A new method of fictitious viscous damping determination for the dynamic relaxation method

Rezaiee‐Pajand, Mohammad; Kadkhodayan, Mehran; Alamatian, Javad; Zhang, L. C.

doi:10.1016/j.compstruc.2011.02.002

Cited by 43 publications

(20 citation statements)

References 37 publications

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“…_ v and v are the nodal acceleration and the velocity respectively. M corresponds to the nodal mass and D to damping with both parameters being fictitious and optimized for the stability and convergence of the method [14][15][16][17].…”

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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“…In this case, the damping coefficient is based on a function of the current system configuration, the internal element force, and the mass matrix. Recently, Rezaiee‐Pajanda et al proposed a method that minimizes errors between two successive iterations to obtain optimum fictitious mass and viscous damping with the aid of the Stodola iterative process.…”

Section: Dynamic Relaxation Processmentioning

confidence: 99%

“…In this case, the damping coefficient is based on a function of the current system configuration, the internal element force, and the mass matrix. Recently, Rezaiee-Pajanda et al [35] proposed a method that minimizes errors between two successive iterations to obtain optimum fictitious mass and viscous damping with the aid of the Stodola iterative process. While working on unstable, geomechanical problems, Cundall [36] first suggested using kinetic damping, which proved to be entirely stable and rapidly converging when dealing with large unbalanced forces [3].…”

Section: Damping Coefficientmentioning

confidence: 99%

The geodesic dynamic relaxation method for problems of equilibrium with equality constraint conditions

Miki

Adriaenssens

Igarashi

et al. 2014

Numerical Meth Engineering

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SUMMARYThis paper presents an extension to the existing dynamic relaxation method to include equality constraint conditions in the process. The existing dynamic relaxation method is presented as a general, gradient‐based, minimization technique. This representation allows for the introduction of the projected gradient, discrete parallel transportation and pull back operators that enable the formulation of the geodesic dynamic relaxation method, a method that accounts for equality constraint conditions. The characteristics of both the existing and geodesic dynamic relaxation methods are discussed in terms of the system's conservation of energy, damping (viscous, kinetic, and drift), and geometry generation. Particular attention is drawn to the introduction of a novel damping approach named drift damping. This technique is essentially a combination of viscous and kinetic damping. It allows for a smooth and fast convergence rate in both the existing and geodesic dynamic relaxation processes. The case study was performed on the form‐finding of an iconic, ridge‐and‐valley, pre‐stressed membrane system, which is supported by masts. The study shows the potential of the proposed method to account for specified (total) length requirements. The geodesic dynamic relaxation technique is widely applicable to the form‐finding of force‐modeled systems (including mechanically and pressurized pre‐stressed membranes) where equality constraint control is desired. Copyright © 2014 John Wiley & Sons, Ltd.

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“…To have an efficient and robust solver, the fictitious mass and damping parameters should be properly assessed to gain a high convergence rate. Extensive effort has been put into the determination of these parameters for the purpose of reaching the solution with minimal iterations [5][6][7][8][9][10][11][12][13][14][15][16][17]. In addition, researchers have also developed some formulations for the fictitious time [9,[18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Fictitious Time Step for the Kinetic Dynamic Relaxation Method

Rezaiee‐Pajand

Rezaee

2014

Mechanics of Advanced Materials and Structures

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Dynamic relaxation (DR) is an iterative method for solving simultaneous sets of equations, which govern the behavior of static structures. One of the most effective techniques in this category is the kinetic damping approach. In this research, a new formula for the fictitious time step is obtained by error analysis to utilize in the kinetic DR method. The developed algorithm is applied to the nonlinear analysis of several plane-and space-trusses, and also structural frames. Numerical results indicate that the proposed fictitious time step has a significant effect on improving the convergence rate of the kinetic DR method. Nomenclature M = artificial mass matrix C = artificial damping matrix S = stiffness matrix X = displacement vectoṙ X = artificial velocity vector X = artificial acceleration vector P = vector of external loads F = vector of internal forces R = vector of residual (i.e., out of balance) forces t = fictitious time step c = artificial damping factor U k = total kinetic energy of structure ndo f = number of degrees of freedom x * = real displacement E = error vector = error declination rate M −1 S i = ith eigenvalue of matrix M −1 S M −1 S 1 = lowest eigenvalue of matrix M −1 S 1 = the lowest natural frequency of the artificial dynamic system e R = convergence criterion for residual force PI = relative performance index Superscript k = iteration number of DR method Address correspondence to M. Rezaiee-Pajand,

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A new method of fictitious viscous damping determination for the dynamic relaxation method

Cited by 43 publications

References 37 publications

Form finding and analysis of inflatable dams using dynamic relaxation

Form finding and analysis of inflatable dams using dynamic relaxation

The geodesic dynamic relaxation method for problems of equilibrium with equality constraint conditions

Fictitious Time Step for the Kinetic Dynamic Relaxation Method

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