1 / 9

Symmetry & boundary conditions

Symmetry & boundary conditions. Joël Cugnoni, LMAF/EPFL, 2009. Using symmetries in FE models. A FE model is symmetric if and only if geometry , materials and loading are symmetric !! Symmetries help to: Reduce the model size => finer meshes => better accuracy!

seanna
Download Presentation

Symmetry & boundary conditions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Symmetry & boundary conditions Joël Cugnoni, LMAF/EPFL, 2009

  2. Using symmetries in FE models • A FE model is symmetric if and only if geometry, materials and loading are symmetric !! • Symmetries help to: • Reduce the model size => finer meshes => better accuracy! • Simplify the definition of isostatic boundary conditions • Reduce the post-processing effort (simpler to visualize) • Show to everybody that you master FE modelling ;-)

  3. Using symmetries in FE models • To use symmetries: • Extract the smallest possible geometric region with « CAD » cut operations (can have multiple symmetries!!) • Model the symmetry planes as imposed displacement / rotations: • No displacement perpendicular to symm. plane • No rotations (shell / beams only) along 2 axis in the symm. Plane • Example: X-symmetry = symmetry wrt a plane of normal along X => U1 = UR2 = UR3 =0 ALWAYS USE SYMMETRIES WHENEVER POSSIBLE !!! (This will be check at the exams)

  4. Symmetry: example U normal = 0 UR inplane = 0 Symmetry plane

  5. Rigid body motions • In statics, rigid body motions are responsible for singular stiffness matrices => no solution • In statics, YOU MUST CONSTRAIN all 6 rigid body motions with suitable boundary conditions. • If you don’t want to introduce additionnal stresses: use isostatic BC • 90 % of the « the solver does not want to converge » problems come from rigid body motions !! => Always double check your boundary conditions

  6. The 3-2-1 trick • Is a simple trick to set isostatic boundary conditions: • Select 3 points (forming a plane) • On a 1st point: block 3 displacements => all translation are constrained • On a 2nd point, block 2 displacements to prevent 2 rotations • On a 3rd point, block 1 displacement to block the last rotation.

  7. Isostatic BC: Example of 3-2-1 rule U1=U2=U3=0 Using the 3-2-1 trick, we introduce isostatic supports which do not overconstrain the system F1 U2=0 U2=U3=0 F2 Loads F1 + F2 = 0 But system cannot be solved because of rigid body motions

  8. Loading: standard type of loads • Pressure: • Units: force / area • Is always NORMAL to the surface • Positive towards the Inside • Non uniform distribution with analytical fields function of coordinates • Surface tractions: • Units: force / area • Can be freely oriented: define • Gravity: • Units: L/T^2 • Defines the accelaration vector of gravity loads. • You must define a Density in material properties • Acceleration, Centrifugal loads …

  9. Demo & tutorials • Demo of Rod FEA • Use partitions to create loading surfaces • Use surface tractions • Show rigid body motion = solver problem • Use 3-2-1 rule to set isostatic BC • Video tutorial BC-Tutorial: • Use symmetries • Use cylindrical coordinate systems to apply BC • Apply non-uniform load distributions

More Related