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.