A new formulation for fictitious mass of the Dynamic Relaxation method with kinetic damping

► A new fictitious mass derives for kinetic DR method based on incremental analysis. ► This formulation combines with the transformed Gerschgörin theory presented here. ► The proposed scheme is used for static and dynamic analyses of structures. ► The convergence rate of the new method is higher than the other DR approaches. This paper deals with the stability and convergence rate of the kinetic damping process in Dynamic Relaxation (DR) method. Based on running an incremental analysis, a new relationship is presented for fictitious mass of the kinetic DR algorithm. This formulation is also combined with a transformational form of the Gerschgörin circles theory, proposed here. For numerical verification, some structures from the finite element models are analyzed statically and dynamically and results are compared with the well-known viscous and kinetic DR algorithms. These examples clearly show that the proposed fictitious mass considerably increases the convergence rate of the kinetic DR iterations.