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Article
Publication date: 19 July 2019

M. Rezaiee-Pajand, Hossein Estiri and Mohammad Mohammadi-Khatami

The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better…

101

Abstract

Purpose

The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms.

Design/methodology/approach

Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures.

Findings

To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments.

Research limitations/implications

To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate.

Practical implications

Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures.

Originality/value

It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.

Details

Engineering Computations, vol. 36 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 2 October 2017

Mohammad Rezaiee-Pajand and Hossein Estiri

Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for…

149

Abstract

Purpose

Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy.

Design/methodology/approach

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration.

Findings

The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths.

Research limitations/implications

Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells.

Practical implications

Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures.

Originality/value

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

Details

World Journal of Engineering, vol. 14 no. 5
Type: Research Article
ISSN: 1708-5284

Keywords

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