Calculation of the characteristics of thin elastic rods with a periodic structure

Abstract A transfer is made from the three-dimensional theory of elasticity in a thin rod to the problem of the theory of beams. The transfer differs from the problems of plates discussed in /1, 2/ (see also the references in /3/), in that the dimensions are reduced, during the passage to the limit, by two, i.e. from three (the dimensions of the initial problem in the theory of elasticity) to one (the dimensions of the limit problem in the theory of beams). In /1, 2/ the dimensions change from three to two. This leads to differences in the form of the asymptotic expansion, in the methods for studying it and in the appearance of new types of cellular problems.