FEM

TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

Integral terms extending on R are reduced to iJc using Boundary Integral Elements on the boundaries of the FEM domain (especially the influence of the source field hs). Inside the FEM domain, edge elements are used to compute the reaction field. 

For precise 3D-FEM simulations, a huge number of nodes is required (>30,000), which results in calculation times of several hours (sun spare 20) for one model. In order to decrease the number of nodes, we took advantage of the symmetry of the coils and calculated only a quarter or half of the test object. The modelled crack has a lenght of 15 mm, a height of 3 mm and is in a depth of 5 mm. The excitation frequency was 200 Hz. 

For the determination of the approximated solution of this equation the finite difference method and the finite element method (FEM) can be used. FEM has advantages because of lower requirements to the diseretization. If the material properties within one element are estimated to be constant the last term of the equation becomes zero. Figure 2 shows the principle discretization for the field computation. 

Earlier research has been focused on laboratory work to determine the feasibility of the method. Both experiments on real components and FEM simulations have been used. Simulations have been used as a guidance when deciding a suitable measurement arrangement. Examples of the information that can be obtained from FEM simulations will be demonstrated. 

Finally, a FEM Analysis has also been perfonned and a very good agreement found with the experimental results. 

A FEM analysis was carried out and the predicted distribution of stresses on the pressure vessel compared with the stress distribution calibration using the SPATE technique. 

A comparison of the results achieved with the FEM Analysis and the rosetta strain gauge measurements is shown in fig. 19. Differences can be noted in areas labeled B and C. The former can be explained as an effect of the discrepancy between the actual shape of the vessel and the ideal one used in the F.E.M. model. The latter can be ascribed to the presence of a muff, located in the centre of the head of the actual vessel, which has not been taken into account in the model. 

Fig. 18 FEM Analysis, sum of the principal stress distribution on the vessel surface on the deformed shape of it for a pressure equal to 5 bar.

Fig. 19 Comparison of the calculation achieved with FEM Analysis and the rosetta strain gauges measurements..

A. Fem dez-Barbero, A. Martin-Rodnguez, J. Callejas-Femandez, and R. Hidalgo-Alvarez, J. Colloid Interface ScL, 162, 257 (1994). 

The field emission microscope (FEM), invented in 1936 by Muller [59, 60], has provided major advances in the structural study of surfaces. The subject is highly developed and has been reviewed by several groups [2, 61, 62], and only a selective, introductory presentation is given here. Some aspects related to chemisorption are discussed in Chapter XVII. 

FEM Field emission microscopy [62, 101, 102] Electrons are emitted from a tip in a high field Surface structure... 

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

Tanner, R.I. 2000. Engineering Rheology, 2nd edti, Oxford University Press, Oxford. Taylor, C., Ranee, J. and Medwell, J. O., 1985. A note on the imposition of traction boundary conditions when using FEM for solving incompressible flow problems. Comnmn. Appl. Numer. Methods 1, 113-121. 

L. Tejmai-Kolai and H. Z Ahnei, FEMS Miciobiol. Lett. 24, FEMS Microbiol Eett. 24, 21 (1984). 

A. Breton, M. Dusser, B. Gaillard-Martinie, B. Guillot, N. Millet and G. Prensier, FEMS Microbiol. Lett., 1993, 82, 1. 

M.G. Doininguez-Bello and C.S. Stewart, FEMS Microb. EcoL, 1990, 73, 283. 

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