عنوان مقاله [English]
In this paper, a new algorithm is presented for Dynamic Relaxation (DR) method with kinetic damping. In the kinetic Dynamic Relaxation algorithm some successive points with maximum kinetic energy are traced during numerical fictitious time integration. In absence of damping forces, the points with maximum kinetic energy are near the static equilibrium position of structure. This paper deals with new formulation for kinetic DR method. For this purpose, Lagrangian interpolation functions is utilized to derive iterative Dynamic Relaxation equations. In the Lagrangian interpolation functions, new estimation of structural displacement vector is obtained based on previous estimations of displacement vector. Therefore, this procedure leads to a try and error method. on the other hand, this procedure leads to a new formulation that, unlike the ubiquitous DR methods, does not require the calculation of nodal velocities, thereby marching forward only through successive nodal displacement. Elimination the nodal velocities from Dynamic Relaxation process increases the simplicity of DR algorithm. Moreover, the requirement analysis memory is reduced in the suggested technique so that velocity vectors do not store in the program memory. 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 considered as one of the drawbacks of the common kinetic DR strategies, is eliminated. To evaluate the performance and efficiency of the proposed method, several truss and a frame structures are analyzed. These structures have geometrically nonlinear behavior (Large Deflection). Results of these analyses are also compared with other conventional Dynamic Relaxation methods. Numerical results show that the convergence rate of the proposed kinetic DR technique is higher than common DR algorithms. In the other words, number of required DR iterations for convergence is reduced in the proposed DR algorithm in comparison with other DR schemes. Moreover, the analysis time of the proposed method is lower than other common techniques.