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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.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE 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 material processing for the last five years, and more than 1100 references are listed.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. 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 the 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 material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

A finite element procedure is presented for refined transient analysis of two‐dimensional (plane or axisymmetric) non‐linear structures involving arbitrarily large displacements, rotations and strains. The finite element model is based on the biquadratic nine‐node element of the Lagrange family. The relevant points pertaining to the equations of motion and their integration and to the spatial description, including geometrical and material non‐linearities, are considered. In particular, stress and strain rates are discussed. Finally, significant numerical applications show the effectiveness of the proposed method.

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.

In this paper the use of classical strain measures in analysis of trusses at finite deformations will be discussed. The results will be compared to the ones acquired using a novel strain measure based on the Hyperbolic Sine function. Through the evaluation of results, algebraic development and graph analysis, the properties of the Hyperbolic Sine strain measure will be examined.

Through graph plotting, comparisons between the novel strain measure and the classic ones will be made. The formulae for the implementation of the Hyperbolic Sine strain measure into a positional finite element method are developed. Four engineering applications are presented and comparisons between results obtained using all strain measures studied are made.

The proposed strain measure, Hyperbolic Sine, has objectivity and symmetry. The linear constitutive model formed by the Hyperbolic Sine strain and its conjugated stress presents an increasing stiffness, both in compression and tension, a behavior that can be useful in the modeling of several materials.

The structural analysis performed on the four examples of trusses in this article did not consider the variation of the cross-sectional area of the elements or the buckling phenomenon, moreover, only elastic behavior is considered.

The present article proposes the use of a novel strain measure family, based on the Hyperbolic Sine function and suitable for structural applications. Mathematical expressions for the use of the Hyperbolic Sine strain measure are established following the energetic concepts of the positional formulation of the finite element method.

Deformations in the plane of a fabric, because of their nature, are almost invariably expressed as "percentage extensions", i.e., as changes in length per unit original length. Such measures of strain only exhibit tensor transformation behaviour when the strains are infinitesimally small; this is rarely the case with textile fabrics. With the growth of engineering end-uses and related design techniques, plus the drive to achieve the virtual reality catwalk, there is a need for deformations of fabrics to be expressed as true finite strains. A method of calculating such strains from experimental data is described, based on the finite element stress analysis methods widely used in engineering. The method involves measuring the displacements during deformation of a grid of points marked on the fabric.

The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.

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.