Finite Element Method Normal Procedure

Finite Element Method Normal Procedure

Finite Element Method Normal procedure 1. Make geometry (3D model) 3D CAD (Salome, freeCAD, etc) 2. Discretize (Make Mesh) Mesh generator (Netgen, gmsh, etc) 3. Solve problem (FEM) Solver (Elmer, CodeAster, CalculiX OpenFOAM, etc) 4. Display result Viewer (Paraview) Salome-meca Finite Element Method Normal procedure 1. Make geometry (3D model) 3D CAD (Salome, freeCAD, etc) freeCAD In this lecture, freeCAD is used as a 3D-modeller. 2. DiscretizeThe other (Make procedures Mesh) are done in Salome-meca. Mesh generator (Netgen, gmsh, etc) 3. Solve problem (FEM) Solver (Elmer, CodeAster, CalculiX OpenFOAM, etc) 4. Display result Viewer (Paraview) Salome-meca Free-software Free ≠ without money Free = freedom (“OpenSource” is similar but not a same meaning) 1. Execute the program for any purpose 2. Modify the program for your needs (source code is required) 3. Distribute the copy of program to help neighbors 4. Improve the program and distribute it (source code is required) Many softwares are distributed as free-software (you can do almost all works using only free-softwares) *GNU/Linux … Operating system *gcc … compilers for C, C++, Fortran, etc. *GIMP … Image manipulation (like as Photoshop) GNU softwares *GNU Octave … like as MatLab *…. *LibreOffice … Office software *gnuplot … draw graph *scilab … like as MatLab Mode-matched resonator X- and Y-resonance frequencies are identical (X and Y oscillations are degenerated) Symmetricity is important C2V symmetry Dyad axis Mirror plane A. A. Trusov et al., Sens. Actuators A, 165, 26 - 34, 2011. M. F. Zaman et al.,J. Microelectromech. Syst, 17, 1526-1536, 2008. X- and Y-axis are not identical ↔ X and Y frequencies are (generally) not matched → to match the frequency, careful design is required. ↔ Damping factors of both axis are (generally) not matched Required symmetricity C4V (or higher symmetry) Axisymmetric Tetragonal axis Mirror plane S. Zotov et al., J. Microelectromech. Syst, 21, 398-405, 2012. J. Y. Cho and K. Najafi, Proc. MEMS 2015, Jan 2015, 821-824. Y Y 1 2 3 1 … Equivalent structure 4 2 3 4 90° rotation X X → X and Y oscillations are intrinsically degenerated Ring resonator Definition of axis is different from the normal spring-mass resonator “X” oscillation “Y” oscillation Required symmetry for ring resonator 1 1 45° rotation “Y” “X” In summary, at least the symmetry below is required 22.5° 1 Mirror symmetry (Rotational symmetry : 45°) Symmetric model for FEM Even if the 3D model with required symmetry is build, generated mesh does not necessarily has a same symmetry. → This mesh assymmetry resolves the degeneracy. → Meshwise symmetry is mandatory ! Geometric model Mesh Symmetric Symmetric Make symmetric mesh Geometric model Geometric model Mirror planes Symmetric Generate mesh Mirror copy Final mesh Symmetric !.

View Full Text

Details

  • File Type
    pdf
  • Upload Time
    -
  • Content Languages
    English
  • Upload User
    Anonymous/Not logged-in
  • File Pages
    10 Page
  • File Size
    -

Download

Channel Download Status
Express Download Enable

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

  • Not to be reproduced or distributed without explicit permission.
  • Not used for commercial purposes outside of approved use cases.
  • Not used to infringe on the rights of the original creators.
  • If you believe any content infringes your copyright, please contact us immediately.

Support

For help with questions, suggestions, or problems, please contact us