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!
 Simplify the definition of isostatic boundary conditions
 Reduce the post-processing effort (simpler to
visualize)
 Show to everybody that you master FE modelling ;-)
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)
Symmetry: example
U normal = 0
UR inplane = 0
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

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.
Isostatic BC: Example of 3-2-1 rule
U1=U2=U3=0
U2=0
Using the 3-2-1 trick, we introduce
isostatic supports which do not
overconstrain the system
F1
U2=U3=0
F2
Loads F1 + F2 = 0
But system cannot be solved because of rigid body motions
Loading: standard type of loads

Pressure:
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Surface tractions:

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Units: force / area
Can be freely oriented: define
Gravity:

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Units: force / area
Is always NORMAL to the surface
Positive towards the Inside
Non uniform distribution with analytical fields function of
coordinates
Units: L/T^2
Defines the accelaration vector of gravity loads.
You must define a Density in material properties
Acceleration, Centrifugal loads …
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