Nonlinear dynamic structural analysis using dynamic relaxation with zero damping

Rezaiee‐Pajand, Mohammad; Sarafrazi, S. R.

doi:10.1016/j.compstruc.2011.04.005

Cited by 42 publications

(19 citation statements)

References 58 publications

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“…Dynamic relaxation has been employed for the static analysis of truss structures [18,19], cable structures [20][21][22], tensegrity structures [23,24], prestressed net structures and membranes [25][26][27], reciprocal frames [28], spline structures [29] as well as for dynamic analyzes [30,31]. In this paper, dynamic relaxation is employed for the cross-sectional analysis of inflatable membrane dams.…”

Section: Dynamic Relaxation: the Basic Schemementioning

confidence: 99%

Form finding and analysis of inflatable dams using dynamic relaxation

Streeter

Rhode-Barbarigos

Adriaenssens

2015

Applied Mathematics and Computation

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Section: Dynamic Relaxation: the Basic Schemementioning

confidence: 99%

Form finding and analysis of inflatable dams using dynamic relaxation

Streeter

Rhode-Barbarigos

Adriaenssens

2015

Applied Mathematics and Computation

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“…a ii m ii (43) In this relationship, a ii m ii are the contributions of each degree of freedom when the other degrees-of freedom are absent. Hence:…”

Section: Zero Damping Techniquementioning

confidence: 99%

“…Rezaiee-Pajand and Sarafrazi suggested the relation between the critical damping ratio and the time step [43]. Then, they assumed the damping parameter to be zero and obtained the following formula for the time step ratio γ:…”

Section: Zero Damping Techniquementioning

confidence: 99%

“…Furthermore, the following equation is utilized instead of Eqs. (5) and (6) in order to calculate the velocity and displacement vectors [43]:…”

Section: Zero Damping Techniquementioning

confidence: 99%

“…Sarafrazi and Rezaiee-Pajand suggested an equation for finding the time step ratio. The damping is zero in their process [43]. Rezaiee-Pajand et al obtained another tactic for artificial time step based on the unbalanced energy [44].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Comparison of Large Deflection Analysis of Bending Plates by Dynamic Relaxation

Rezaiee‐Pajand

Estiri²

2016

Period. Polytech. Civil Eng.

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Dynamic relaxation method based on Lanczos algorithm

Namadchi

Alamatian

2017

Int. J. Numer. Meth. Engng

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This paper tries to accelerate the convergence rate of the general viscous dynamic relaxation method. For this purpose, a new automated procedure for estimating the critical damping factor is developed by employing a simple variant of the Lanczos algorithm, which does not require any re-orthogonalization process. All of the computational operations are performed by simple vector-matrix multiplication without requiring any matrix factorization or inversion. Some numerical examples with geometric nonlinear behavior are analyzed by the proposed algorithm. Results show that the suggested procedure could effectively decrease the total number of convergence iterations compared with the conventional dynamic relaxation algorithms.A. H. NAMADCHI AND J. ALAMATIAN time integration process. Large amount of research has been directed toward both improving the DR parameters and application of the DR method in various engineering problems. Otter employed DR to analyze axially symmetric pressure vessels and a three-dimensional elastic arch dam using central finite differences [5,6]. Cassel investigated the application of DR technique in analyze of cylindrical shells [7]. Rushton proposed a systematic procedure to tackle rectangular plate problems including small and large deflection of elastic plates as well as the buckling behavior [8][9][10]. In order to damp out the artificial oscillations as quick as possible, Rushton suggested that the critical damping of fundamental mode of vibration is selected as the fictitious damping factor, and an automated process for estimating this factor was also introduced [8]. Considering DR as a fictitious time-marching scheme, Brew and Brotton investigated DR characteristics based on the concept of amplification matrix and employed DR to analyze frame structures [11]. Pseudo-transient analysis of linear and geometric nonlinear Mindlin plates using finite element method was successfully carried out by adopting a specific form of DR. Some empirically based suggestions regarding time-step selection and fictitious mass matrix were also reported [12]. By assuming a load vector proportional to diagonal entries of the artificial mass matrix, which is formulated using Gershgorin's circle theorem, Bunce proposed a new technique to determine critical damping in DR algorithm based on the Rayleigh's principle [13]. In another study, Papadrakakis evaluated DR properties by transforming the fundamental difference equations into the error space, which leads to an eigenvalue problem. By examining the resultant characteristic equation, a new automated procedure for estimating DR fictitious parameters was proposed that improves the convergence rate of the method [3]. Zienkiewicz and Löhner studied the concept of viscous relaxation in which the inertial term is removed from the virtual dynamic system. They then utilized a line search technique to accelerate the convergence [14]. Instead of applying the external load in an incremental form, which is conventional in nonlinear quasi-static analyses, a novel techniq...

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Nonlinear dynamic structural analysis using dynamic relaxation with zero damping

Cited by 42 publications

References 58 publications

Form finding and analysis of inflatable dams using dynamic relaxation

Form finding and analysis of inflatable dams using dynamic relaxation

A Comparison of Large Deflection Analysis of Bending Plates by Dynamic Relaxation

Dynamic relaxation method based on Lanczos algorithm

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