Finite Element Analysis Boundary Condition for Simulating Symmetry:

 

Many structures have one or more planes of symmetry. It is possible to take advantage
of this in FEA, and model just one portion of the structure. Through various devices it
is possible to analyze structures with a plane of symmetry but subject to non-symmetric
loads. Such approaches are used to reduce modelling and computational effort.

In engineering applications, the most commonly encountered types of symmetry are
reflective symmetry, rotational symmetry and inversion symmetry as shown in Figure

In engineering problems the characterization of symmetry requires not only geometrical
symmetry, but also symmetry with respect to material properties and restraints.

When only part of a symmetric structure is modelled, the symmetric or anti symmetric
boundary conditions must be applied at artificial boundaries introduced because of
symmetry. If the y-z plane is the plane of symmetry, and Ux, Uy, Uz, and Rx, Ry, Rz
are assumed as the x, y and z components of displacement and rotation respectively,
the following boundary conditions have to be applied to the nodes on the plane of
symmetry or anti symmetry:

Ux = Ry = Rz = 0 - for symmetry

Rx = Uy = Uz = 0 - for antisymmetry