Stresses simulation

When lamellar structures are formed, it is necessary to ensure that the dimensions of the simulation cell are commensurate with the intrinsic periodicity of the lamellae. This process prevents unintentionally subjecting the system to artificial pressure as a result of the geometric constraints. Subjecting the system to a predetermined pressure, or stress, in a controlled manner can be achieved by allowing the system to fluctuate parallel to solid directions, which are introduced in Figure 14. For these directions, it would be appropriate to employ the usual techniques related to constant stress simulations.52,53... 

Procedure for Integrated Modeling 10.2.1 Introduction to Stress Simulations... 

The flow of the structural analyses is illustrated in Figure 10.2. The stress simulation is coupled with the other simulations such as fluid dynamics, and all the simulations are integrated. Before performing the stress simulations for SOFCs, the origin of the stress must be made clear and the stress conditions of the cells or stacks must be clarified. The following four stress conditions are considered here ... 

Stresses are induced by piling the cells or binding each bundle. Mechanical loads or pressure are also considered in the stress simulations. During cell operation, thermally induced stresses are superposed on the stresses induced by the mechanical loads. This state can be treated by the stress calculations. 

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. 

Table 10.5 Mechanical properties and cell sizes used for the stress simulation. ...

From these stress simulations, the following points have been clarified ... 

Table 10.6 Physical and mechanical properties used for the stress simulations. 

Numerical simulation of stress distribution In the process of stress simulation, the front, back and bottom of the model are fixed, and each of the left and right boundary of the model are exerted the horizontal compression in 5.2 MPa, then simulate the horizontal stress distribution station along the seam after the fold formation by using the creep model, the result of which is shown in figure 3. 

Results of 2D plane stress simulations are presented using the new procedure in this publication. The 2D plane stress modelling is performed because the core research topic for which the procedure is developed was aplane stress problem (Saharan Mitri, 2009). Also, plane stress modelling provides a convenient mean to undertake and understand fundamental studies for the dynamic rock fracturing processes. In past, the laboratory scale studies were undertaken using this plane stress concept (e. g., see Kutter Fairhurst, 1971 Foumey et al., 1993). The extension ofthe developed procedure for 3D problems is not difficult but will involve enormous computational resources. 

Natsuki Toshiaki, Endo Morinobu. (2004). Stress Simulation of Carbon Nanotubes in Tension and CompressioiL Carbon, 42, 2147-2151. 

Orru, S., Amoresano, A., Siciliano, R., Napoleoni, R., Finocchiaro, O., Datola, A., De Luca, E., Sima, A., Pucci, P. (2000) Structural analysis of modified forms of recombinant IFN-P produced under stress-simulating conditions. BfoZ. Chem., 381,1-11. 

Schlottermiiller, M., Lu, H., Roth, Y., HimmeL N., Schledjewski, R. and Mitschang, R, Thermal residual stress simulation in thermoplastic filament winding process . Journal of Thermoplastic Composite Materials, 2003,16(6), 497. 

Lu J P (1997) Elastic properties of carbon nanotubes and nanoropes, Phys Rev Lett 79 1297-1300. Natsuki T and Endo M (2004) Stress simulation of carbon nanotubes in tension and compression, Carbon 42 2147-2151. 

It is crucial to simulate the in-service stress distribution of the component as closely as possible during the proof test. This is not always feasible, for example in the case of thermal stresses simulated by mechanical ones. To gain sufficient safety, a large value of the proof stress can be chosen, although this has the disadvantage of producing unnecessary scrap parts. 

To date, results have been obtained for minimum-energy type simulations of elastic deformations of a nearest-neighbor face-centered cubic (fee) crystal of argon [20] with different inclusion shapes (cubic, orthorhombic, spherical, and biaxially ellipsoidal). On bisphenol-A-polycarbonate, elastic constant calculations were also performed [20] as finite deformation simulations to plastic unit events (see [21]). The first molecular dynamics results on a nearest-neighbor fee crystal of argon have also become available [42]. The consistency of the method with thermodynamics and statistical mechanics has been tested to a satisfactory extent [20] e.g., the calculations with different inclusion shapes all yield identical results the results are independent of the method employed to calculate the elastic properties of the system and its constituents (constant-strain and constant-stress simulations give practically identical values). 

As mentioned previously, the driver for undertaking this type of modeling is to optimize the mixing within the melter, to supply temperature boundary conditions to the melter walls for stress simulations, and to explore the relative importance of the different heat transfer mechanisms. 

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