The state of the art in Dynamic Relaxation methods for structural mechanics Part 1: Formulations

In the last sixty years‎, ‎the Dynamic Relaxation methods have evolved significantly‎. ‎These explicit and iterative procedures are frequently used to solve the linear or nonlinear response of governing equations resulted from structural analyses‎. ‎In the first part of this study‎, ‎the common DR formulations are reviewed‎. ‎Mathematical bases and also physical concepts of these solvers are explained briefly‎. ‎All the DR parameters‎, ‎i.e‎. ‎fictitious mass‎, ‎fictitious damping‎, ‎fictitious time step and initial guess are described‎, ‎as well‎. ‎Furthermore‎, ‎solutions of structural problems along with kinetic and viscous damping formulations are discussed‎. ‎Analyses of the existing studies and suggestions for future research trends are presented‎. ‎In the second part‎, ‎the applications of Dynamic Relaxation method in engineering practices are reviewed.