On Flat Thin Elastic Rods with Rapidly Varying Periodic Characteristics

A thin elastic rod is considered on a plane. The free shape of the rod is described by a periodic curve. It is shown that, under constant loads, its equilibrium shape tends to the equilibrium shape of a thin rectilinear rod when the frequency of the function describing the free shape increases infinitely. The problem under study is solved on the basis of modeling the three-dimensional shapes of circular DNA molecules by a thin rectilinear elastic rod.