Adaptive damping for dynamic relaxation problems with non‐monotonic spectral response

Metzger, Don R.

doi:10.1002/nme.555

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…Instead of critically damping the system of equations from the beginning, as suggested by all the standard DR procedures, the motion is kept as strong as possible through underdamping the system, so that the local movement provoked at the loading area or at the crack tip can spread to the rest of the system. No-damping or low damping would not work since this may lead to a persistent noisy response (Metzger 2003). By under-damping the system the convergence process is enhanced, but at the same time, the risk of overshooting is also increased.…”

Section: The Modified Concept To Apply the Dr Methodsmentioning

confidence: 94%

“…The standard estimation of the critical damping coefficient through Rayleigh's quotient damps the system from higher frequency modes to lower frequency modes, therefore avoids overshooting the solutions sought. However, during the calculations for non-linear problems, when the estimation gives a higher frequency mode, the damping coefficient adopted will over-damp the global motion and actually stall the system, making the convergence rate unacceptably slow (Metzger 2003). We adopt a modified technique illustrated in Yu and Ruiz (2004) in order to sidestep this difficulty.…”

Section: The Modified Concept To Apply the Dr Methodsmentioning

confidence: 98%

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Explicit finite element modeling of static crack propagation in reinforced concrete

Ruiz

2006

Int J Fract

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We propose a methodology to model complex fracture processes in reinforced concrete beams subjected to static loading. The discrete cohesive approach, accompanied by an insertion algorithm, is adopted and a modified dynamic relaxation method is chosen as an alternative solver. The concrete matrix and steel re-bars are modeled explicitly; the connection in between is represented by means of interface elements. Such elements allow for slip of re-bars and transmit forces to the matrix that may generate secondary cracking around the reinforcement. The methodology is validated against three-point bending tests on lightly reinforced concrete (LRC) beams.

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Section: The Modified Concept To Apply the Dr Methodsmentioning

confidence: 94%

Section: The Modified Concept To Apply the Dr Methodsmentioning

confidence: 98%

Explicit finite element modeling of static crack propagation in reinforced concrete

Ruiz

2006

Int J Fract

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“…Underestimating

ω_{\min}^{n}

leads to an underdamped response, which increases the number of iterations. On the other hand, overestimating

ω_{\min}^{n}

yields an overdamped vibration, which, as reported in , could impede the convergence even more than the underdamped case. Performing nonproductive iterations is one of the classical approaches for estimation of critical damping .…”

Section: Viscous Dynamic Relaxation Methodsmentioning

confidence: 89%

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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“…Furthermore, damping is a key parameter in the DR method. 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).…”

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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Adaptive damping for dynamic relaxation problems with non‐monotonic spectral response

Cited by 14 publications

References 19 publications

Explicit finite element modeling of static crack propagation in reinforced concrete

Explicit finite element modeling of static crack propagation in reinforced concrete

Dynamic relaxation method based on Lanczos algorithm

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

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