Joël Cugnoni, LMAF/EPFL, 2011

 A FE model has a symmetry if and only if geometry, materials and loading all have the same symmetry !!  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 modeling ;-)

 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)

U normal = 0 UR inplane = 0 Symmetry plane

 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 appropriate isostatic BC  90 % of the « the solver does not want to converge » problems come from rigid body motions !! => Always double check your boundary conditions F F This system is in static equilibrium, but is not determined because it has 6 possible rigid body motions

 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 2 nd point, block 2 displacements to prevent 2 rotations ◦ On a 3rd point, block 1 displacement to block the last rotation. F F

U1=U2=U3=0 Loads F1 + F2 = 0 But system cannot be solved because of rigid body motions F1 F2 U2=U3=0 U2=0 Using the trick, we introduce isostatic supports which do not overconstrain the system

 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 ◦ Oriented stress vector; can be freely oriented;  Gravity: ◦ Units: L/T^2 ◦ Defines the accelaration vector of gravity loads. ◦ You must define a Density in material properties  Acceleration, Centrifugal loads …

 Demo of Rod FEA ◦ Use partitions to create loading surfaces ◦ Use surface tractions ◦ Show rigid body motion = solver problem ◦ Use rule to set isostatic BC  Video tutorial BC-Tutorial: ◦ Use symmetries ◦ Use cylindrical coordinate systems to apply BC ◦ Apply non-uniform load distributions