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Article
Publication date: 1 March 1993

XIKUI LI, A.J.L. CROOK and L.P.R. LYONS

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically…

Abstract

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

Details

Engineering Computations, vol. 10 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 1997

Jaroslav Mackerle

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

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Abstract

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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 degrees of…

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

Article
Publication date: 1 January 1989

Nielen Stander, Anton Matzenmiller and Ekkehard Ramm

A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which…

Abstract

A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which sometimes caused difficulties for other assumed strain techniques. For efficient computation in the non‐linear range, linearization of the virtual work equation is done to yield the consistent tangent stiffness. The shell formulation is done for stress and strain tensors based on local element coordinates. To demonstrate the effectiveness and rapid convergence of the non‐linear formulation, three examples are tested for large displacements.

Details

Engineering Computations, vol. 6 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 28 June 2021

Faiçal Boussem, Abderahim Belounar and Lamine Belounar

This paper aims to describe the formulation of a new finite element by assuming the strain field rather than the displacement field and by using the Reissner–Mindlin plate theory…

Abstract

Purpose

This paper aims to describe the formulation of a new finite element by assuming the strain field rather than the displacement field and by using the Reissner–Mindlin plate theory for the free vibration analysis of bending plates. This quadrilateral element consists of four-nodes and twelve degrees of freedom. The suggested element is based on assumed functions of the strain field that satisfy the compatibility equation.

Design/methodology/approach

After the proposition of the new element, several numerical tests for plates with regular and distorted meshes are presented to assess the performance of the new element. In addition, a parametric study is carried out to analyze the effects of biaxial loads on the natural frequencies of square plates with various boundary conditions. Detailed discussions are proposed after each benchmark problem.

Findings

The formulated element has verified the shear locking test and passes the patch test. The obtained results from the developed element show an excellent accuracy and fast convergence, and the natural frequencies are in excellent agreement when compared with analytical and other available numerical solutions.

Originality/value

The present element is simple in its formulation and has been proven to be applicable to thin or thick plate situations with sufficient accuracy. This element with full integration is free from shear locking, however, the numerical results provided by the standard four-node plate element R4 element show locking phenomena in thin plates. In addition to these features, the imposition of the compatibility conditions and the rigid body modes allow obtaining a finite element with higher-order terms for displacements field, which can increase the performance of the finite elements.

Details

World Journal of Engineering, vol. 19 no. 5
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 1 May 1995

Adnan Ibrahimbegović

Implementation details of the assumed shear strain method in a novelfinite rotation shell theory are discussed. Careful considerations of thepertinent aspects of the Newton…

Abstract

Implementation details of the assumed shear strain method in a novel finite rotation shell theory are discussed. Careful considerations of the pertinent aspects of the Newton solution procedure are given. The latter results in a very robust performance of the presented 4–node shell element in some challenging finite rotation problems.

Details

Engineering Computations, vol. 12 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 December 2000

R. Piltner

The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu‐Washizu variational formulation with orthogonal stress and strain…

Abstract

The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu‐Washizu variational formulation with orthogonal stress and strain functions is considered. The use of orthogonal functions leads to a formulation with B (overline) ‐strain matrices which avoids numerical inversion of matrices. Depending on the choice of the stress and strain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P‐S of Pian‐Sumihara or the Trefftz‐type element QE2 of Piltner and Taylor. With the mixed formulation discussed in this paper a simple extension of the high precision elements P‐S and QE2 to general non‐linear problems is possible, since the final computer implementation of the mixed element is very similar to the implementation of a displacement element. Instead of sparse B‐matrices, sparse B (overline) ‐matrices are used and the typical matrix inversions of hybrid and mixed methods can be avoided. The two most efficient four‐node B (overline) ‐elements for plane strain and plane stress in this study are denoted B (overline)(x, y)‐QE4 and B (overline)(ξ, η)‐QE4.

Details

Engineering Computations, vol. 17 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 16 August 2013

Mário Pimentel and Joaquim Figueiras

The purpose of this paper is to present the implementation in a finite element (FE) code of a recently developed material model for the analysis of cracked reinforced concrete…

Abstract

Purpose

The purpose of this paper is to present the implementation in a finite element (FE) code of a recently developed material model for the analysis of cracked reinforced concrete (RC) panels. The model aims for the efficient nonlinear analysis of large‐scale structural elements that can be considered as an assembly of membrane elements, such as bridge girders, shear walls, transfer beams or containment structures.

Design/methodology/approach

In the proposed constitutive model, the equilibrium equations of the cracked membrane element are established directly at the cracks while the compatibility conditions are expressed in terms of spatially averaged strains. This allows the well‐known mechanical phenomena governing the behaviour of cracked concrete elements – such as aggregate interlock (including crack dilatancy effects), tensile fracture and bond shear stress transfer – to be taken into account in a transparent manner using detailed phenomenological models. The spatially averaged stress and strain fields are obtained as a by‐product of the local behaviour at the cracks and of the bond stress transfer mechanisms, allowing the crack spacing and crack widths to be obtained directly from first principles. The model is implemented in an FE code following a total formulation.

Findings

The fact that the updated stresses at the cracks are calculated explicitly from the current spatially averaged total strains and from the updated values of the state variables that are used to monitor damage evolution contributes to the robustness and efficiency of the implementation. Some application examples are presented illustrating the model capabilities and good estimates of the failure modes, failure loads, deformation capacity, cracking patterns and crack widths were achieved.

Originality/value

While being computationally efficient, the model describes the complex stress and strain fields developing in the membrane element, and retrieves useful information for the structural engineer, such as concrete and reinforcement failures as well as the crack spacing and crack widths.

Details

Engineering Computations, vol. 30 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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 2022

Can Ban, Na Na Pu, Yi Fei Zhang and Ma Wentao

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Abstract

Purpose

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Design/methodology/approach

This paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.

Findings

On the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.

Originality/value

This study provides an accurate and efficient meshfree method for simulating crack growth.

Details

Engineering Computations, vol. 39 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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