On Flat Thin Elastic Rods with Rapidly Varying Periodic Characteristics / E.I. Kugushev and D.I. Sabitov // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 4. P. 42-46 [Moscow Univ. Mech. Bulletin. Vol. 64, No 4, 2009. P. 81-85.]
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.
Key words: thin elastic rods, weak convergence, spatial DNA forms.