# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 176-189     https://doi.org/10.1007/s11709-018-0486-2
 RESEARCH ARTICLE |
A fast and accurate dynamic relaxation scheme
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 Abstract Dynamic relaxation method (DRM) is one of the suitable numerical procedures for nonlinear structural analysis. Adding the fictitious inertia and damping forces to the static equation, and turning it to the dynamic system, are the basis of this technique. Proper selection of the DRM artificial factors leads to the better convergence rate and efficient solutions. This study aims to increase the numerical stability, and to decrease the analysis time. To fulfil this objective, the reduction rate of analysis error for consecutive iterations is minimized. Based on this formulation, a new time step is found for the viscous dynamic relaxation. After combining this novel relationship with the other DRM factors, various geometrical nonlinear structures, such as trusses, frames, and shells, are analyzed. The obtained results verify the efficiency of authors’ scheme. Corresponding Authors: Mohammad REZAIEE-PAJAND Just Accepted Date: 29 May 2018   Online First Date: 17 July 2018    Issue Date: 04 January 2019