TY - JOUR ID - 24575 TI - The state of the art in Dynamic Relaxation methods for structural mechanics Part 1: Formulations JO - Iranian Journal of Numerical Analysis and Optimization JA - IJNAO LA - en SN - 2423-6977 AU - Rezaiee-Pajand, Mohammad AU - Alamatian, J. AU - Rezaee, Hasine AD - Department of Civil Engineering, Factualy of Engineering, Ferdowsi Unversity of Mashhad, Mashhad, Iran. AD - Civil Engineering Department, Mashhad Branch, Islamic Azad Unversity, Mashhad, Iran. Y1 - 2017 PY - 2017 VL - 7 IS - 2 SP - 65 EP - 86 KW - dynamic relaxation method‎ KW - ‎formulation‎ KW - ‎solver‎ KW - ‎review‎ KW - ‎iterative technique‎ KW - ‎state of the art DO - 10.22067/ijnao.v7i2.60552 N2 - 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. UR - https://ijnao.um.ac.ir/article_24575.html L1 - https://ijnao.um.ac.ir/article_24575_c993a459a801bdd6171650a1130226da.pdf ER -