A New Formulation for Fictitious Mass in the Viscous Dynamic Relaxation Method

In this paper, new algorithm is proposed for fictitious mass of Dynamic Relaxation (DR) method with viscous damping. First, the incremental equations are derived for DR procedure. By using the transformed Gershgörin theory, new boundaries are achieved for fictitious mass. This formulation leads to a new algorithm for viscous DR method. For evaluating the efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed by elastic linear and geometrically nonlinear behaviors. Results show that the proposed scheme for fictitious mass improves the convergence rate of DR method so that the suggested algorithm presents the structural response with less iteration in comparison with other common DR techniques.