Homogenization of Kirchhoff plates joined by rivets which are modeled by the Sobolev point conditions

Two Kirchhoff plates, which are described by Neumann problems for biharmonic equations, overlap along a thin strip. In the interior of the strip, the plates are connected by rivets, which are modeled by the Sobolev point transmission conditions. By taking the boundary layer phenomenon into account, homogenization with respect to a small parameter (the relative period of the distribution of rivets) is done, and transmission conditions are obtained on the common edge of two touching plates (in the limiting case, overlapping disappears). Differences are found between a single row and multiple row riveting that appear in different types of limiting transmission conditions, and the reasons are shown for the preference of double row riveting in practical engineering. Several related unsolved problems are formulated.