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The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z²) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L² and L^∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.

Focuses on the inverse problems arising from the simulation of forming processes. Considers two sets of problems: parameter identification and shape optimization. Both are solved using an optimization method for the minimization of a suitable objective function. The convergence and convergence rate of the method depend on the accuracy of the derivatives of this function. The sensitivity analysis is based on a discrete approach, e.g. the differentiation of the discrete problem equations. Describes the method for non‐linear, non‐steady‐state‐forming problems involving contact evolution. First, it is applied to the parameter identification and to the torsion test. It shows good convergence properties and proves to be very efficient for the identification of the material behaviour. Then, it is applied to the tool shape optimization in forging for a two‐step process. A few iterations of the inverse method make it possible to suggest a suitable shape for the preforming tools.

In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is used to obtain non‐linear discretized equations, solved by an iterative Picard (fixed point) algorithm. At each step, two sub‐systems are successively solved. The first one represents a Newtonian fluid flow (Stokes equations) perturbed by known pseudo‐body forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second sub‐system reduces to the tensorial differential evolution equation of the extra‐stress tensor for a given velocity field. It is solved by the so‐called ‘non‐consistent Petrov‐Galerkin streamline upwind’ method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods.

The paper aims to present a way of engine model integration, an aircraft (multitask) and the mission into the single model that allows to study, from the level of selection of the engine cycle parameters, the feasibility of a specific mission with the assumed aerodynamic characteristics exemplified by a multitask airplane.

There were introduced dimensionless geometric and energetic criteria, binding parameters of the engine and the airplane. The following models were built: of the turbofan engine and the aircraft movements with the application of these criteria, creating a dimensionless model allowing for measuring the impact of engine design parameters on the efficiency of the mission undertaken.

The results were limited to the presentation of the impact of circuit parameters, such as engine TIT, OPR, BR on the defined criteria. The application of dimensionless criteria reduced the dimension of the task.

The presented method can be useful for engineers involved in the task of engine integration and the airplane at the preliminary design stage.

The originality of the presented solutions is reduced to provide a different, unconventional approach to the design process and not (so far) the engine itself but the entire aviation system.

The purpose of this paper is to propose a hybridization numerical method to solve the plastic deformation of metal working based on the flow function method and meshless method.

The proposed method is named as flow function-element free Galerkin (F-EFG) method. It uses the flow function as the basic unknown quantity to get the basic control equation, the compactly supported approximate function to establish a local approximate flow function by means of moving least square approximation, and the element free Galerkin (EFG) method to solve variational equation. The F-EFG method takes the upper limit method essence of flow function method, and the convergence, stability, and error characteristics of EFG method.

The steady extrusion process of the axisymmetric extrusion problems as well as the extrusion deformation law and main field variables are subjects in the modeling and simulation analysis using F-EFG method. The results show that the F-EFG method has good computational efficiency and accuracy.

The F-EFG method proposed in this paper has the advantages of high-solution precision of flow function method and large deformation solution of element free method. It overcomes the difficulties in global flow function establishment in flow function method and low-solution efficiency in element free method. The method is beneficial to the development of flow function method and element free method.

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

A complete thermo‐mechanical model for the simulation of the inertia welding process of two similar parts is described. The material behaviour is represented by an incompressible viscoplastic Norton—Hoff law in which the rheological parameters are dependent on temperature. The friction law was determined experimentally and depends on the prescribed pressure and the relative rotating velocity between the two parts. The mechanical problem is solved considering the virtual work principle including inertia terms. The computation of the three components of the velocity field such as radial, longitudinal and rotational velocity, in an axisymmetric approximation allows to take into account the torsional effects. The domain is updated based on a Lagrangian formulation. The non‐linear heat transfer equation with boundary conditions (convection, radiation and friction flux) is solved separately for each time step. Error estimators on mechanical and thermal computation are devised to adapt the mesh in an automatic way. Finally, numerical results concerning evolution of parts shape, strain, temperature, rotating velocity, upsetting are compared with actual industrial welds.

This paper seeks to extend the application of the natural neighbour Galerkin method to vibration analysis of fluid‐structure interaction problems.

The natural element method (NEM) which is a meshless technique is used to simulate the vibration analysis of the fluid‐structure interaction systems. The method uses the natural neighbour interpolation for the construction of test and trial functions. Displacement variable is used for both the solid and the fluid domains, whereas the fluid displacement is written as the gradient of a potential function. Two classical examples are considered: free vibration of a flexible cavity filled with liquid and vibration of an open vessel containing liquid. The corresponding eigenvalue problems are solved and the results are compared with the finite element method (FEM) and analytical solutions to show the accuracy and convergence of the method.

The performance of the NEM is investigated in the computation of the vibration modes of the fluid‐structure interaction problems. Good agreement with analytical and FEM solutions are observed. Through the notable obtained results, it is found that the NEM can also be used in vibration analysis of fluid‐structure interaction problems as it has been successfully applied to some problems in solid and fluid mechanics during the recent years.

In spite of notable achievements in solving some problems in solid and fluid mechanics using NEM, the vibration analysis of fluid‐structure interaction problems, as considered in this paper, has not been investigated so far.