Abstract. The aim of this paper is to propose a three-dimensional weld pool model for the
moving gas tungsten arc welding (GTAW) process, in order to understand the main factors that limit the weld quality and improve the productivity, especially with respect to the welding speed. Simulation is a very powerful tool to help in understanding the physical phenomena in the weld process. A 3Dfiniteelement model of heat and fluid flow in weld pool considering free surface of the pool and traveling speed has been developed for the GTAW process. Cast3M software is used to compute all the governing equations. The free surface of the weld pool is calculated by minimizing the total surface energy. The combined effects of surface tension gradient, buoyancy force, arc pressure, arc drag force to drive the fluid flow is included in our model. The deformation of the weld pool surface and the welding speed affect fluid flow, heat flow and thus temperature gradients and molten pool dimensions. Welding trials study is presented to compare our numerical results with macrograph of the molten pool.
Index Terms—Finiteelement, inductive power transfer, surface impedance boundary condition
I. I NTRODUCTION
T HE wireless power transfer (WPT) is a trending topic. Indeed, the recent progresses in power electronics have paved the way to the implementation of resonant inductive power transfer for energy-greedy applications, such as the supply of electric vehicles . Bringing significative infor- mation, the 3Dfiniteelement (FE) modeling of the coils used for resonant WPT as massive conductors is neverthe- less submitted to important computational burden. The skin and proximity effects appearing at the working frequency level (tens of kHz for the transfer of high power) require a high refinement of the conductors volume mesh, making massive conductors formulations hardly applicable. The resorts to stranded conductors  or homogenization technique  have therefore been investigated. Here, profit is taken from a 3D surface impedance boundary condition (SIBC) - to avoid the volume mesh inside the conductors and relax the computational constraints without using homogenization. Reflecting the important influence of the external circuit on the power transfer (through the resonant effect), a circuit coupling needs to be applied in order to model the resonant conditions at the circuit and field levels. The combination of SIBC with a circuit-coupled t-φ formulation (with t the electric vector potential and φ the magnetic scalar potential) has already been addressed in . Here, an a-v formulation (with a the magnetic vector potential and v the electric scalar potential) is considered. A natural strong circuit coupling method for a-v formulation involving massive conductors has been proposed in . In this work, this last contribution is adapted and extended to the use of SIBC, leading to a new way to implement SIBC with circuit coupling.
The stretch blow molding process of PET bottles is a two-step process. First, a cold tube- shape preform is heated using an infrared oven above PET glass transition temperature (about 80°C) in order to reach the forming temperature. The softened preform is then simultaneously stretched and inflated with a rod and air pressure. The final wall thickness of the bottle is both related to heating parameters as well as stretch blow molding ones. It leads to a complex thermo-mechanical problem for which specific numerical models must be developed. In this work, a complete 3Dfiniteelement modeling of the stretch blow molding process has been developed including both infrared heating and forming steps.
Besides the volume evaluation of the intra orbital soft tissues, the surgery planning has been studied by the way of a 3DFiniteElement mesh. Since the decompression act is a relatively rare surgery, the orbit has not been modelled by a FE mesh previously. Nevertheless, the ocular globe has been studied using a FE model . Our FE orbital cavity model has been manually meshed with hexahedrons and wedges to accurately fit the splines obtained after the segmentation step. The mesh obtained is complex since it has to respect the topography of the orbit, that is to say it contains above 3000 elements (Figure 2).
Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio- economical cost. At the cellular scale, recent research efforts have focussed on primary injuries by making use of models aimed at simulating mechani- cal deformation induced axonal electrophysiological functional deficits. The overwhelming majority of these models only consider axonal stretching as a loading mode, while other modes of deformation such as crushing or mixed modes—highly relevant in spinal cord injury—are left unmodelled. To this end, we propose here a novel 3Dfiniteelement framework coupling mecha- nics and electrophysiology by considering the electrophysiological Hodgkin- Huxley and Cable Theory models as surface boundary conditions introduced directly in the weak form, hence eliminating the need to geometrically ac- count for the membrane in its electrophysiological contribution. After valida- tion against numerical and experimental results , the approach is leveraged to model an idealised axonal dislocation injury. The results show that the sole consideration of induced longitudinal stretch following transverse loading of a node of Ranvier is not necessarily enough to capture the extent of axonal elec- trophysiological deficit and that the non-axisymmetric loading of the node participates to a larger extent to the subsequent damage. On the contrary,
A. Capacity Computation
The capacitances are computed by energy consideration. The results in Fig. 5 represent the self capacitances of the rotor ( ) and of one phase of the stator for a mesh step of and an irregular mesh step, which takes the values 3, 5, or 6 , with a ro- tation step of 1 . The differences between the two computations do not depend on the angular position of the rotor. This tends to show that the errors are mainly due to the approximation by finiteelement method, when the characteristic dimension of the elements increase. The error introduced by the OLM method can be neglected.
 H. C. Lai, D. Rodger, and P. J. Leonard, “Coupling meshes in 3d prob- lems involving movements,” IEEE Transactions on Magnetics, vol. 28, pp. 1732–1734, Mar. 1992.
 C. Golovanov, J. L. Coulomb, Y. Maréchal, and G. Meunier, “3d mesh connection techniques applied to movement simulation,” IEEE Trans-
Abstract This paper presents the theoretical analysis of the transverse flux linear actuator used for fast and accurate positioning of the lens of a CD-rom player. The purpose is to compute the thrust force as a function of the mover position for different values of the design parameters. A series of models (2D and 3D) corresponding to different levels of approximation of the original problem are considered. A particular attention has been paid to the control of the accuracy of the results by using dual formulations. In particular, the relevance and the accuracy of 2D computations, compared to 3D computations, are discussed in detail.
development of new and more efficient modeling techniques adapted to the requirements of MEMS, has to be carried out .
Several numerical methods have been proposed for the simulation of MEMS. Lumped or reduced or- der models and semi-analytical methods  allow to predict the behaviour of simple micro-structures. However they are no longer applicable for devices, such as comb drives, electrostatic motors or de- flectable 3D micromirrors, where fringing electrostatic fields are dominant . The FE method can accurately compute these fringing effects at the expense of a dense discretization near the corners of the device . Further the FE modeling of MEMS accounting for their movement needs a completely new mesh and computation for each new position what is specially expensive when dealing with 3D models.
Laboratoire de Mecanique des Solides, Ecole Polytechnique, 91128 Palaiseau Cedex, France
CEA, DEN, DM2S, SEMT, DYN, F-91191 Gif-sur-Yvette, France
This paper suggests a 3D ﬁnite element method based on the modal theory in order to analyse linear periodically time-varying systems. Presentation of the method is given through the particular case of asymmetric rotating machines. First, Hill governing equations of asymmetric rotating oscillators with two degrees of freedom are investigated. These differential equations with periodic coefﬁcients are solved with classic Floquet theory leading to parametric quasimodes. These mathematical entities are found to have the same fundamental properties as classic eigenmodes, but contain several harmonics possibly responsible for parametric instabilities. Extension to the vibration analysis (stability, frequency spectrum) of asymmetric rotating machines with multiple degrees of freedom is achieved with a fully 3D ﬁnite element model including stator and rotor coupling. Due to Hill expansion, the usual degrees of freedom are duplicated and associated with the relevant harmonic of the Floquet solutions in the frequency domain. Parametric quasimodes as well as steady-state response of the whole system are ingeniously computed with a component-mode synthesis method. Finally, experimental investigations are performed on a test rig composed of an asymmetric rotor running on nonisotropic supports. Numerical and experimental results are compared to highlight the potential of the numerical method.
(plusieurs dizaines de fois supérieur à l’épaisseur de la tôle afin de réduire l’effet de flexion), le rayon d’entrée R h de la matrice étant de 10 mm (Figure 67). La tôle est fixée
entre la matrice et le serre-flan avec un effort de serrage de 104 tonnes. Un jonc de retenu au niveau du flan, empêche tout avalement de matière et assure ainsi une expansion equibiaxiale au niveau du sommet de la tôle déformée. Il est à noter que l’utilisation de serre-flans elliptiques permet de faire varier le chemin de déformation de la matière, ce qui est très utile lorsque l’on veut construire une CLF. Durant l’essai, la tôle est gonflée sous l’action d’un liquide sous pression et des images de la tôle déformée sont prises avec deux caméras pour permettre une analyse stéréo 3D. Au préalable, un motif aléatoire a été imprimé par dépôt électrolytique sur la tôle non déformée afin d’utiliser le logiciel de corrélation d’images Aramis pour mesurer le champ de déplacement. Notons que ce type d’essai présente l’avantage d’être effectué dans des conditions expérimentales proches de celles rencontrées lors d’une mise en forme par hydroformage (en terme de chemin de déformation). Il est généralement analysé en utilisant une approximation polynomiale de la surface de la tôle déformée.
In the literature, there have been many experimental investigations of machining chips compaction as part of metal waste recycling effort (e.g. [1, 2, 3]). However, little exists on the numerical modeling of compaction. Relevant studies have been focused on the compaction of powders. Computational modeling of compaction of powders has been applied using two methods: the discrete model and the continuum model methods. In the discrete model method, powder particles are modeled as individual uniform spheres (in 3D) or circular cylinders (in 2D) and the contact interaction and deformation of the particles are analyzed [4, 5, 6, 7], whereas in the continuum model method the collection of powders is modeled as a continuous media whose deformation with a changing density is analyzed [8, 9, 10, 11, 12].
Figure 47: Heaviside functions and domains definitions. In the case of junctions, only the nodes whose support is intersected by multiple cracks are enriched with junction enrichment functions.
The X-FEM and GFEM formulations describe exactly the same approximation space and so does the new enrichment strategy proposed (see table 4), which is an extension to junctions of the formulation proposed in [Ndeffo**]. The motivation for this new enrichment strategy is the following. When the crack surface gets close to the nodes of the mesh, condition number soars with quadratic elements. Thus, a special treatment is needed to improve the numerical behavior of the approximation space. Ndeffo et al suggested that X-FEM signs functions performed rather poorly and may lead to bad results. Therefore, X-FEM couldn’t be used directly even if the X-FEM junction functions are more convenient when level-sets information is used. So, we considered a reshape of X-FEM approximation to solve those conditioning issues. The construction of the new enrichment suggested above follows the principle of complementary element or complementary nodes that is encountered also in the literature [AFEM**]. For the same arguments underlined in the paper of Ndeffo et al, this new formulation combines features of both X-FEM and GFEM:
Figure 1: Exaggerated deflection of the 3D disk
4 Objects and functions available in the library
Much of sparselizard is written in C++ in an object-oriented way. It should thus be no surprise that most of the code you write consists in creating and managing objects. Below is the list of the main objects (and namespaces) that you can use in your simulations. In any case we recommend to follow the examples in the examples folder to get used to sparselizard.
3.2 Vector classes
The library contains a wide variety of vector classes to define and manipulate vectors. All these classes are template classes, the template parameter being data type. A basic class called Vect<T> derives from the familiar standard vector<T> and adds some methods and operators that are specific to scientific computing and finiteelement techniques. Other vector classes are more finiteelement oriented.
reach the desired accuracy and how coarser it can be at other places. The convergence of the force computed by the 2D dual formulations as a function of the total number of nodes of the mesh, is shown on Fig. 5. The values obtained with the dual approach give a valuable control on the accuracy. On basis of this curve, a relation can be found between the characteristic length of the elements of the mesh and the ac- curacy of the global quantities (force, energy). This relation helps designing the 3D model, by giving an approximation of the size and the distribution of the elements in the 3D mesh in order to reach a given accuracy. To illustrate the relative computation cost of the models, a 3D mesh of more than 500000 nodes is necessary to obtain the same accuracy as a 2D mesh of 20000 nodes.
This report explains the steps followed in performing finiteelement analysis. First a wire frame was developed of Wang’s design. Then the elements were given properties. Followed by applying the loads and defining the boundary conditions. Finally the program calculated the stresses and natural frequencies needed.