  Post buckling problem of a large deformed beam is analyzed using canonical
dual finite element method (CD-FEM). The feature of this method is to choose
correctly the canonical dual stress so that the original non-convex potential
energy functional is reformulated in a mixed complementary energy form with
both displacement and stress fields, and a pure complementary energy is
explicitly formulated in finite dimensional space. Based on the canonical
duality theory and the associated triality theorem, a primal-dual algorithm is
proposed, which can be used to find all possible solutions of this nonconvex
post-buckling problem. Numerical results show that the global maximum of the
pure-complementary energy leads to a stable buckled configuration of the beam.
While the local extrema of the pure-complementary energy present unstable
deformation states, especially. We discovered that the unstable buckled state
is very sensitive to the number of total elements and the external loads.
Theoretical results are verified through numerical examples and some
interesting phenomena in post-bifurcation of this large deformed beam are
observed.

Computational Engineering, Finance, and Science;Numerical Analysis