Abstract
This research presents a new algorithm for the Dynamic Relaxation (DR) method with kinetic damping by utilizing Lagrangian interpolation functions to derive new iterative kinetic DR equations. This procedure leads to an algorithm that, unlike the ubiquitous DR methods, does not require the calculation of nodal velocities, thereby marching forward only through successive nodal displacement. Also, the power iteration method is used to determine the optimal time step ratio. By utilizing this time step, the restarting analysis phase, which is one of the drawbacks of the kinetic DR strategy, is eliminated. In order to evaluate the performance and efficiency of the proposed method, some truss and frame structures with geometrically nonlinear behavior are analyzed. Results prove that the number of convergence iterations and analysis duration is reduced in the new kinetic DR scheme compared to other conventional DR methods.
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