A DIRECT METHOD FOR THE COMPUTATION OF BIFURCATION BUCKLING IN GEOMETRIC NONLINEAR ANALYSIS OF STRUCTURES

Based on the solution of the bifurcation point and corresponding buckling modes by using the guided and guarded Newton method, this paper develops a reliable algorithm to compute the bifurcated branches. The solutions of the structural equilibrium equations are regarded as continuous functions of the arc-length of the solution path. The governing equations for the bifurcated directions are established from the first derivative of the equilibrium equations to the arc-length. Thus the first derivative of structural nodal displacement vector to the arc length along the bifurcated directions is expressed as the linear combination of the buckling modes and a special solution of these equations, which converses the bifurcated branch problem to the solution of the linear combination coefficients. A set of equations for these coefficients are set up from the dot products of the second derivative of the equilibrium equations to the arc-length with all buckling modes. These equations are solved by Newton-Raphson iteration from which the bifurcated directions are obtained. Extended along the bifurcated directions, the solution path is switched to the bifurcated branches. By tracing the bifurcated branches, the structure’s post-buckling behaviors can be obtained completely. Numerical examples show that this method is accurate, reliable and efficient, and that it can be used to the bifurcation buckling problems of large skeletal structures.