FEM-Simulations

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. 

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. 

Louisnard O, Gonzalez-Garcia J, Tudela I et al (2009) FEM simulation of a son-reactor accounting for vibrations of the boundaries. Ultrason Sonochem 16 250-259... 

The suggested procedure to arrive at this goal is presented in Fig. 3.1. It starts with the transfer of a certain microhotplate layout into a geometry model for a complex FEM simulation. This step is shown in Fig. 3.2 and will be explained in more detail in one of the next sections. A complex 3-d FEM simulation is then performed. The results of this simulation are used to produce a lumped-element model. This model is translated into a hardware description language (HDL). Using the resistances of the device elements such as the heater resistance, Rheat> and the resistance of the temperature sensor, Rx. co-simulations with the circuitry can be performed. 

The aim in converting the microhotplate into a geometry model for the FEM simulation was to find a model that is as simple as possible but includes all relevant processes. The model assumptions to be explained in detail in the following section and the steps to arrive at the model are represented in fig. 3.2. The feature on the bottom left-hand side represents the microhotplate schematic. The microhotplate exhibits a symmetric design so that a simulation of one quarter is adequate. Geomet-... 

Fig. 3.2. Schematic showing the translation of a microhotplate layout into a geometry model description for FEM simulations...

The circular microhotplate was thermally characterized, and the results were compared with simulations carried out according to the approach discussed in Chap. 3. Applying FEM simulations as described in Sect. 3.3 generate a temperature field, and the temperature in the membrane center represents the overall membrane temperature according to Eq. (3.21). The values that have been used for the simulation are summarized in Table 4.2. 

Table 4.2. Thermal conductivities and heat capacities as used for the FEM simulations...

The measurement results have been compared to the corresponding values of a FEM simulation in Sect. 4.2.2, and the vahdity of the model for simulations of the temperature distribution has been established. 

Figure 1. Qualitative comparison of a free swelling experiment on a soot-coloured hydrogel disc (experiment by J. M. Huyghe, 1999) with the 3-d FEM simulation via PANDAS...

Figure 17.12 fem simulation of cantilever potential distribution to calculate parasitic stray... 

If we look more closely at these changes, which was done by fem simulations by Prume in [10], we can find a correction factor, which helps to derive the electrical properties precisely for measurements down to 1 /rm2. Figure 17.12 shows the influence of the cantilever tip and the body part of the cantilever in fem simulation. 

The SIMBLOW3 integrated FEM simulation commercial software for the extrusion blow molding process also uses the K-BKZ fluid (79), which accounts for shear thinning,... 

S. Wang, A. Makinouchi, and T. Nakagawa, Three-dimensional Viscoplastic FEM Simulation of a Stretch Blow Molding Process, Adv. Polym. Technol., 17, 189-202 (1998). 

Even though in principal, the visualization of ID simulations in a three-dimensional space is not too meaningful, the visualization of a number of ID-functions with exact geometrical placement can be an interesting alternative. In addition to that, the simple and natural interaction metaphors that are used in VEs can ease the task of configuration construction. Figure 3.53 depicts the prototype we developed for the interactive configuration of twin screw extruders that uses fast ID simulations to prepare functional zones for expensive FEM simulations. 

Fig. 6.1.5 FEM simulation of the capacitance of parallel plate style combs...

Results of FEM simulations for acid-base distributions are provided in refs. [36,46,53,54]. Shapiro et al. [52] similarly have calculated pH profiles for the downstreeim H ion flux but Included multicomponent ion fluxes, when two kinematic waves result. Neither model includes any complications arising from nonlinear, radial concentration fluxes or from the acid-base neutralization reaction eqn. (19). The latter will create a heated, dilute zone of neutral pH close to the cathode. 

A 3D FEM simulation for coupled THM process of fractured rocks for heat extraction in HDR was reported by Zhao Yangsheng et al. (2002). 

For each weld, the Vickers hardness distribution on a transverse section with and without postweld heat treatment (PWHT) was determined. The PWHT was 24 h at 121 °C (250 °F). A hnite element modeling (FEM) simulation was used to calculate the time/temperature history for a subset of the welds. 

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