Performance of the Generalized-α (G-α) Algorithm for Discontinuous Dynamics by the Numerical Manifold Method

Abstract

Performance of the generalized-α (G-α) time integration scheme using the numerical manifold method was examined for the continuous and discontinuous rock dynamic problems in the present paper. Influence of the generalized-α time integration scheme on the numerical stability and accuracy were studied using the dynamic equation of motion, in which various parameters such as control parameters and kinetic damping were compared by the amplification matrix A. Furthermore, convergence productiveness of the open–close iterations for the generalized-α time integration with the case of contact was also investigated. The validations of the generalized-α algorithm were conducted by a transient response analysis of an elastic strip subjected to harmonic function loading, contact analysis of layered rock deflection, and mechanical behavior of dynamical tunneling of jointed rock masses, respectively. It can be concluded from the numerical results that the proposed generalized-α scheme used in the present study has superior qualities compared to the original algorithm in solving rock dynamic problems involving more nonlinear contacts using the numerical manifold method.