Introduction
Quite often industrial processes that need to be analyzed involve sections that repeat in a simple pattern and move through a process zone. A prominent example is a conveyor belt with regularly spaced packages, as illustrated schematically in Figure 1 and exemplified with a finite element mesh in Figure 2. Continuous forming operations such as metal rolling are also good examples because the deforming material can be broken up into an arbitrary number of identical sections.
For the sake of clarity we will use the conveyor belt example throughout this discussion to illustrate many of the concepts associated with the periodic media analysis technique. Figure 1 shows a conceptual decomposition of the conveyor belt; in reality, the belt is a continuous entity.
Conceptually, the overall model can be decomposed into blocks (topologically identical meshed structures) that are connected together and span the process zone. You create a part that defines a “building block” (the meshed structure that is repeated to model the entire periodic media) and then construct the whole model via a chain of appropriately positioned instances. The periodic media analysis technique provides a simple way to automatically connect these instances together at the front and back ends of adjacent blocks. This technique also provides a convenient way to define loads and boundary conditions that represent the physical system at the unconnected ends of the first and last blocks in the chain. The first block of the chain is referred to as the inlet, and the last block is referred to as the outlet. Finally, when the periodic media moves through the process zone, blocks from the outlet are automatically shuffled to the inlet. The blocks (meshed structures) defined with this technique can interact via contact with other modeling features that are not periodic in nature, such as the rollers depicted in Figure 1.
At the core of the periodic media analysis technique lies the concept of shuffling blocks from the outlet back to the inlet. A dedicated algorithm is used to detect when the inlet has moved too far into the process zone and to shuffle a block from the outlet directly to the inlet. The dashed arrow in Figure 1 illustrates the shuffling process. To ensure a smooth transition, the necessary nodal and element state data from the inlet block are stored at the beginning of the current step. When shuffling occurs, the stored nodal and element state data are mapped to the new inlet block and any inlet/outlet loads or boundary conditions are transferred to the newly exposed block ends.
Thus, the periodic media analysis technique offers a convenient way for an Eulerian-like view into the moving repetitive structure. For example, you may be interested in assessing the package dynamics on the belt at a location somewhere between the rollers in both transient and steady-state conditions. You define several blocks around that location, you define contact with the rollers as necessary, and you provide appropriate inlet and outlet loading conditions. The periodic media analysis technique provides a convenient and economical way to create and analyze this system. By re-using elements that have left the process zone via this shuffling process, you can avoid the large meshes at the inlet end required for purely Lagrangian simulations.