- Title
- On SPD method for solving canonical dual problem in post buckling of large deformed elastic beam
- Creator
- Ali, Elaf; Gao, David
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/167618
- Identifier
- vital:13673
- Identifier
-
https://doi.org/10.4310/CMS.2018.v16.n5.a3
- Identifier
- ISBN:1539-6746
- Abstract
- This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex potential leads to a stable configuration of the buckled beam, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. However, the local minimum solution leads to an unstable buckled state, which is very sensitive to axial compressive forces, thickness of beam, numerical precision, and the size of finite elements. The method and algorithm proposed in this paper can be used for solving general nonconvex variational problems in engineering and sciences.
- Publisher
- International Press of Boston, Inc.
- Relation
- Communications in Mathematical Sciences Vol. 16, no. 5 (2018), p. 1225-1240
- Rights
- Copyright © 2018 International Press.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0102 Applied Mathematics; 1502 Banking, Finance and Investment; Post buckling; Nonlinear Gao beam; Canonical dual finite element method; Global optimization; Triality theory
- Full Text
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