Finite element method simulation

In these last researches, a continuous feedback between the process study and the prototype design and development was established. In this way FEM (Finite element method) simulation has provided useful information about geometry, ultrasound intensity distribution and structural material coupling [37, 48, 49] for the design of an optimized sonoelectrochemical reactor. 

Loren, N., Hagslatt, H., Nyden, M., and Hermansson, A.M. (2005). Water mobility in heterogeneous emulsions determined by a new eombination of confocal laser scanning microscopy, image analysis, NMR diflusometry and finite element method simulation. J. Chem. Phys. 122, 024716... 

Wei J, Cui Y and Shao J. 2000. 3-D Finite Element method simulation of ground water and land subsidence in Jining City. J. of Changchun Univ. of Sci. Tech.,3(X4), pp. 376-381... 

Validation of sensor properties by finite element method simulation... 

Ubong et al. also presented a three-dimensional model of a channel pair [32]. The isothermal model incorporated a Butler-Vohner-type equation for electrochemistry and was solved with the finite element method. Simulations were vahdated against a single cell with triple serpentine flow field, which was operated in the temperature range 120-180 °C. The results showed that there is no drastic decrease in cell voltage at high current density due to mass transport hmitation. This is explained by the absence of accumulation of liquid water. It was also concluded that reaction gases need not be humidified. 

D. Somin, A. Karch, D. Nunes, Finite element method simulation of the hot extrusion of a powder metallurgy stainless steel grade, Int. J. Mater. Form. 8 (March 2015) 145—155. 

To get more detailed information of distributive and dispersive mixing, we performed statistic methods using the results of a 3D finite element method simulation. In the paper, distributive mixing is estimated by RTD and dispersive mixing is estimated by max shear rate distribution. 

In reality, heat is conducted in all three spatial dimensions. While specific building simulation codes can model the transient and steady-state two-dimensional temperature distribution in building structures using finite-difference or finite-elements methods, conduction is normally modeled one-... 

It is the interplay of universal and material-specific properties which causes the interesting macroscopic behavior of macromolecular materials. This introduction will not consider scales beyond the universal or scaling regime, such as finite element methods. First we will give a short discussion on which method can be used under which circumstances. Then a short account on microscopic methods will follow. The fourth section will contain some typical coarse-grained or mesoscopic simulations, followed by some short general conclusions. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

The beauty of finite-element modelling is that it is very flexible. The system of interest may be continuous, as in a fluid, or it may comprise separate, discrete components, such as the pieces of metal in this example. The basic principle of finite-element modelling, to simulate the operation of a system by deriving equations only on a local scale, mimics the physical reality by which interactions within most systems are the result of a large number of localised interactions between adjacent elements. These interactions are often bi-directional, in that the behaviour of each element is also affected by the system of which it forms a part. The finite-element method is particularly powerful because with the appropriate choice of elements it is easy to accurately model complex interactions in very large systems because the physical behaviour of each element has a simple mathematical description. 

While most authors have used the finite-difference method, the finite element method has also been used—e.g., a two-dimensional finite element model incorporating shrinkable subdomains was used to de.scribe interroot competition to simulate the uptake of N from the rhizosphere (36). It included a nitrification submodel and found good agreement between ob.served and predicted uptake by onion on a range of soil types. However, while a different method of solution was used, the assumptions and the equations solved were still based on the Barber-Cushman model. 

The focus of the remainder of this chapter is on interstitial flow simulation by finite volume or finite element methods. These allow simulations at higher flow rates through turbulence models, and the inclusion of chemical reactions and heat transfer. In particular, the conjugate heat transfer problem of conduction inside the catalyst particles can be addressed with this method. 

Mechanical properties of PNCs can also be estimated by using computer modeling and simulation methods at a wide range of length and time scales. Seamless movement from one scale to another, for example, from the molecular scale (e.g., MD) and microscale (e.g., Halphin-Tsai) to macroscale (e.g., finite element method, FEM), and the combination of scales (or the so-called multiscale methods) is the most important prerequisite for the efficient transfer and extrapolation of calculated parameters, properties, and numerical information across length scales. 

Stress calculations are carried out by the finite element method. Here, the commercial finite method code ABAQUS (Hibbit, Karlsson, and Sorensen, Inc.) is used. Other codes such as MARC, ANSYS are also available. To calculate the stresses precisely, appropriate meshes and elements have to be used. 2D and shell meshes are not enough to figure out stress states of SOFC cells precisely, and thus 3D meshes is suitable for the stress calculation. Since the division of a model into individual tetrahedral sometimes faces difficulties of visualization and could easily lead to errors in numbering, eight-comered brick elements are convenient for the use. The element type used for the stress simulation here is three-dimensional solid elements of an 8-node linear brick. In the coupled calculation between the thermo-fluid calculation and the stress calculation a same mesh model have to be used. Consequently same discrete 3D meshes used for the thermo-fluid analysis are employed for the stress calculation. Using ABAQUS, the deformations and stresses in a material under a load are calculated. Besides this treatment, the initial and final conditions of models can be set as the boundary conditions and the structural change can thus be treated. 

S, -W. Kim. Three-Dimensional Simulation for the Filling Stage of the Polymer Injection Molding Process Using the Finite Element Method. PhD thesis, University of Wisconsin-Madison, 2005. 

L.-S. Turng and S.-W. Kim. Three-dimensional simulation for the filling stage of the polymer injection molding process using the finite element method. To be published, 2005. 

---