OS-E: 0705 Periodic Boundary Conditions

Periodic Boundary Conditions via PERBC can be used to match results from one part of the structure to another. This allows using a truncated model to reduce runtime if there is sufficient symmetry in the original model.

RELOC entry is used to provide mapping for grids that require to be matched on both sides of the truncated structure.

Model Files

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

Model 1, which is the full model, consists of an annular ring and Model 2, which is the truncated model, is a quarter ring. The operational loading involves a single linear static subcase with symmetric loading applied radially outward at each node of the inner circle. This loading is similarly adjusted and applied on the truncated model.

FE Model
2D Elements: CQUAD4

The linear material properties are:

MAT1
Young’s Modulus: 2.1E5
Poisson's Ratio: 0.3

PERBC entry is used to match results from one side to another. RELOC is used to only provide the mapping for the grids that need to be matched on both sides of the truncated structure.

If RELOC(ROTATE) is specified, then all matching grids on both sides of the truncated structure should have a cylindrical coordinate system assigned with the Z-axis matching the axis used for RELOC rotation. The origin of the cylindrical system should coincide with the center of the ring.

In the current example, a grid set for one end of the truncated ring is created. This grid set is referenced on the GSID field of the PERBC entry. A corresponding tolerance is specified via the TOL field depending on model quality. A RELOC entry is defined purely to map the locations of the grids from one end to the other.

The TYPE field is set to ROTATE mapping is based on rotation. The GID1 on RELOC entry references the center of the ring (which is also the center of the local cylindrical system).

The ang_x and ang_y fields are set to 0.0 and ang_z is set to 90.0 on the RELOC entry.

In this way, RELOC will rotate the grids on one end of the truncated ring to the other end (within the specified tolerance).

Tip: Ensure that the mesh is sufficiently symmetric (this symmetry check is also required to generate equivalent results with the full model).

The RELOC entry should be referenced on the PERBC entry on the RLID field.

If the mesh is symmetric and the rotation angle is correctly specified, then RELOC will accurately find the grids at the other end of the truncated ring.

Full model loading on the grids at the corners of the truncated ring are proportionally reduced (typically halved for shells) since the force that was initially applied on multiple elements is being applied to one.

Results

From the results in Figure 2, the displacement contour and results match between the full model and the quarter ring.