Search results

1 – 10 of over 1000
Article
Publication date: 6 September 2021

Bruna Caroline Campos, Felicio Bruzzi Barros and Samuel Silva Penna

The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of…

Abstract

Purpose

The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.

Design/methodology/approach

The cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.

Findings

When compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.

Originality/value

This work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

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…

6041

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: 1 August 2016

K K Tamma and Siti Ujila Masuri

The purpose of this paper is to describe how a generalized single-system-single-solve (GS4-1) computational framework, previously developed for linear first order transient…

Abstract

Purpose

The purpose of this paper is to describe how a generalized single-system-single-solve (GS4-1) computational framework, previously developed for linear first order transient systems, can be properly extended for use in nonlinear counterparts, with particular applications to time dependent Burgers’ equation, which is well-known to serve as a simplified model of fluid dynamics, for illustrations of the essential concepts.

Design/methodology/approach

The framework permits, for a very general family of time integrators where traditional methods are a subset, much needed desirable features including second order time accuracy, robustness and unconditional stability, zero-order overshoot behavior, and additionally, a selective control of high frequency damping for both the primary variable and its time derivative. The latter, which is a new, key desirable feature not available in past/existing methods to-date, allows for different amounts of high frequency damping for both the primary variable and its time derivative to ensure physically accurate solutions of these variables. This is in contrast to having only limited control of these numerical dampings, often indiscriminately, as in some past developments which can lead to numerical instabilities in the time derivative variable. The extension of the framework to nonlinear problems, as described in this paper, is achieved via the use of a normalized time weighted residual approach, which naturally allows the time discretization of the transient nonlinear systems as being the natural extensions of the linear systems.

Findings

The primary aim is also to demonstrate the advantage of the selective control feature inherit in the present numerical methodologies for these nonlinear first order transient systems as in the linear counterparts.

Originality/value

The authors wish to tackle the challenges to further enable extensions to nonlinear first order transient systems that frequently arise in fluid dynamics problems; this is the focus of this paper. The primary wish is to demonstrate the ability of the GS4-1 framework for nonlinear first order transient systems as seen in the linear transient counterparts; while on one hand the authors show that an equal amount of high frequency damping (i.e. ρ = ρ s) leads to non-physical instability in the time derivative variable for a minimal damping required to obtain acceptable solution of the primary variable, on the other hand, the authors particularly demonstrate how this instability can be easily tuned off via the selective control feature (i.e. ρ ρ s) offered by the developed framework; thereby, demonstrating its robustness and superiority.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 January 2020

Chinedu Nwaigwe

The purpose of this paper is to formulate and analyse a convergent numerical scheme and apply it to investigate the coupled problem of fluid flow with heat and mass transfer in a…

Abstract

Purpose

The purpose of this paper is to formulate and analyse a convergent numerical scheme and apply it to investigate the coupled problem of fluid flow with heat and mass transfer in a porous channel with variable transport properties.

Design/methodology/approach

This paper derives the model by assuming a fully developed Brinkman flow with temperature-dependent viscosity and incorporating viscous dissipation, variable transport properties and nonlinear heat and mass sources. For the numerical formulation, the nonlinear sources are treated in semi-implicit manner, whereas the non-constant transport properties are treated by lagging in time leading to decoupled diagonally dominant systems. The consistency, stability and convergence results are derived. The method of manufactured solutions is adopted to numerically verify the theoretical results. The scheme is then applied to investigate the impact of relevant parameters, such as the viscosity parameter, on the flow.

Findings

Based on the numerical findings, the proposed scheme was found to be unconditionally stable and convergent with first- and second-order accuracy in time and space, respectively. Physical results showed that the flow parameters have influence on the flow fields, particularly, the flow is enhanced by increasing porosity and viscosity parameters and the concentration decreases with increasing diffusivity, whereas both the temperature and Nusselt number decrease with increasing thermal conductivity.

Practical implications

Numerically, the proposed numerical scheme can be applied without concerns on time steps size restrictions. Non-physical solutions cannot be computed. Physically, the flow can be increased by increasing the viscosity parameters. Pollutants with higher diffusivity will have their concentration decreased faster than those of lower diffusivity. The fluid temperature would decrease faster if its thermal conductivity is higher.

Originality/value

A fully coupled fluid flow with heat and mass transfer problem having nonlinear properties and nonlinear fractional sources and sink terms, presumably, has not been investigated in a general form as done in this study. The detailed numerical analysis of this particular scheme for the identified general model has also not been considered in the past, to the best of the author’s knowledge.

Article
Publication date: 2 March 2015

Pawel Stapór

Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing or…

Abstract

Purpose

Of particular interest is the ability of the extended finite element method (XFEM) to capture transient solution and motion of phase boundaries without adaptive remeshing or moving-mesh algorithms for a physically nonlinear phase change problem. The paper aims to discuss this issue.

Design/methodology/approach

The XFEM is applied to solve nonlinear transient problems with a phase change. Thermal conductivity and volumetric heat capacity are assumed to be dependent on temperature. The nonlinearities in the governing equations make it necessary to employ an effective iterative approach to solve the problem. The Newton-Raphson method is used and the incremental discrete XFEM equations are derived.

Findings

The robustness and utility of the method are demonstrated on several one-dimensional benchmark problems.

Originality/value

The novel procedure based on the XFEM is developed to solve physically nonlinear phase change problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 September 2019

Muhammad Ayub, Muhammad Yousaf Malik, Misbah Ijaz, Marei Saeed Alqarni and Ali Saeed Alqahtani

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov…

Abstract

Purpose

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Design/methodology/approach

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

  • It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

  • It guarantees the convergence of series solutions for nonlinear problems.

  • It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

(1) N [ u ( x ) ] = 0 ,

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

(2) ( 1 q ) L [ u ˆ ( x ; q ) u o ( x ) ] = q h H ( x ) N [ u ˆ ( x ; q ) ] ,

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, uo(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

(3) u ˆ ( x ; 0 ) = u o ( x ) and u ˆ ( x ; 1 ) = u ( x ) ,

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

(4) u ˆ ( x ; q ) = u o ( x ) + m = 1 u m ( x ) q m , where u m ( x ) = 1 m ! m u ˆ ( x ; q ) q m | q = 0 .

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

(5) u ( x ) = u o ( x ) + m = 1 + u m ( x ) .

By defining a vector u = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

(6) L [ u ˆ m ( x ) χ m u m 1 ( x ) ] = h H ( x ) R m [ u m 1 ] ,

where:

(7) R m [ u m 1 ] = 1 ( m 1 ) ! m 1 N [ u ( x ; q ) ] q m 1 | q = 0 and χ m = | 0 m 1 1 m > 1 .

Applying L−1 on both sides of Equation (6), we get:

(8) u m ( x ) = χ m u m 1 ( x ) + h L 1 [ H ( x ) R m [ u m 1 ] ] .

In this way, we obtain um for m ⩾ 1, at mth-order, we have:

(9) u ( x ) = m = 1 M u m ( x ) .

Findings

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P1) and (P2), respectively. Moreover, temperature Θ(Ω1) enhances for greater values of Brownian motion parameter (Nb), non-uniform heat source/sink parameter (B1) and thermophoresis factor (Nt). Reverse behavior of concentration ϒ(Ω1) field is remarked in view of (Nb) and (Nt). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

Originality/value

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 7 July 2020

Lorena Leocádio Gomes, Felicio Bruzzi Barros, Samuel Silva Penna and Roque Luiz da Silva Pitangueira

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of…

Abstract

Purpose

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

Design/methodology/approach

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

Findings

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

Originality/value

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

Article
Publication date: 1 July 2014

Janne P. Aikio, Timo Rahkonen and Ville Karanko

The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs…

Abstract

Purpose

The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs.

Design/methodology/approach

The polynomial fitting is improved by amplitude normalization, reducing the order of the model, utilizing Chebychev polynomials and finally perturbing the correlating controlling voltage spectra. The fitting process is estimated by the reliability figure and the condition number.

Findings

It is shown in the paper that perturbing one of the controlling voltages reduces the correlation to a large extend especially in the cross-terms of the multi-input polynomials. Chebychev polynomials reduce the correlation between the higher-order spectra derived from the same input signal, but cannot break the correlation between correlating input and output voltages.

Research limitations/implications

Optimal perturbations are sought in a separate optimization loop, which slows down the fitting process. This is due to the fact that each nonlinear source that suffers from the correlation needs a different perturbation.

Originality/value

The perturbation, harmonic balance run and refitting of an individual nonlinear source inside a device model is new and original way to characterize and fit polynomial models.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 24 February 2012

Smitha Gopinath, Nagesh Iyer, J. Rajasankar and Sandra D'Souza

The purpose of this paper is to present integrated methodologies based on multilevel modelling concepts for finite element analysis (FEA) of reinforced concrete (RC) shell…

Abstract

Purpose

The purpose of this paper is to present integrated methodologies based on multilevel modelling concepts for finite element analysis (FEA) of reinforced concrete (RC) shell structures, with specific reference to account for the nonlinear behaviour of cracked concrete and the other associated features.

Design/methodology/approach

Geometric representation of the shell is enabled through multiple concrete layers. Composite characteristic of concrete is accounted by assigning different material properties to the layers. Steel reinforcement is smeared into selected concrete layers according to its position in the RC shell. The integrated model concurrently accounts for nonlinear effects due to tensile cracking, bond slip and nonlinear stress‐strain relation of concrete in compression. Smeared crack model having crack rotation capability is used to include the influence of tensile cracking of concrete. Propagation and change in direction of crack along thickness of shell with increase in load and deformation are traced using the layered geometry model. Relative movement between reinforcing steel and adjacent concrete is modelled using a compatible bond‐slip model validated earlier by the authors. Nonlinear iterative solution technique with imposed displacement in incremental form is adopted so that structures with local instabilities or strain softening can also be analysed.

Findings

Proposed methodologies are validated by evaluating ultimate strength of two RC shell structures. Nonlinear response of McNeice slab is found to compare well with that of experiment available in literature. Then, a RC cooling tower is analysed for factored wind loads to study its behaviour near ultimate load. Numerical validation demonstrates efficacy and usefullness of the proposed methodologies for nonlinear FEA of RC shell structures.

Originality/value

The present paper integrates critical methodologies used for behaviour modelling of concrete and reinforcement with the physical interaction among them. The study is unique by considering interaction of tensile cracking and bond‐slip which are the main contributors to nonlinearity in the nonlinear response of RC shell structures. Further, industrial application of the proposed modelling strategy is demonstrated by analysing a RC cooling tower shell for its nonlinear response. It is observed that the proposed methodologies in the integrated manner are unique and provide stability in nonlinear analysis of RC shell structures.

Article
Publication date: 8 October 2018

Jalil Manafian and Cevat Teymuri sindi

This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the…

Abstract

Purpose

This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.

Design/methodology/approach

This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.

Findings

The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.

Originality/value

The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of over 1000