual mixed finite element method (CD-FEM). The total potential energy of this beam is a nonconvex functional which can be used to model both pre-and post-buckling problems. Different types of dual stress interpolations are used in order to verify the triality theory. Applications are illustrated with different boundary conditions and external loads by using semi-definite programming (SDP) algorithm. The results show that the global minimum of the total potential energy is stable buckled configuration, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. While the local minimum is unstable buckled configuration and very sensitive to both stress interpolations and the external loads.
- Publisher
- American Institute of Physics Inc.
- Relation
- 2nd International Conference on Numerical Computations : Theory and Algorithms, NUMTA 2016; Pizzo Calabro, Italy; 19th-25th June 2016; published in AIP Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms Vol. 1776, p. 1-4
- Rights
- Copyright © The authors.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Numerical solutions; Buckling; Finite element methods; Interpolation; Elasticity theory
- Full Text
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