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This paper deals with the periodic unfolding for sequences defined on one dimensional lattices in RN. In order to transfer the known results of the periodic unfolding in RNto lattices, the investigation of functions defined as interpolation on lattice nodes play the main role. The asymptotic behavior for sequences defined on periodic lattices with information until the first and until the second order derivatives are shown. In the end, a direct application of the results is given by homogenizing a 4th order Dirichlet problem defined on a periodic lattice.

We consider a perforated half-cylindrical thin shell and investigate the limit behavior when the period and the thickness simultaneously go to zero. By using the decomposition of shell displacements presented in Griso [JMPA89(2008) 199–223] we obtain a prioriestimates. With the unfolding and rescaling operator we transform the problem to a reference configuration. In the end this yields a homogenized limit problem for the shell.

We consider in this work general curved rods with a circular cross‐section of radius δ. Our aim is to study the asymptotic behaviour of such rods as δ→0, in the framework of the linear elasticity according to the unfolding method. It consists in giving some decompositions of the displacements of such rods, and then in passing to the limit in a fixed domain.