Application of homogenization method to justification of 1-D model for beam of periodic structure having initial stresses

In this paper a 1-D model of the beam theory is derived from the 3-D elasticity theory problem for a beam having initial stresses. We consider a thin inhomogeneous beam of periodic structure whose diameter and period are comparable in order (the classical approach cannot be applied). The transition from the 3-D elasticity theory problem to the I-D beam problem is made on the basis of a modified two-scale expansion homogenization method without any simplified assumptions. The obtained 1-D modes correspond to the model of the beam subjected to the axial force and beam subjected to moments. The obtained models are in agreement with the classical models for homogeneous cylindrical beams. ~) 1998 Elsevier Science Ltd. All rights reserved