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A generalized weighted residual method is used to formulate the discrete element method (DEM) for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A covergence proof for the two‐dimensional beam element is given for mathematical validation. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems.

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.

The paper addresses the issue of the modelling of the mechanical behaviour of yarns using a massspring system of discrete elements. For this purpose, the yarn is discretized into straight, elastic bars modelled by stretching springs which are connected at frictionless hinges by rotational springs. Shear springs are used, in order to model the shearing stiffness of the yarn. An energy study is conducted, taking into account the various strain energy contributions of the yarn and the work of the external forces. From the energy expression, a stability analysis is performed, relying on the Dirichlet‐Lagrange stability criterion. The effects of boundary conditions as well as the heterogeneity of the nodes’ rigidity are analysed. The equilibrium shapes of the structure, submitted to its own weight, are obtained as shapes associated to the minimum of the total potential energy versus the whole set of kinematic translational and rotational variables. The obtained results show that the effects of boundary conditions and heterogeneity of the yarn’s rigidity on the stability of the structure are important.