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This paper presents a mixed Eulerian and Lagrangian finite element method for solving 2‐D transient flows involving a moving/free boundary. The method combines the simplicity of a solution with a fixed computational grid associated with the Eulerian concept and the computational power of Lagrangian approach which is especially effective for a moving grid defined in the physical domain. The method employs a time‐dependent boundary‐fitted coordinate transformation to allow the physical grid to follow the moving boundary which remains always an element boundary while the computational grid is held fixed. The method is demonstrated by an example in which transient wave propagation in an open channel is simulated. The method is efficient and requires no iterative procedures and no mesh re‐zoning.

This paper, which is concerned with fluid‐structure interaction analysis, is a sequel to our earlier paper which gave an introduction to the numerical treatment of such systems. The paper is divided into five main sections. In the first two, a state‐of‐the‐art review on near‐field and far‐field fluid structure interaction is presented. In attempting to highlight where current research should be directed, only the most widely used computer codes are reviewed in the third section. Conclusions are presented in the fourth section.

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 is concerned with the treatment of fluid‐structure interaction problems. The paper is divided in a number of sections. The first is an introduction to the historical background which lead to the numerical approach being used today. In the second the main factors affecting the numerical treatment of fluid‐structure interaction problems are identified. The next eight sections discuss each of these factors separately. Conclusions are drawn in section eleven.

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.

The paper describes developments in the numerical analysis of metal forming processes mainly motivated by industrial applications. It deals with a complete consideration of the unsteady contact developing between the material and the die, the regeneration of the finite element mesh during the course of the calculation, and with the simulation of superplastic forming processes. In particular, an approach relating both the contact pressure and the friction force to the motion of the material relative to the die surface leads to a convenient computational procedure and to a smooth numerical behaviour under friction. The topological part of the contact algorithm appears well‐suited also for the redefinition of the discretization mesh. As a selected application, superplastic forming is considered in conclusion. Industrial practice requires the adjustment of the forming pressure to a prescribed value of the maximum rate of deformation in the material.

The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid‐structure interaction fields, is extended to materials with memory, namely, non‐ linear path‐dependent materials. Previous attempts to treat non‐ linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast‐transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non‐linear solid mechanics and, in particular, to impact, coining or forming analysis.

Inside the finite element framework of LAGAMINE code, the contact conditions are introduced with specific two‐node interface elements and four‐node quadrangular elements or four‐node one point quadrature elements. A non‐associated flow rule is involved for sliding unilateral contact modelling. Two methods of penalty factor computations in the penalty contact algorithms are presented. These methods are then used for contact modelling of two isothermal examples: axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto‐plastic.

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.

This study aims to propose a numerical modeling procedure for response analysis of elastic body floating in water and submitted to regular waves. An equivalent simplified mechanical single-degree-of-freedom system allowing to reproduce the heave movements is first developed, then the obtained lumped characteristics are used for elastic analysis of the floating body in heave motion.

First, a two-dimensional numerical model of a rigid floating body in a wave tank is implemented under DualSPHysics, an open source computational fluid dynamics (CFD) code based on smoothed particle hydrodynamics method. Then, the obtained results are exploited to derive an equivalent mechanical mass-spring-damper model. Finally, estimated equivalent characteristics are used in a structural finite element modeling of the considered body assuming elastic behavior.

Obtained results concerning the floating body displacements are represented and validated using existing experimental data in the literature. Wave forces acting on the body are also evaluated. It was found that for regular waves, it is possible to replace the complex CFD refined model by an equivalent simplified mechanical system which makes easy the use of structural finite element analysis.

The originality of this work lies in the proposed procedure to evaluate the mechanical properties of the equivalent elastic system. This allows to couple two different software tools and to take advantages of their features.