Abstract
In this paper, a computationally implementable and feasible two-mode asymptotic bifurcation theory is proposed for structural buckling analysis. Using this theory, snap-through, asymmetric bifurcation, unstable and stable symmetric bifurcation might be reliably diagnosed by solely solving two simultaneous polygonal equations which can be derived by exact first and second order directional derivatives of singular tangent stiffness matrices with respect to nodal degree-of-freedoms along critical and non-critical modes. The error-free computation of the derivatives is accomplished by using hyper-dual numbers. Graphical tool such as Matlab is useful to visualize the existence of the solutions of the two resulting simultaneous polygonal equations and number of possible real roots can well predict post-buckling behavior. Numerical examples of nonlinear finite element stability analysis verify the robustness of the proposed two-mode asymptotic bifurcation theory.
