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

Document Type : Research Article

Authors

• Mohammad Rezaiee-Pajand ¹
• J. Alamatian ²
• Hasine Rezaee ¹

¹ Department of Civil Engineering, Factualy of Engineering, Ferdowsi Unversity of Mashhad, Mashhad, Iran.

² Civil Engineering Department, Mashhad Branch, Islamic Azad Unversity, Mashhad, Iran.

10.22067/ijnao.v7i2.60552

Abstract

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.

Keywords

• dynamic relaxation method‎
• ‎formulation‎
• ‎solver‎
• ‎review‎
• ‎iterative technique‎
• ‎state of the art

20.1001.1.24236977.2017.7.2.5.6

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