Optimum load time history for non‐linear analysis using dynamic relaxation

Rericha, P.

doi:10.1002/nme.1620231212

Cited by 12 publications

(4 citation statements)

References 8 publications

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“…Otherwise, this would signal an actual dynamic process. Therefore, we consider the explicit dynamic relaxation (DR) method as a feasible alternative solver (Day 1965;Brew and Brotton 1971;Papadrakakis 1981;Rericha 1986;Sauvé and Metzger 1995;Siddiquee et al 1995). The solution procedure for a standard DR method is described below (Oakley and Knight 1995a).…”

Section: The Standard Dynamic Relaxation Methods As An Alternative Solvermentioning

confidence: 99%

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 Standard Dynamic Relaxation Methods As An Alternative Solvermentioning

confidence: 99%

Explicit finite element modeling of static crack propagation in reinforced concrete

Ruiz

2006

Int J Fract

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“…The solution is to use nonlinear dynamic analysisexplicit integration (Němeček [14], Němeček et al [15]). To solve a static loading, we used a special form of the load time function d(t) that minimizes inertia forces (Řeřicha [20]). The formula has the form…”

Section: Structural Analysismentioning

confidence: 99%

Effect of Stirrups on Behavior of Normal and High Strength Concrete Columns

Němeček¹,

Padevět²

2004

Acta Polytech

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This paper deals with an experimental investigation and numerical simulation of reinforced concrete columns. The behavior of normal and high strength columns is studied, with special attention paid to the confinement effects of transversal reinforcement in columns with a square cross section. The character of a failure, and the strengths, ductility and post-peak behavior of columns are observed in experiments and also in numerical solution. A three-dimensional computational model based on the microplane model for concrete was constructed and compared with experimental data. The results of the numerical model showed good agreement in many aspects, and proved the capabilities of the used material model.

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“…Instead of applying the external load in an incremental form, which is conventional in nonlinear quasi‐static analyses, a novel technique was presented in which a continuous load time history is assumed throughout the analysis. This optimum load function was determined by minimizing the residual force vector in the DR process using variational methods . In spite of sequential nature of the DR algorithm, Oakley and Knight exploited one‐dimensional strip partitioning and two‐dimensional block partitioning in order to divide the problem domain among the available processors and introduced a parallel adaptive DR strategy to solve large‐scale nonlinear hyperelastic problems with structured meshes .…”

Section: Introductionmentioning

confidence: 99%

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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Optimum load time history for non‐linear analysis using dynamic relaxation

Cited by 12 publications

References 8 publications

Explicit finite element modeling of static crack propagation in reinforced concrete

Explicit finite element modeling of static crack propagation in reinforced concrete

Effect of Stirrups on Behavior of Normal and High Strength Concrete Columns

Dynamic relaxation method based on Lanczos algorithm

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