This paper develops the optimal time-step ratio and the critical damping for nonlinear structural analysis, when using dynamic relaxation method (DRM). The convergence rate of the DRM depends on the value of the time step and the critical damping factor. In the present study, the effect of the time-step ratio is separated from the time-step value. Additionally, the effect of the eigenvalue on the error function is investigated. Using the eigenvalue definition, the critical damping is updated in each dynamic relaxation (DR) step to decrease the required computations. Moreover, the optimal time-step ratio is calculated. It is also shown that the value of the constant time step has no effect on the rate of convergence. The proposed procedure provides a simple and accelerated DRM, which can be used in the linear and nonlinear analyses of structures. The efficiency of the new method was verified by its application to a wide range of typical structures. The results show that the suggested scheme accelerates the convergence rate of the DR process.

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