Abstract
This paper deals a study on post-buckling problem of a large deformed elastic beam by using a canonical dual mixed finite element method (CD-FEM). The nonconvex total potential energy of this beam can be used to model post-buckling problems. To verify the triality theory, different types of dual stress interpolations are used. Applications are illustrated with different boundary conditions and different external loads using semi-definite programming (SDP) algorithm. The results show that the global minimizer of the total potential energy is stable buckled configuration, the local maximizer solution leads to the unbuckled state, and both of these two solutions are numerically stable. While the local minimizer is unstable buckled configuration and very sensitive.
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Acknowledgements
The research is supported by US Air Force Office of Scientific Research under grants FA2386-16-1-4082 and FA9550-17-1-0151.
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Ali, E.J., Gao, D.Y. (2017). Improved Canonical Dual Finite Element Method and Algorithm for Post-Buckling Analysis of Nonlinear Gao Beam. In: Gao, D., Latorre, V., Ruan, N. (eds) Canonical Duality Theory. Advances in Mechanics and Mathematics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-58017-3_14
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DOI: https://doi.org/10.1007/978-3-319-58017-3_14
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