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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…

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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Article
Publication date: 11 April 2020

Mohammad Rezaiee-Pajand, Nima Gharaei-Moghaddam and Mohammadreza Ramezani

This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11…

Abstract

Purpose

This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF.

Design/methodology/approach

The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation.

Findings

To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements.

Originality/value

According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

Details

Engineering Computations, vol. 37 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 4 September 2019

Mohammad Rezaiee-Pajand and Amir R. Masoodi

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large…

Abstract

Purpose

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Design/methodology/approach

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Findings

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

Research limitations/implications

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

Practical implications

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

Social implications

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Originality/value

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Details

World Journal of Engineering, vol. 16 no. 5
Type: Research Article
ISSN: 1708-5284

Keywords

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Article
Publication date: 27 September 2011

Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Abstract

Purpose

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Design/methodology/approach

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

Findings

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

Research limitations/implications

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Practical implications

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

Originality/value

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

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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…

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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