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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.

The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.

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.

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.

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.

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.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

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.

The purpose of this paper is to provide industrial, education and academic users of computer programs a basic overview of finite elements in metal forming that will enable them to recognize the pitfalls of the existing formulations, identify the possible sources of errors and understand the routes for validating their numerical results.

The methodology draws from the fundamentals of the finite elements, plasticity and material science to aspects of computer implementation, modelling, accuracy, reliability and validation. The approach is illustrated and enriched with selected examples obtained from research and industrial metal forming applications.

The presentation is a step towards diminishing the gap being formed between developers of the finite element computer programs and the users having the know‐how on the metal forming technology. It is shown that there are easy and efficient ways of refreshing and upgrading the knowledge and skills of the users without resorting to complicated theoretical and numerical topics that go beyond their knowledge and most often are lectured out of metal forming context.

The overall content of the paper is enhancement of previous work in the field of sheet and bulk metal forming, and from experience in lecturing these topics to students in graduate and post‐graduate courses and to specialists of metal forming from industry.

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.

Incremental sheet forming represents a promising process in the manufacturing of metallic components, particularly its variant known as single point incremental forming (SPIF). The purpose of this paper is to test and validate the results coming from numerical simulation of SPIF processes using the reduced enhanced solid‐shell formulation, when compared to the solid finite elements available in ABAQUS software. The use of SPIF techniques in the production of small batch components has a potential wide application in fields such as rapid prototyping and biomechanical devices.

Incremental forming processes differ from conventional stamping by not using a press and by requiring a lower number of tools, since no dedicated punches and dies are necessary, which lowers the overall production costs. In addition, it shows relative simplicity and flexible setup for complex parts, when compared with conventional technologies. However, the low speed of production and low‐dimensional accuracy levels are still the main obstacles for a wider application of this technique in the context of large production batches.

In this sense, the use of numerical simulation tools based on the finite element method (FEM) can provide a better understanding of the process' peculiarities. However, there are differences on using distinct finite element formulations, regarding accuracy as well as CPU times during simulations, which can be prohibitive in some cases.

Aiming to provide sounding improvements in these two fields (robustness and cost effectiveness of FEM solutions), the present work encloses a preliminary study about some relevant parameters in the FEM simulation of SPIF. Special focus is given to the use of solid‐shell and solid finite elements, for the sake of generality in modelling, as well as implicit solution schemes for the sake of accuracy. Finally, results coming from both experimental data and commercial FEM packages are compared to those obtained by a reliable and cost‐effective solid‐shell finite element formulation developed and implemented by the authors.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.

The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.

Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.

A complete investigation of the stabilized formulation of the compressible problem is addressed.