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 in the course of numerical fictitious time integration. In the absence of damping forces, the points with maximum kinetic energy are close to the static equilibrium position of structure. This paper deals with a new formulation for kinetic DR method. For this purpose, Lagrangian interpolation functions were utilized to derive iterative Dynamic Relaxation equations. In the Lagrangian interpolation functions, new estimation of structural displacement vector was obtained based on previous estimations of displacement vector. Therefore, this procedure leads to adopting a trial 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 using the suggested technique so that velocity vectors would not be stored in the program memory. Also, the power iteration method was used to determine the optimal time step ratio. By utilizing this time step, the restarting analysis phase, 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 frame structures were analyzed. These structures had geometrically nonlinear behavior (Large Deflection). Results of these analyses were also compared with those of other conventional Dynamic Relaxation methods. Numerical results showed that the convergence rate of the proposed kinetic DR technique was higher than that of common DR algorithms. In other words, the number of the required DR iterations for convergence was reduced using the proposed DR algorithm in comparison with other DR schemes. Moreover, the analysis time of the proposed method was shorter than that of other common techniques.