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

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 7، شماره 2 - شماره پیاپی 12، دی 2017، صفحه 65-86   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v7i2.60552

نویسندگان

Mohammad Rezaiee-Pajand^{* 1}؛ J. Alamatian²؛ Hasine Rezaee¹

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

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

چکیده

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.

کلیدواژه‌ها

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

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