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Article
Publication date: 17 June 2020

Tiago Oliveira, Wilber Vélez and Artur Portela

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Abstract

Purpose

This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

Design/methodology/approach

In the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.

Findings

The reduced integration, performed by this linearly integrated formulation, plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy and, which is most important, presents no instabilities, unlike nodal integration methods without stabilization. As a consequence of using such a convenient linearly integrated local form, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. Three benchmark problems were analyzed with these techniques, in order to assess the accuracy and efficiency of the new integrated local formulations of meshfree and finite element numerical methods. The results obtained in this work are in perfect agreement with those of the available analytical solutions and, furthermore, outperform the computational efficiency of other methods. Thus, the accuracy and efficiency of the local numerical methods presented in this paper make this a very reliable and robust formulation.

Originality/value

Presentation of a new local mesh-free numerical method. The method, linearly integrated along the boundary of the local domain, implements an algorithm with no further integration required. The method is absolutely reliable, with remarkably-accurate results. The method is quite robust, with extremely-fast computations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 September 1999

Jaroslav Mackerle

This paper gives a review of the finite element techniques (FE) applied in the analysis and design of machine elements; bolts and screws, belts and chains, springs and…

4308

Abstract

This paper gives a review of the finite element techniques (FE) applied in the analysis and design of machine elements; bolts and screws, belts and chains, springs and dampers, brakes, gears, bearings, gaskets and seals are handled. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of this paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An Appendix included at the end of the paper presents a bibliography on finite element applications in the analysis/design of machine elements for 1977‐1997.

Details

Engineering Computations, vol. 16 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 April 2008

Ludvík Prášil and Jaroslav Mackerle

The finite element method (FEM) has become the prevalent technique used for analyzing physical phenomena in the field of structural, solid and fluid mechanics. The output…

3074

Abstract

Purpose

The finite element method (FEM) has become the prevalent technique used for analyzing physical phenomena in the field of structural, solid and fluid mechanics. The output of scientific papers is fast growing and professionals are no longer able to be fully up‐to‐date with all the relevant information. The purpose of this paper is to provide a bibliographical review on the application of FEM in mechanical engineering, specifically for the analyses and simulations of gears and gear drives from the theoretical as well as practical points of view.

Design/methodology/approach

The following topics on gears and gear drives are handled from the computational points of view: gears in general, spur gears, helical gears, spiral bevel and hypoid gears, worm gears and other gear types and gear drives. The paper is organized into two parts. In the first one each topic is handled in a short text, relevant keywords are presented and current trends in applications of finite element techniques are briefly mentioned. The second part lists references of papers published for the period 1997‐2006.

Findings

This bibliography is intended to serve the needs of engineers and researchers as a comprehensive source of published papers on design, analysis and simulation of gears and gear drives.

Originality/value

The bibliography listed is by no means complete but it gives a comprehensive representation of different finite element applications on the subjects. It will save time for readers looking for information dealing with described subjects, not having an access to large databases or willingness to spend time with uncertain information retrieval.

Details

Engineering Computations, vol. 25 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 30 March 2022

Ayoub Bellouch, Amine El Alami, Frederic Messine and Nathalie Raveu

The purpose of this sudy is to provide a complete optimization-based methodology to design waveguides with metamaterial walls. The present methodology is based on…

Abstract

Purpose

The purpose of this sudy is to provide a complete optimization-based methodology to design waveguides with metamaterial walls. The present methodology is based on optimization. Indeed, the inverse problems of design are formulated as nonlinear black-box optimization problems with constraints. Two inequality black-box constraints are taken into account as penalized terms that are added to the objective function when the constraints are not satisfied. The numerical steps are done by using a finite element method solver (GetDP). Thus, different optimization software are tested to solve the nonlinear black-box optimization problems such as IPOPT, NLOPT and NOMAD from the Opti ToolBox in MatLab.

Design/methodology/approach

In this work, a methodology to design waveguides with metamaterial walls is proposed. The aim is to solve an inverse problem to find the best design where the electric field cartography is the closest to an imposed one.

Findings

The present methodology is applied to solve inverse problems of design and satisfactory results were provided by the three solvers IPOPT, NLOPT and NOMAD. Those numerical experiments show that NOMAD is the most efficient method to optimize the design of those cylindrical waveguide structures with metamaterial walls.

Research limitations/implications

The model is set to find solutions using a specific pattern of metamaterials. This is promising to take those geometries as variables of the optimization problems. Moreover, in this exploratory work, no constraint on the fabrication limits has been taken into account.

Originality/value

The originality is to formulate design problems of waveguide with metamaterial walls into optimization problems. These optimization problems are difficult to solve because the objective function and two inequality constraints are computed via a numerical simulation code based on finite element methods. Thus, an original approach based on penalization is implemented and three optimization software are used. Hence, the authors propose an optimization-based methodology and apply to solve two inverse problems of design.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 19 September 2018

Niraj Kumar Jha and Udo Nackenhorst

The purpose of this paper is to develop a progressive damage framework to predict the fatigue life of cord-reinforced rubber composite under cyclic loadings. Special…

Abstract

Purpose

The purpose of this paper is to develop a progressive damage framework to predict the fatigue life of cord-reinforced rubber composite under cyclic loadings. Special attention has been paid to failure mechanisms, like cord–rubber interfacial debonding, and rubber matrix damage.

Design/methodology/approach

The constitutive modeling is based on the continuum damage mechanics (CDMs) and the thermodynamics of irreversible process. The damage in rubber is described by an istropic law, whereas elasto-plastic continuum model has been proposed for cord–rubber interphase layer. The numerical framework is implemented into commercial finite element code Abaqus/Standard via user subroutine (UMAT).

Findings

One of the most important findings obtained from reviewing various techniques is that meso-level fatigue damage modeling based on developed framework can simulate competitive damage scenarios, e.g. debonding, delamination or matrix failure.

Originality/value

A systematic framework for predicting failure in cord-reinforced rubber composite is formulated within the context of CDMs that can also be applied for industrial components, such as tires and airsprings.

Details

Engineering Computations, vol. 35 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic…

1004

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 May 2000

D.S. Liyanapathirana, A.J. Deeks and M.F. Randolph

In finite element analysis of pile driving, the nodes of the finite element mesh are the most important locations for output stresses. Especially at the pile‐soil…

1010

Abstract

In finite element analysis of pile driving, the nodes of the finite element mesh are the most important locations for output stresses. Especially at the pile‐soil interface, it is essential to obtain accurate nodal stresses. Several global and local stress smoothing methods available in the literature were reviewed and examined. Global methods are found to be computationally expensive, so results obtained from several local stress smoothing methods are compared. It is shown that accurate nodal stresses can be obtained by approximating the stress distribution inside four‐element patches by a polynomial with order equal to the order of the shape functions. Equally good results can be obtained by approximating the stress distribution inside each element by a bilinear surface. When a method taking into account both equilibrium and boundary conditions was applied, a set of ill‐conditioned matrices was produced for the four‐element patches. Such methods are therefore not recommended.

Details

Engineering Computations, vol. 17 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…

5388

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 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…

1629

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 31 December 2021

Alexander Idesman and Bikash Dey

The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world…

Abstract

Purpose

The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry).

Design/methodology/approach

This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes.

Findings

The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry).

Originality/value

It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.

Details

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

Keywords

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