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Finding buckling points for nonlinear structures by dynamic relaxation scheme

Frontiers of Structural and Civil Engineering 2020年第1期14卷 23-61页

作者： mohammad rezaiee-pajand Hossein ESTIRI Civil Engineering Department Ferdowsi University of MashhadMashhad 91775-1111Iran

Dynamic Relaxation Method(DRM)is an explicit approach for solving the simultaneous systems of *** this tactic,the fictitious mass and damping are added to the static governing equations,and an artificial dynamic system is *** using DRM for nonlinear analysis,the structural static equilibrium path is *** outcome is extremely valuable,since it leads to the behavior of *** the finding related to the structural static path are the critical and buckling points for nonlinear *** this paper,a new way for calculating the load factor is proposed by setting the external work *** the dynamic relaxation scheme with external work technique has not been formulated so *** all incremental-iterative methods,the load factor increment sign should be determinated by extra *** sign leads to increase or decrease of the load *** is worth emphasizing that sign of the load factor increment changes at the load limit ***,the sign determinations are required in the common work control *** disadvantages are eliminated in the proposed *** fact,the suggested load factor depends only on the Dynamic Relaxation(DR)fictitious ***,all DR calculations are performed via vector ***,the load factor is calculated only by one formula,and it has the same relation in the all solution *** contrast to the arc length techniques,which requires the sign determined,the proposed scheme does not need any sign *** is shown that author’s technique is quicker than the other dynamic relaxation *** prove the capability and efficiency of the presented scheme,several numerical tests are *** results indicate that the suggested approach can trace the complex structural static paths,even in the snap-back and snap-through parts.

关键词： load factor external work dynamic relaxation static equilibrium path large displacement

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Nonlinear analysis of cable structures using the dynamic relaxation method

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Frontiers of Structural and Civil Engineering 2021年第1期15卷 253-274页

作者： mohammad rezaiee-pajand mohammad mohammadI-KHATAMI Department of Civil Engineering Ferdowsi University of MashhadMashhad ***Iran

The analysis of cable structures is one of the most challenging problems for civil and mechanical *** they have highly nonlinear behavior,it is difficult to find solutions to these *** far,different assumptions and methods have been proposed to solve such *** dynamic relaxation method(DRM)is an explicit procedure for analyzing these types of *** utilize this scheme,investigators have suggested various stiffness matrices for a cable *** this study,the efficiency and suitability of six well-known proposed matrices are assessed using the *** achieve this goal,16 numerical examples and two criteria,namely,the number of iterations and the analysis time,are *** on a comprehensive comparison,the methods are ranked according to the two *** numerical findings clearly reveal the best ***,a variety of benchmark problems are suggested by the authors for future studies of cable structures.

关键词： nonlinear analysis cable structure stiffness matrix dynamic relaxation method

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A fast and accurate dynamic relaxation scheme

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Frontiers of Structural and Civil Engineering 2019年第1期13卷 176-189页

作者： mohammad rezaiee-pajand mohammad mohammadI-KHATAMI Department of Civil Engineering Ferdowsi University of MashhadMashhadIran

Dynamic relaxation method (DRM)is one of the suitable numerical procedures for nonlinear structural *** the fictitious inertia and damping forces to the static equation,and turning it to the dynamic system,are the basis of this *** selection of the DRM artificial factors leads to the better convergence rate and efficient *** study aims to increase the numerical stability,and to decrease the analysis *** fulfil this objective,the reduction rate of analysis error for consecutive iterations is *** on this formulation,a new time step is found for the viscous dynamic *** combining this novel relationship with the other DRM factors,various geometrical nonlinear structures,such as trusses,frames,and shells,are *** obtained results verify the efficiency of authors'scheme.

关键词： viscous dynamic relaxation time step displacement error geometric nonlinear analysis

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