A new fictitious time for the dynamic relaxation (DXDR) method

Kadkhodayan, Mehran; Alamatian, Javad; Turvey, G.J.

doi:10.1002/nme.2201

Cited by 48 publications

(27 citation statements)

References 29 publications

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“…(3) in each time step [34]. Simplicity, vector operators, and higher e ciency in nonlinear systems are other advantages of DR method [34,35]. As described in the recent papers, this method has been successfully combined with implicit time integrations so that it can cause a considerable reduction in numerical errors [34,36].…”

Section: Numerical Examples and Discussionmentioning

confidence: 99%

Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

Alamatian

2017

Scientia Iranica

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Abstract. This paper deals with a generalized multi-time-step integration used for structural dynamic analysis. The proposed method presents three kinds of implicit schemes in which the accelerations and velocities of the previous steps are utilized to integrate the equations of motion. This procedure employs three groups of weighted factors calculated by minimizing the numerical errors of displacement and velocity in Taylor series expansion. Moreover, a comprehensive study on mathematical stability of the proposed technique, which is performed based on the ampli cation matrices, proves that the new method is more stable than existing schemes such as IHOA. For numerical veri cation, a wide range of dynamic systems, including linear and nonlinear, single and multi degrees of freedom, damped and undamped, as well as forced and free vibrations from nite-element and nitedi erence methods, are analyzed. These numerical studies demonstrate that e ciency and accuracy of the proposed method are higher than those of other techniques.

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Section: Numerical Examples and Discussionmentioning

confidence: 99%

Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

Alamatian

2017

Scientia Iranica

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“…This value should be obtained is such a way as to not only maintain the numerical stability of the scheme, but also reduce the number of iterations required for convergence. Kadkhodayan et al proposed an optimum time step by minimizing the unbalanced forces [39]. Eq.…”

Section: Minimum Residual Force Methodsmentioning

confidence: 99%

“…Kadkhodayan et al obtained a relationship for the time step by minimizing the residual forces [39]. Rezaiee-Pajand and Sarafrazi presented the optimal time step ratio and the critical damping for nonlinear structural analysis [40].…”

Section: Introductionmentioning

confidence: 99%

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

Rezaiee‐Pajand

Estiri²

2016

Period. Polytech. Civil Eng.

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“…Overdamping or underdamping impedes the convergences to a stable equilibrium state (Metzger, 2003). Various approaches to the selection of the foregoing parameters have been published in the literature (Underwood, 1983;Kadkhodayan et al, 2008;Metzger, 2003;Papadrakakis, 1981;Rezaiee-pajand and Alamatian, 2010). The most common method of determining mass terms is to use Gerschgörin's theorem.…”

Section: Fictitious Masses and Kinetic Dampingmentioning

confidence: 98%

“…In the DR method the mass matrix, damping and time increment should be defined in such way that the stability and convergence of the iterative procedure is guaranteed (Kadkhodayan et al, 2008). Generally, if the time interval is too large or the masses too small, then instability of the iteration may occur.…”

Section: Fictitious Masses and Kinetic Dampingmentioning

confidence: 99%

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Ali

Rhode-Barbarigos

Smith

2011

International Journal of Solids and Structures

162

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a b s t r a c tTensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently.

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A new fictitious time for the dynamic relaxation (DXDR) method

Cited by 48 publications

References 29 publications

Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

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

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

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