Finding limit points by dynamic relaxation method

The numerical structural analysis schemes are extensively developed by progress of modern computer processing power. One of these approximate approaches is called Dynamic Relaxation (DR) method. This technique explicitly solves the simultaneous system of equations. For analyzing the static structures, the DR strategy transfers the governing equations to the dynamic space. By adding the fictitious damping and mass to the static equilibrium equations, the corresponding artificial dynamic system is achieved. The static equilibrium path is required in order to investigate the structural stability behavior. This path shows the relationship between the loads and the displacements. In this way, the critical points and buckling loads of the nonlinear structures can be obtained. The corresponding load to the first limit point is known as buckling limit load. For estimating the buckling load, the variable load factor is used in the DR process. A new procedure for finding the load factor is presented by minimizing external work and kinetic energy, simultaneously. The proposed formula only requires the fictitious parameters of the DR scheme. To prove the efficiency and robustness of the suggested algorithm, various geometric nonlinear analyses are performed. Several trusses, frames and shells structures with nonlinear geometrically behavior is analyzed. The obtained results demonstrate that the new method can successfully estimate the buckling limit load of structures.