Abstract: Shapeable materials of interest are modeled with a rectangular mesh having N columns and M rows of substantially similar shell elements. The shapeable materials of interest are held in tension between a sink and a source. A column of fictitious elements is added to make the mesh wrapped-around continuous. The fictitious elements are marked as inactive, while other elements are marked as active. As the simulation moves on, the active elements are marched in the product producing direction of the machinery. When a pre-defined distance has traveled in the simulation the present invention performs the following: Activate inactive elements at the source; Copy all history data including stresses from the last column of active elements to newly activated elements; Deactivate the lead column of active elements at the sink; and Move the set of nodal boundary conditions to newly established boundary nodes at the sink and the source.