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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…

6101

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.

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

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Article
Publication date: 1 January 1992

ZHI‐HUA ZHONG and JAROSLAV MACKERLE

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite…

563

Abstract

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

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Engineering Computations, vol. 9 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 January 1990

R.C. Averill and J.N. Reddy

A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new…

185

Abstract

A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side‐to‐thickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and are interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various plate elements. These include bilinear, biquadratic, eight‐node serendipity and heterosis elements. These analytical findings are compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behaviour of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.

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Engineering Computations, vol. 7 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 21 February 2020

Changsheng Wang, Xiao Han, Caixia Yang, Xiangkui Zhang and Wenbin Hou

Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present…

94

Abstract

Purpose

Numerous finite elements are proposed based on analytical solutions. However, it is difficult to find the solutions for complicated governing equations. This paper aims to present a novel formulation in the framework of assumed stress quasi-conforming method for the static and free vibration analysis of anisotropic and symmetric laminated plates.

Design/methodology/approach

Firstly, an initial stress approximation ruled by 17 parameters, which satisfies the equilibrium equations is derived to improve the performance of the constructed element. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the Timoshenko’s laminated composite beam functions are adopted as boundary string-net functions for strain integration.

Findings

Several numerical examples are presented to show the performance of the new element, and the results obtained are compared with other available ones. Numerical results have proved that the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

Originality/value

This paper proposes a new QC element for the static and free vibration analysis of anisotropic and symmetric laminated plates. In contrast with the complicated analytical solutions of the equilibrium equations, an initial stress approximation ruled by 17 parameters is adopted here. The Timoshenkos laminated composite beam functions are introduced as boundary string-net functions for strain integration. Numerical results demonstrate the new element is free from shear locking and possesses high accuracy for the analysis of anisotropic and symmetric laminated plates.

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Engineering Computations, vol. 37 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 February 2025

Sinan Maraş

This study aims to investigate the effects of layering sequence, aspect ratios, fiber orientation angles, loading types and boundary conditions on the buckling behavior of…

58

Abstract

Purpose

This study aims to investigate the effects of layering sequence, aspect ratios, fiber orientation angles, loading types and boundary conditions on the buckling behavior of glass/carbon/hybrid fiber-reinforced epoxy laminated composites using the differential quadrature (DQ) approach.

Design/methodology/approach

In total, different hybrid combinations are considered separately for angle-ply, cross-ply and antisymmetric layup schemes. For this purpose, a DQ code is developed using MATLAB.

Findings

The results obtained from the study reveal that the lamination arrangements and varying loading conditions of the hybrid laminated structures have a significant effect on the buckling performance of these materials.

Originality/value

This is the first study to investigate how the critical buckling loads of glass fiber/epoxy and carbon fiber/epoxy laminated hybrid composite plates are influenced by fiber orientation angles, aspect ratios, stacking sequences, loading conditions and boundary conditions using the DQ method. This study contributes to the literature in this regard.

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Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 11 October 2011

V.P. Vallala, J.N. Reddy and K.S. Surana

Most studies of power‐law fluids are carried out using stress‐based system of Navier‐Stokes equations; and least‐squares finite element models for vorticity‐based equations of…

468

Abstract

Purpose

Most studies of power‐law fluids are carried out using stress‐based system of Navier‐Stokes equations; and least‐squares finite element models for vorticity‐based equations of power‐law fluids have not been explored yet. Also, there has been no study of the weak‐form Galerkin formulation using the reduced integration penalty method (RIP) for power‐law fluids. Based on these observations, the purpose of this paper is to fulfill the two‐fold objective of formulating the least‐squares finite element model for power‐law fluids, and the weak‐form RIP Galerkin model of power‐law fluids, and compare it with the least‐squares finite element model.

Design/methodology/approach

For least‐squares finite element model, the original governing partial differential equations are transformed into an equivalent first‐order system by introducing additional independent variables, and then formulating the least‐squares model based on the lower‐order system. For RIP Galerkin model, the penalty function method is used to reformulate the original problem as a variational problem subjected to a constraint that is satisfied in a least‐squares (i.e. approximate) sense. The advantage of the constrained problem is that the pressure variable does not appear in the formulation.

Findings

The non‐Newtonian fluids require higher‐order polynomial approximation functions and higher‐order Gaussian quadrature compared to Newtonian fluids. There is some tangible effect of linearization before and after minimization on the accuracy of the solution, which is more pronounced for lower power‐law indices compared to higher power‐law indices. The case of linearization before minimization converges at a faster rate compared to the case of linearization after minimization. There is slight locking that causes the matrices to be ill‐conditioned especially for lower values of power‐law indices. Also, the results obtained with RIP penalty model are equally good at higher values of penalty parameters.

Originality/value

Vorticity‐based least‐squares finite element models are developed for power‐law fluids and effects of linearizations are explored. Also, the weak‐form RIP Galerkin model is developed.

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Article
Publication date: 11 December 2024

Gollapalli Shankar and Siva Reddy Sheri

This research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and…

8

Abstract

Purpose

This research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and electrically conductive fluid over a vertically oscillating flat plate. The study highlights the significance of magnetic fields in influencing thermal and mass transfer, particularly in the context of thermal radiation. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the finite element method (FEM) numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. Key parameters such as skin friction, temperature, concentration, velocity and Sherwood numbers are derived and analyzed. The results demonstrate that viscous dissipation significantly elevates the fluid temperature, while an increase in the radiation parameter is associated with a decrease in internal friction at the plate. These findings provide critical insights into the interplay between thermal radiation and magnetic fields in MHD flows, with potential applications in engineering systems involving heat and mass transfer, such as cooling systems and material processing. This study underscores the importance of understanding these dynamics for optimizing the performance of MHD applications in various industrial settings.

Design/methodology/approach

The mainly authorized and energetic FEM to explain the non-linear, dimensionless partial differential equations (11–13) via equation with boundary conditions (14) makes use of Bathe (36), Reddy (37), Connor (38) and Chung (39). Following are the key steps that make up the method: discretize the domain, derivation of element equation, assembly of element equation, imposition of boundary condition and solution of assembly equation.

Findings

This study examined the impact of viscid dissipative radiation and the Dufour effect on unsteady one-dimensional MHD natural convective flow of a viscous, incompressible, electrically conducting fluid past an infinite moving vertical flat plate with a chemical reaction. Numerically solving the governing equations using the FEM approach is efficient and precise, aiming to be applied to fluid mechanics and related problems. Along with their effects on temperature, concentration and velocity, the following parameters are included: the mass Grashof number, the Soret number, the Grashof number, the Prandtl number, chemical reaction, the Schmidt number, radiation and the Casson parameter. Both the Grashof numbers of thermal and mass rates (Gr, Gm) make an increment in the velocity region. The velocity decreases with an increase in the magnetic parameter. The velocity increases with an increase in the permeability of the porous medium parameter. The temperature flow rate is higher for both Dufour and Viscid dissipation, while a decrement is noted of both Prandtl number and radiation effects. The decrementing behavior of the concentration region is observed at supreme inputs of chemical reaction coefficient and Schmidt number.

Originality/value

This is an original paper and not submitted anywhere.

Details

Multidiscipline Modeling in Materials and Structures, vol. 21 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 11 February 2021

J.N. Reddy, Matthew Martinez and Praneeth Nampally

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear…

228

Abstract

Purpose

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.

Design/methodology/approach

In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).

Findings

Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.

Originality/value

To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 29 December 2017

O.K. Koriko, I.L. Animasaun, M. Gnaneswara Reddy and N. Sandeep

The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm…

110

Abstract

Purpose

The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm alumina-water nanofluid within the thin boundary layer in the presence of quartic autocatalytic kind of chemical reaction effects, and to unravel the effects of a magnetic field parameter, random motion of the tiny nanoparticles and volume fraction on the flow.

Design/methodology/approach

The chemical reaction between homogeneous (Eyring-Powell 36 nm alumina-water) bulk fluid and heterogeneous (three molecules of the catalyst at the surface) in the flow of magnetohydrodynamic three-dimensional flow is modeled as a quartic autocatalytic kind of chemical reaction. The electromagnetic radiation which occurs within the boundary layer is treated as the nonlinear form due to the fact that Taylor series expansion may not give full details of such effects within the boundary layer. With the aid of appropriate similarity variables, the nonlinear coupled system of partial differential equation which models the flow was reduced to ordinary differential equation boundary value problem.

Findings

A favorable agreement of the present results is obtained by comparing it for a limiting case with the published results; hence, reliable results are presented. The concentration of homogeneous bulk fluid (Eyring-Powell nanofluid) increases and decreases with ϕ and Pr, respectively. The increase in the value of magnetic field parameter causes vertical and horizontal velocities of the flow within the boundary layer to decrease significantly. The decrease in the vertical and horizontal velocities of Eyring-Powell nanofluid flow within the boundary layer is guaranteed due to an increase in the value of M. Concentration of homogeneous fluid increases, while the concentration of the heterogeneous catalyst at the wall decreases with M.

Originality/value

Considering the industrial applications of thermal stratification in solar engineering and polymer processing where the behavior of the flow possesses attributes of Eyring-Powell 36 nm alumina-water, this paper presents the solution of the flow problem considering 36 nm alumina nanoparticles, thermophoresis, stratification of thermal energy, Brownian motion and nonlinear thermal radiation. In addition, the aim and objectives of this paper fill such vacuum in the industry.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 2
Type: Research Article
ISSN: 1573-6105

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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…

36

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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