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This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.

The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.

This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

In certain cases, traction–separation laws do not reflect the behaviour sufficiently so that thin volumetric elements, Internal Thickness Extrapolation formulations, bulk material projections or various other approaches are applied. All of them have disadvantages in the formulation or practical application.

Damage within thin layers is often modelled using at cohesive zone elements (CZE). The constitutive behaviour of cohesive zone elements is usually described by traction–seperation laws (TSLs) that consider the (traction separation) relation in normal opening and tangential shearing direction. Here, the deformation (separation) as well as the reaction (traction) are vectorial quantities.

In this contribution, a CZE is presented that includes damage from membrane modes.

Membrane mode-related damaging effects that can be seen in physical tests that could not be simulated with standard CZEs are well captured by membrane mode–enhanced cohesive zone elements.

Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.

Several mechanical models can be employed for the analysis of thin walled structures. A bending indicator is developed for a nonlinear adaptive process and applied to thin walled axisymmetric shell problems incorporating membrane and bending elements. If the structural response of the model including bending is available the error made by the reduced membrane model is easy to evaluate. Thus an indication for the bending has to be found from the structural response of the reduced membrane model. This is done by an approximation of the rotations of the membrane part of the structure and by an evaluation of the bending energy leading to the bending indicator with these approximated rotations. Finally a criterion for the change of the models is proposed based on the bending indicator and some examples are presented.

The paper aims to introduce an efficient contact detection algorithm for smooth convex particles.

The contact points of adjacent particles are defined according to the common‐normal concept. The problem of contact detection is formulated as 2D unconstrained optimization problem that is solved by a combination of Newton's method and a Levenberg‐Marquardt method.

The contact detection algorithm is efficient in terms of the number of iterations required to reach a high accuracy. In the case of non‐penetrating particles, a penetration can be ruled out in the course of the iterative solution before convergence is reached.

The algorithm is only applicable to smooth convex particles, where a bijective relation between the surface points and the surface normals exists.

By a new kind of formulation, the problem of contact detection between 3D particles can be reduced to a 2D unconstrained optimization problem. This formulation enables fast contact exclusions in the case of non‐penetrating particles.

This paper aims to construct smooth poly-ellipsoid shapes from synchrotron microcomputed tomography (SMT) images on sand and to develop a new discrete element method (DEM) contact detection algorithm.

Voxelated images generated by SMT on Colorado Mason sand are processed to construct smooth poly-ellipsoidal particle approximations. For DEM contact detection, cuboidal shape approximations to the poly-ellipsoids are used to speed up contact detection.

The poly-ellipsoid particle shape approximation to Colorado Mason sand grains is better than a simpler ellipsoidal approximation. The new DEM contact algorithm leads to significant speedup and accuracy is maintained.

The paper limits particle shape approximation to smooth poly-ellipsoids.

Poly-ellipsoids provide asymmetry of particle shapes as compared to ellipsoids, thus allowing closer representation of real sand grain shapes that may be angular and unsymmetric. When incorporated in a DEM for computation, the poly-ellipsoids allow better representation of particle rolling, sliding and interlocking phenomena.

Method to construct poly-ellipsoid particle shapes from SMT data on real sands and computationally efficient DEM contact detection algorithm for poly-ellipsoids.

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 first purpose of this paper is to identify – by an inverse problem – the unknown material characteristics in a permanent magnet synchronous machine in order to obtain a numerical model that is a realistic representation of the machine. The second purpose is to optimize the machine geometrically – using the accurate numerical model – for a maximal torque to losses ratio. Using the optimized geometry, a new machine can be manufactured that is more efficient than the original.

A 2D finite element model of the machine is built, using a nonlinear material characteristic that contains three parameters. The parameters are identified by an inverse problem, starting from torque measurements. The validation is based on local BH‐measurements on the stator iron.

Geometrical parameters of the motor are optimized at small load (low‐stator currents) and at full load (high‐stator currents). If the optimization is carried out for a small load, the stator teeth are chosen wider in order to reduce iron loss. An optimization at full load results in a larger copper section so that the copper loss is reduced.

The identification of the material parameters is influenced by the tolerance on the air gap – shown by a sensitivity analysis in the paper – and by 3D effects, which are not taken into account in the 2D model.

The identification of the material parameters guarantees that the numerical model describes the real material properties in the machine, which may be different from the properties given by the manufacturer because of mechanical stress and material degradation.

The optimization is more accurate because the material properties, used in the numerical model, are determined by the solution of an inverse problem that uses measurements on the machine.

When establishing a mathematical model to simulate solid mechanics, considering realistic geometries, special tools are needed to translate measured data, possibly with noise, into idealized geometrical entities. As an engineering application, wheel-rail contact interactions are fundamental in the dynamic modeling of railway vehicles. Many approaches used to solve the contact problem require a continuous parametric description of the geometries involved. However, measured wheel and rail profiles are often available as sets of discrete points. A reconstruction method is needed to transform discrete data into a continuous geometry.

The authors present an approximation method based on optimization to solve the problem of fitting a set of points with an arc spline. It consists of an initial guess based on a curvature function estimated from the data, followed by a least-squares optimization to improve the approximation. The authors also present a segmentation scheme that allows the method to increment the number of segments of the spline, trying to keep it at a minimal value, to satisfy a given error tolerance.

The paper provides a better understanding of arc splines and how they can be deformed. Examples with parametric curves and slightly noisy data from realistic wheel and rail profiles show that the approach is successful.

The developed methods have theoretical value. Furthermore, they have practical value since the approximation approach is better suited to deal with the reconstruction of wheel/rail profiles than interpolation, which most methods use to some degree.

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.