The dynamic relaxation method using new formulation for fictitious mass and damping

Rezaiee‐Pajand, Mohammad; Alamatian, Javad

doi:10.12989/sem.2010.34.1.109

Cited by 55 publications

(29 citation statements)

References 28 publications

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“…8. The achieved responses are the same as those reported by Ref [41]. The ranking of the methods is inserted in Table 9.…”

Section: The Circular Platementioning

confidence: 81%

“…In 2002, Rezaiee-Pajand and Alamatian presented another equality for the fictitious mass by minimizing the displacement error between two successive iterations and the linearity assumption [41].…”

Section: Rezaiee-pajand and Alamatian Proceduresmentioning

confidence: 99%

“…7 is investigated. Rezaiee-Pajand and Alamatian have analyzed this structure before [41]. In the current paper, this plate will be solved with 20 X 20 mesh.…”

Section: The Circular Platementioning

confidence: 99%

“…Rezaiee-Pajand and Sarafrazi presented the optimal time step ratio and the critical damping for nonlinear structural analysis [40]. Moreover, Rezaiee-Pajand and Alamatian proposed a new approach for estimating the fictitious damping and mass [41]. In addition, Rezaiee-Pajand et al presented a new algorithm for the calculation of the damping matrix [42].…”

Section: Introductionmentioning

confidence: 99%

See 3 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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“…8. The achieved responses are the same as those reported by Ref [41]. The ranking of the methods is inserted in Table 9.…”

Section: The Circular Platementioning

confidence: 81%

Section: Rezaiee-pajand and Alamatian Proceduresmentioning

confidence: 99%

“…7 is investigated. Rezaiee-Pajand and Alamatian have analyzed this structure before [41]. In the current paper, this plate will be solved with 20 X 20 mesh.…”

Section: The Circular Platementioning

confidence: 99%

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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“…The classic form of the dynamic relaxation (see for example [10] or [11]) mainly is to use an artificial viscosity to damp the movement, and to search for the critical damping value (see [12] for a comprehensive review). However, among the existing dynamic relaxation methods, we are interested in a different method; the one proposed by Barnes [13].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

Rodríguez

Rio

Cadou

et al. 2011

Thin-Walled Structures

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Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior. Thin-Walled Structures, Elsevier, 2011, 49 (11) This work mainly deals with the numerical study of inflatable fabric structures. As implicit integration schemes can lead to numerical difficulties such as singular stiffness matrices, explicit schemes are preferred. Since the final objective of this study is to obtain the final shape of a structure, a dynamic relaxation (DR) method is used. These methods allow us to obtain the final and stable shape of the inflatable fabric structures without doing so many time increments, which is the case when using a classical explicit integration method. Han and Lee [5] proposed an extension of the DR method stated by Barnes [13] suitable for triangular elements and elastic behavior. There are two main contributions in this paper. Firstly, we propose a modification of Han and Lee's method, allowing it to be used with any kind of membrane or solid finite elements and any reversible behavior. Secondly, we propose to rewrite the expression initially introduced by Barnes. Furthermore, these proposals are adapted for incremental loadings, allowing this way to obtain the pseudo-equilibriums of the intermediate phases.Numerical examples from academic problems (rectangular and circular membranes) show the efficiency and the reliability of proposed methods, with linear elasticity behavior, and also with a non-linear incremental behavior and finite deformation states.

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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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The dynamic relaxation method using new formulation for fictitious mass and damping

Cited by 55 publications

References 28 publications

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

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

Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

Dynamic relaxation method based on Lanczos algorithm

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