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Article
Publication date: 11 October 2011

Rabe Alsafadie, Mohammed Hjiaj, Hugues Somja and Jean‐Marc Battini

The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams…

Abstract

Purpose

The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

Design/methodology/approach

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

Findings

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

Originality/value

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.

Article
Publication date: 30 October 2018

Changsheng Wang, Xiaoxiao Sun, Xiangkui Zhang and Ping Hu

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A…

Abstract

Purpose

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.

Design/methodology/approach

First, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.

Findings

The proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.

Originality/value

This work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.

Article
Publication date: 1 April 1987

Xiao‐Jun Wang and Ted Belytschko

A hexahedral 8‐node element based on the Hellinger—Reissner principle is formulated with the γ projection operator so that it can achieve engineering accuracy for plate and beam…

Abstract

A hexahedral 8‐node element based on the Hellinger—Reissner principle is formulated with the γ projection operator so that it can achieve engineering accuracy for plate and beam problems with a single layer of elements. It passes the patch test and is less sensitive to mesh shape since the local coordinates are used to describe the stress fields. The resulting element stiffness is simple and only 3×3 submatrix inversions are needed. Numerical results show that the new element is both accurate and efficient.

Details

Engineering Computations, vol. 4 no. 4
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 6 November 2017

Zilong Cao, Yupu Guan and Wei Chen

To increase the use of the meshless method, a hybrid stress method is introduced into the meshless method.

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Abstract

Purpose

To increase the use of the meshless method, a hybrid stress method is introduced into the meshless method.

Design/methodology/approach

The method is based on the radial point interpolation method (RPIM). According to the Hellinger Reissner principle, stress functions are introduced into the solution procedure. Finite elements are used as background cells for integration. All cells are divided into two types – the H cells, which are around the traction-free circular boundary, and the G cells. For the H cells, stress functions in polar coordinates are created. For the G cells, 12-parameter stress functions in Cartesian coordinates are used. Stress functions are based on equilibrium equations and stress compatible equation.

Findings

Numerical results show that this method is reliable.

Originality/value

Hybrid stress methods have been applied to finite element methods, but the finite element methods have not been applied into meshless methods.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 6 November 2017

Changzheng Cheng, Zhilin Han, Zhongrong Niu and Hongyu Sheng

The state space method (SSM) is good at analyzing the interfacial physical quantities in laminated materials, while it has difficulty in calculating the mechanical quantities of…

Abstract

Purpose

The state space method (SSM) is good at analyzing the interfacial physical quantities in laminated materials, while it has difficulty in calculating the mechanical quantities of interior points, which can be easily evaluated by the boundary element method (BEM). However, the material has to be divided into many subdomains when the traditional BEM is applied to analyze the functionally graded material (FGM), so that the computational amount will be increased enormously. This study aims to couple these two methods to strengthen their advantages and overcome their disadvantages.

Design/methodology/approach

Herein, a state space BEM in which the SSM is coupled by the BEM is proposed to analyze the elasticity of FGMs, where one BEM domain is set and the others belong to SSM domains. The discretized elements occur only on the boundary of the BEM domain and at the interfaces between different SSM domains. In SSM domains, the horizontal interfaces of FGMs are discretized by linear elements and the variables along the vertical direction are yielded by the precise integration method.

Findings

The accuracy of the proposed method is verified by comparing the present results with the ones from the finite element method (FEM). It is found that the present method can provide accurate displacements and stresses in the FGMs by fewer freedom degrees in comparison with the FEM. In addition, the present method can provide continuous interfacial stresses at the interfaces between different material domains, while the interfacial stresses by the FEM are discontinuous.

Originality/value

The system equations of the state space BEM are built by combining the boundary integral equation with the state equations according to the continuity conditions at the interfaces. The mechanical parameters of any inner point can be evaluated by the boundary integral equation after the unknowns on the boundaries and interfaces are determined by the system equation.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 1988

Ahmed K. Noor and Jeanne M. Peters

Error indicators are introduced as part of a simple computational procedure for improving the accuracy of the finite element solutions for plate and shell problems. The procedure…

Abstract

Error indicators are introduced as part of a simple computational procedure for improving the accuracy of the finite element solutions for plate and shell problems. The procedure is based on using an initial (coarse) grid and a refined (enriched) grid, and approximating the solution for the refined grid by a linear combination of a few global approximation vectors (or modes) which are generated by solving two uncoupled sets of equations in the coarse grid unknowns and the additional degrees of freedom of the refined grid. The global approximation vectors serve as error indicators since they provide quantitative pointwise information about the sensitivity of the different response quantities to the approximation used. The three key elements of the computational procedure are: (a) use of mixed finite element models with discontinuous stress resultants at the element interfaces; (b) operator splitting, or additive decomposition of the finite element arrays for the refined grid into the sum of the coarse grid arrays and correction terms (representing the refined grid contributions); and (c) application of a reduction method through successive use of the finite element method and the classical Bubnov—Galerkin technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Bubnov—Galerkin technique. The similarities between the proposed computational procedure and a preconditioned conjugate gradient (PCG) technique are identified and are exploited to generate from the PCG technique pointwise error indicators. The effectiveness of the proposed procedure is demonstrated by means of two numerical examples of an isotropic toroidal shell and a laminated anisotropic cylindrical panel.

Details

Engineering Computations, vol. 5 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 February 1984

R.D. Wood

A Fortane shape function routine is presented for the constant moment triangular plate bending element. The routine also contains the shape functions for the constant inplane…

Abstract

A Fortane shape function routine is presented for the constant moment triangular plate bending element. The routine also contains the shape functions for the constant inplane stress triangular element enabling it to be used for facet shell analysis. Details are included on calculation of the element stiffness matrix and equivalent nodal forces.

Details

Engineering Computations, vol. 1 no. 2
Type: Research Article
ISSN: 0264-4401

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 deformation…

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

Article
Publication date: 31 March 2022

Daouda Kane, Guilherme Gomes, Vanessa Macanhan and Antonio Ancelotti Jr

In laminate composite structure design, it is common to deal with the need of varying thickness to reach project requirement or improve performance. This change of thickness can…

Abstract

Purpose

In laminate composite structure design, it is common to deal with the need of varying thickness to reach project requirement or improve performance. This change of thickness can be achieved by terminating or adding plies at different locations over the laminate. Unfortunately, the inherent weakness of this construction is the presence of material and geometric discontinuities at the ply drop region that induce premature interlaminar failure at interfaces between dropped and continuous plies.

Design/methodology/approach

In this work, tensile strength tests were performed on tapered laminates with internal ply drop-off using digital image correlation (DIC) technique. The laminate based on a new thermoplastic ELIUM® 150 reinforced by a plain weave carbon fabric was manufactured via VARTM. Stress, strain, displacement and tensile strength were analyzed. A 3D finite element analysis (FEA) and design of experiments (DOEs) were carried out for the analysis of effect of position and angle orientation of dropped plies near the thinner section of the tapered laminate. Tsai Wu's criterion was implemented to predict initiation of first ply failure.

Findings

Numerical and experimental results showed that position and angle orientation of ply drop-off near the thinner thickness influence tensile strength of tapered laminate. Tensile static strength increases 12% when drop-off near the midplane is oriented at ±45° instead of 0°. Results showed a trend of improvement in the tensile strength when drop-off is positioned over midplane of the laminate composite. Results obtained through the DOEs were able to adjust the metamodel according to a linear model with great efficiency. They show the significant relevance of the manufacturing variables and the interaction between the factors.

Originality/value

The present work aims to evaluate the effect of ply drop-off on the strength of carbon fiber thermoplastic composite laminates with internal drop-off under tensile load and propose a design guideline about angle orientation and position of dropped plies closer to the thinner section of the laminate.

Details

Engineering Computations, vol. 39 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 1989

Peter M. Pinsky and Raja V. Jasti

A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The…

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Abstract

A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuška—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.

Details

Engineering Computations, vol. 6 no. 4
Type: Research Article
ISSN: 0264-4401

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