Main Help → All Commands → FEA Boundary Conditions → Periodic
NairnFEA can do truly periodic simulations with optional extra degrees of freedom for periodic strains and rotations. The details on running periodic conditions on given on the OSUPDocs wiki. The command to set up periodic calculations in FEA us:
Periodic (dir),<(dof1),(value1)>,<(dof2),(value2)>
where
(dir)
defines the periodic direction. NairnFEA allows periodicity in the x
direction only, in the y
direction only, or in both the x
and y
directions. For axisymmetric problems, periodicity is allowed in the z
direction only.(dof1,value1)
and (dof2,value2)
optional pairs specify options to the periodic calculations. In periodic calculations, the displacements on the two edges must be related by a translation and a rotation or a translation and shear. If nothing is specified, the translation and rotation or shear are degrees of freedom in the problem. Alternatively, you can specify them with the for options for (dof1)
and (dof2)
:
Delta
: defines the translation or displacement jump between the two sides of the periodic direction (entered in length units). When applied, the average strain in the periodic direction is <ε> = Delta
/ΔL
, where L
is the length in the periodic direction.
Slope
: When periodic in only one direction, Slope
defines the rotation or relative slopes between the two sides of the periodic direction (dimensionless). For axisymmetric analyses, physical contraints require the slope to be zero. If you do not set it, it will automatically be set to zero for you.
Shear
: When periodic in both x
and y
directions, Shear
defines a component of average shear displacement. For (dir)
= x
, Shear
gives the x
-direction displacement jump in the y
direction of the specimen (dudy
). For #2
= y
, Shear
gives the y
-direction displacement jump in the x
direction of the specimen (dvdx
). The average shear strain is <γxy> = dudy
/Δy
+ dvdx
/Δx
, where Δx
and Δy
are the specimen lengths in those directions.
For periodicity to work, the edges of the specimen on the two ends of the periodic direction must be orthogonal to that direction, they must each have the same number of nodes, and the orthogonal coordinate (e.g., y
coordinate for x
periodicity, x
coordinate for y
periodicity, or r
coordinate for z
periodicity) of each node on one side must match the corresponding node on the other side.
Periodic
command is only allowed for FEA analyses.