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

In the last sixty yearsý, ýthe Dynamic Relaxation methods have evolved significantlyý. ýThese explicit and iterative procedures are frequently used to solve the linear or nonlinear response of governing equations resulted from structural analysesý. ýIn the first part of this studyý, ýthe common DR formulations are reviewedý. ýMathematical bases and also physical concepts of these solvers are explained brieflyý. ýAll the DR parametersý, ýi.eý. ýfictitious massý, ýfictitious dampingý, ýfictitious time step and initial guess are describedý, ýas wellý. ýFurthermoreý, ýsolutions of structural problems along with kinetic and viscous damping formulations are discussedý. ýAnalyses of the existing studies and suggestions for future research trends are presentedý. ýIn the second partý, ýthe applications of Dynamic Relaxation method in engineering practices are reviewed.