Homogenization of Reticulated Structures

Doina Cioranescu Jeannine Saint Jean Paulin, Ute Rosenbaum

This book presents recent works on lattice type structure. Its aim is to give continuous simple models for thin reticulated structures which may have a very complex pattern. For this reason, the authors treat partial differential equations depending on several small parameters, and give the asymptotic behavior with respect to these parameters. Attention has been paid to mathematical rigor, convergence results and error estimates. Chapter 1 gives an introduction to homogenization methods in perforated domains. Chapter 2 offers the main ideas to study thin reticulated structures. Chapters 3 and 4 are dedicated to the study of networks in thermal and elasticity problems. Chapter 5 and 6 treat similar problems to those in Chapter 3 and 4, but in this instance, the structure is thin and tall, tower-like.