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Symmetry & boundary conditions

Symmetry & boundary conditions. Joël Cugnoni , LMAF/EPFL, 2011. Using symmetries in FE models. A FE model has a symmetry if and only if geometry , materials and loading all have the same symmetry !! Symmetries help to:

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Symmetry & boundary conditions

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  1. Symmetry & boundary conditions Joël Cugnoni, LMAF/EPFL, 2011

  2. Using symmetries in FE models • A FE model has a symmetryif and only if geometry, materials and loading all have the samesymmetry!! • Symmetries help to: • Reduce the model size => finermeshes => betteraccuracy! • Simplify the definition of isostaticboundary conditions • Reduce the post-processing effort (simpler to visualize) • Show to everybodythatyou master FE modeling;-)

  3. Using symmetries in FE models • To use symmetries: • Extract the smallest possible geometricregionwith « CAD » cutoperations (can have multiple symmetries!!) • Model the symmetry planes as imposeddisplacement / rotations: • No displacementperpendicular to symm. plane • No rotations (shell / beamsonly) along 2 axis in the symm. Plane • Example: X-symmetry = symmetrywrt 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 singularstiffness matrices => no solution • In statics, YOU MUST CONSTRAINall 6 rigid body motions withsuitableboundary conditions. • If youdon’twant to introduceadditionnal stresses: use appropriateisostatic BC • 90 % of the « the solverdoes not want to converge » problems come fromrigid body motions !! => Always double check yourboundary conditions F This system is in staticequilibrium, but is not determinedbecauseit has 6 possible rigid body motions F

  6. The 3-2-1 trick • Is a simple trick to set isostaticboundary 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. F F

  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 alwaysNORMAL to the surface • Positivetowards the Inside • Non uniform distribution withanalyticalfieldsfunction of coordinates • Surface tractions: • Units: force / area • Oriented stress vector; canbefreelyoriented; • Gravity: • Units: L/T^2 • Defines the accelarationvector of gravityloads. • You must define a Density in materialproperties • Acceleration, Centrifugalloads …

  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

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