Symmetry & boundary conditions

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