A simple explicit arc-length method using the dynamic relaxation method with kinetic damping

The explicit arc-length method is simulated to trace the post-buckling equilibrium path of structures by using dynamic relaxation method with kinetic damping. This method based on the cylindrical arc-length method does not require the computation and formulation of any tangent stiffness matrix to search the snap-through or snap-back problems. The convergence to the solution is achieved by using only vector equation with kinetic damping technique. Two approaches for cylindrical arc-length control are formulated with incremental and total displacement constraint. The merits of the explicit arc-length method, in tracing the post-buckling behavior of structures, are demonstrated by analyzing the numerical examples.