Comparative analysis of three-dimensional frames by dynamic relaxation methods

Analysis of three-dimensional frames is a complex process. Each node of these structures has six degrees of freedom, which results in a large set of governing equations. Investigators have utilized the computer power to extend the application of numerical approaches. One of these methods is named dynamic relaxation technique. This strategy explicitly solves the simultaneous system of equations. In this scheme, the static structural equilibrium equations are converted into a dynamic one by adding fictitious mass and damping. To perform nonlinear geometric analysis of 3D frames, 12 classical DR methods are exploited. Previously, the abilities of these approaches in analyzing these structures have not been compared. In each technique, time step, mass, and damping matrices are obtained based on other researchers' works. The structural behavior is assessed with and without considering the shear deformations. For both cases, the load–displacement curves are depicted. In this article, 11 different frames are analyzed. Since a few nonlinear solutions of 3D frames are available, these structures can be used as a benchmark in the future studies. Finally, the used algorithms are graded based on their required number of iterations and analysis time. Findings prove that the Qiang, Rezaiee-Pajand and Sarafrzi techniques perform more successfully in comparison to the other schemes.