Tetrahedral mesh modeling

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. 

The NRI group selected very simple input model since the ISP-43 represented our first larger application of the FLUENT 5 code and mainly of the GAMBIT pre-processor. After several attempts we decided not to model the flaps in the lower part of the downcomer, the perforated bottom of the core barrel, lower support plate, and the heater rods, and spent the capacity of the computer on the rest of the domain. Also the outlet plane was situated at the position of the support plate, quite near the downcomer outlet. Hexahedral control volumes were used throughout the domain with the exception of the region of cold leg nozzles, where unstructured tetrahedral mesh was generated. 

The latest wrist implant, ReMotion produced by Small Bone Innovations was used in the simulation [9]. The model was constructed using a CAD software, Solidwork 2009. The 3D models were turned into surface triangular elements and positioned onto the Rheumatoid Arthritis model. Surgical preparation of the bone was carried out prior to insertion of the implant. The implants were then placed in their respective bone model and then converted into solid tetrahedral mesh. 

Meshing for 3-D model, generate tetrahedral mesh (in steps Extremely coarse, coarse, normal, and so on, and investigate changes in results, if any)... 

FIG. C-8 Tetrahedral mesh used in IcePak 2.2 to model a complex fan/heat sink with radial fins. (Source Fluent Inc.)... 

The next adaptation of this product, Version 2.2, was intended to deliver more flexible model building capability, with tetrahedral as well as hexahedral meshes supported. Tetrahedral meshes can handle extremely complex geometries. The combination of automated hex and tet meshing gives IcePak users better strategies when confronted with difficult modeling. 

In order to reduce the computational effort, without losing correspondence with the experimental counterparts, a slice of the specimen, 1.6 mm thick (1/4 of the real specimen thickness), is modelled. The out of plane displacements along the surfaces of the plate are constrained to avoid buckling. The computational mesh comprises 65365 nodes and 32482 10-node quadratic tetrahedrons. Fig. 5. The core is modeled using a uniform minimum mesh size of 0.8 mm the mesh coarsens in the steel layer, with one tetrahedral element aeross the thickness. The cohesive elements are adaptively inserted along previously eoherent interfaces when the local effective stress attains a eritieal value [6]. 

A number of commercially available computational fluid dynamics (CFD) models could be used for the prediction of squat. At the core of any CFD problem is a computational grid or mesh where the solution is divided into thousands of elements. These elements are usually 2D quadrilaterals or triangles and three-dimensional (3D) hexahedral, tetrahedral, or prisms. Mathematical equations are solved for each element by the numerical model. For hydrodynamics the Navier-Stokes equations (NSEs) can be solved to include viscosity and turbulence. The NSEs provide detailed prediction (vortices) of the flow field, but require very thin meshes, high central processing unit (CPU) time, and memory storage. Its resolution is also quite difficult with numerical instabilities. Examples of commercial CFD models include Fluent and Fidap. 

As shown on Fig. 26.24, the system starts from the rest position of the ship with a sinkage equal to its draft T. A 3D mesh of Unite elements (tetrahedral) is constructed with the ship features (i.e., Lpp, B, T, and Cb) and the fluid domain (i.e., h, channel shape, boundary conditions, etc.). A first run of the model is done with null velocity of the ship. The equilibrium model is then calibrated with the ship weight (VFb) and the position of the center of gravity (Aq, Tg), as all hull nodes must have no displacements with the hydrodynamic model results. Once these ship features are set up, the system is ready to start. A small ship velocity AV is imposed in the hydrodynamic model, which gives hull pressure to the equilibrium model. The latter displaces the hull, so the mesh has to be updated by the third model. The system checks the hull displacement. If it is negligible, the ship velocity is increased by AV or the same velocity is retained and a new cycle is begun. The system stops when the velocity has reached the velocity specified by the user or if the ship has grounded. 

All the analysis models have been meshed in tetrahedral finite elements, C3D4, accounting for a total of 243032 elements and 49154 nodes. 

The boundary condition was fixed at the cross sections of the regional mandible. Occlusive forces of 150N were applied at the buccal cusp along a 45-degree inclination and center fossa parallel to a longitudinal axis of the premolar model (Fig.2) [5-6]. The nodes and elements of the FE models in the split-shank, core crown and non split-shank post were 41435 and 30580, 33287 and 23925 as well as 49432 and 42086 respectively. The tetrahedral element of 10 nodes was utilized for meshing in this study. 

A commercially available FEA software (CosmosWorks 2009, Dassault Systemes, USA) was used for static analysis of the model. The models were meshed using 0.5 mm parabolic tetrahedral elements with an average number of 547500 elements and 759150 nodes per model. A 50 N static load was applied UnguaUy to the middle of lingual surface of the crown at 70° to the occlusal plan (Fig. 1) to simulate masticatory force. In order to maxilla has no movement, the models were fixed on the outer surface of the maxilla with no rotation or translation allowed. 

The generation of the finite element model and analysis were carried out using CosmosWorks 2009 (Dassault Systemes, USA). The model was meshed using 1.0 mm parabolic tetrahedral elements, consists of 821439 elements and 1170674 nodes. To validate the model, a 10 Nm torque applied to the model with IVD to simulate flexion motion and range of motion (ROM) was calculated. A 10 Nm torque and 150 N vertical axial static loads were applied to the superior surface of the L2 to simulate flexion, and extension. All of the materials were assumed as homogenous, isotropic and linear elastic. 

A concave lens cavity model with heater and cooling chaimels as shown in Fig.l were utilized for the simulation and experiment. The heater was put in the vicinity of the lens center, and the cooling chaimels were put around the cavity. Fig.2 is the cut view of the meshed cavity and coolant chaimel. The lens part is meshed by the hexahedral element, and the coolant chaimels are meshed via the combination of prismatic element in the axial direction and the tetrahedral element in the juncture region. The mold base is meshed by the tetrahedral element except in the region adjacent to the coolant surface, where only pyramid element can be used. 

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