Homogenisation of periodic beams: limit of the expansions

Starting from the equations of two-dimensional elasticity, a double-scale a symptotic expansion method is applied to a thin structure which is periodic in the direction perpendicular to the thickness. Under the given loading a ll the terms of the displacement and stress expansions are determined These expansions have finite limits under some conditions depending on the numbe r of cells and the solutions of the cellular problems. Application examples show the contribution of higher-order terms in case the number of cells is small. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.