FINITE ELEMENT RESOLUTION OF CONVECTION-DIFFUSION EQUATIONS WITH INTERIOR AND BOUNDARY LAYERS

We present a new algorithm for the resolution of both interior and boundary layers present in the convection-diffusion equation in laminar regimes, based on the formulation of a family of polynomial-exponential elements. We have carried out an adaptation of the standard variational methods (finite element method and spectral element method), obtaining an algorithm which supplies non-oscillatory and accurate solutions. The algorithm consists of generating a coupled grid of polynomial standard elements and polynomial-exponential elements. The latter are able to represent the high gradients of the solution, while the standard elements represent the solution in the areas of smooth variation.

A gradient-based decomposition approach to optimize pressure path and counterpunch action in Y-shaped tube hydroforming operations

International audience; In tube hydroforming, the concurrent actions of pressurized fluid and mechanical feeding allows obtaining tube shapes characterized by complex geometries such as different diameters sections and/or bulged zones. Main process parameters are material feeding history (i.e., the punches velocity history), internal pressure path during the process, and (in T- or Y-shaped tube hydroforming) counterpunch action. What is crucial, in such processes, is the proper design of operative parameters aimed to avoid defects (for instance underfilling or ductile fractures). Actually, the design of tube hydroforming operations is mainly aimed to prevent bursting or buckling occurrence …

Meshless Simulation of Friction Stir Welding

This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these ap…

An advanced system for the simulation and planning of orthodontic treatment

This paper presents a new system for three-dimensional (3-D) orthodontic treatment planning and movement of teeth. We describe a computer vision technique for the acquisition and processing of 3-D images of the profile of hydrocolloid dental imprints. Profile measurement is based on the triangulation method which detects deformation of the projection of a laser line on the dental imprints. The system is computer-controlled and designed to achieve depth and lateral resolutions of 0.1 and 0.2 mm, respectively, within a depth range of 40 mm. The 3-D image of the imprint is segmented in order to identify different teeth. Two operators are presented: one for the detection of molars and premolars…

Kinetic Parameters for Thermal Degradation of Green Asparagus Texture by Unsteady-state Method

An unsteady-state method was developed for estimating texture degradation during heating-cooling of green asparagus spears. The method used a mathematical model of heat transmission for time-temperature history estimation, and a nonlinear regression of texture measurements of asparagus spears to estimate kinetic parameters. The specific heat, conductivity and convective coefficient of green asparagus were determined experimentally and used In the mathematical model for temperature estimation. Values obtained were Ea = 76.19±0.13 kJ/mol and k 1158°C = 0.00528±0.00005 s -1 . Good agreement was found between predicted and observed texture values. The method was compared with the classical stea…

Statistical Modeling for the Flow of Short Fibers Composites

Numerical results are given for the flow of fiber composites modelled as suspensions of non spherical particles. In this framework, because the many particles rotate, their state of orientation is described with a statistical approach. We used these methods to compute coupled solutions in which the orientation of the particles is affected by the flow and the flow itself depends on the orientation of the particles. The computation methods involve an augmented lagrangian approach and a streamline upwind petrov galerkin formulation to solve the convective orientation equation.

A simple inverse procedure to determine heat flux on the tool in orthogonal cutting

The applications of numerical simulation to machining processes have been more and more increasing in the last decade: today, a quite effective predictive capability has been reached, at least as far as global cutting variables (for instance cutting forces) are concerned. On the other hand, the capability to predict local cutting variables (i.e. stresses acting on the tool, temperature distribution, residual stresses in the machined surface) has to be furtherly improved, as well as effective experimental procedures to validate numerical results have to be developed. The aim of this paper is the proposition of an innovative approach, based on an simple inverse procedure, in order to identify…

A Pareto optimal design approach for simultaneous control of thinning and springback in stamping processes

One of the most relevant research issues in automotive field is focused on the reduction of stamped parts weight also increasing their strength. In this way, a strong research effort is developed on high strength steels which are widely utilized and they require a proper springback control. Springback reduction in sheet metal forming is a typical goal to be pursued which is conflicting with thinning reduction for instance. Thus, such problems can be considered as multi-objective ones characterized by conflicting objectives. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an indu…

Integration of gradient based and response surface methods to develop a cascade optimisation strategy for Y-shaped tube hydroforming process design

International audience; In the last years a strong research effort was produced in order to develop and design new forming technologies able to overcome the typical drawbacks of traditional forming operations. Among such new technologies, hydroforming proved to be one of the most promising. The design of tube hydroforming operations is mainly aimed to prevent bursting or buckling occurrence and such issues can be pursued only if a proper control of both material feeding history and internal pressure path during the process is performed.In this paper, a proper optimisation strategy was developed on Y-shaped tube hydroforming process which is characterized by a quite complex process mechanics…

Filling defects in a ceramics forming process

Publisher Summary This paper presents a simple semi-heuristic method to predict mold filling defects in a porcelain forming process. It involves both a mechanical modelling of this process as a squeezing flow, and a postprocessing calculus that unable a defects prediction as soon as the shape and the size of artistic reliefs are known. This shape analysis is carried out with a multi resolution wavelet analysis. The chapter models the filling stage and to propose a criterium to avoid any filling defect that could waste the quality of the drawings. It illustrates a simplified modelling of the process during which the “turning” stage is approximated by the deformation under pressure of a Norto…

Numerical Simulation of Friction Stir Welding by Natural Element Methods

In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatment of the advancing pin, and many others. Meshless methods somewhat alleviate these problems, allowing for an updated Lagrangian framework in the simulation. Accuracy is not affected by mesh distortion (and hence the name mes…

Assessment of material models through simple machining tests

The accuracy of the results obtained from FEM simulation of machining operations depends on the accuracy of input data. Among these, the flow stress data of the workpiece are extremely important together with the friction along the tool-chip interface. In this study, an identification procedure for the determination of material parameters that are used for the FEM simulation of machining processes is proposed. The procedure is based on the coupling of a numerical identification procedure and Arbitrarian Lagrangian Eulerian (ALE) Finite Element simulations of turning operations. An experimental campaign was developed in order to calibrate the model and to validate the procedure. The basic id…

Cross Extrusion With Asymmetric Die: A Comparison Between Finite Element and Meshless Formulation Predictions

A preliminary comparison between finite element and meshless simulations of extrusion

In this paper the extrusion process of a cross-shaped profile was investigated. In particular, the study was focused on the distortion of extruding profiles when the workpiece and die axis are not aligned. The process was simulated using the finite element method (FEM) and the natural element method (NEM), both implemented in an updated-Lagrangian formulation, in order to avoid the burden associated with the description of free surfaces in ALE or Eulerian formulations. Furthermore, an experimental equipment was developed in order to obtain reliable data in terms of deformed entity, required process load and calculated pressure. At the end, a comparison between the numerical predictions and …