Description:
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.
Description:
This paper presents a canonical duality theory for solving general nonconvex/discrete constrained minimization problems. By using the canonical dual transformation, these challenging problems can be reformulated as a unified canonical dual problem (i.e., with zero duality gap) in continuous space, which can be solved easily to obtain global optimal solution. Some basic concepts and general theory in canonical systems are reviewed. Applications to Boolean least squares problems are illustrated.