ABSTRACT
Deterministic structural bifurcation buckling analysis has been widely utilized as an effective safety assessment for engineering structures against unstably large displacements. Although the conventional buckling analysis involves geometric nonlinearity, the deterministic structural bifurcation buckling analysis has facilitated the nonlinear analysis into an eigenvalue problem by assuming an inert stiffness matrix of structure against externally applied loads (Przemieniecki, 1985). The Bifurcation Buckling Load (BBL) factor can be calculated by solving the following eigenvalue problem:
( ) z 0m hλcr (1)
where Km, Kg denote the conventional material and geometric stiffness matrices in the reference configuration respectively; λcr denotes the deterministic BBL factor which is the minimum positive eigenvalue of Eq. (1); z is an non-zero vector which denotes the eigenvector corresponding to λcr. The eigen-analysis presented in Eq. (1) is indeterminate, so the eigenvector z denotes the structural buckled shape instead of actual buckling deformations (Przemieniecki, 1985). In traditional deterministic bifurcation buckling analysis, it involves two stages to complete the calculation process (Przemieniecki, 1985). In the first stage of analysis, a linear problem is solved in the reference configuration to determine the axial stress within each element so the geometric stiffness matrix can be obtained for that reference configuration. Subsequently, the second stage involves an eigenvalue calculation in which the BBL factor can be obtained.
