Thermal Problem For Gridworks

  • Doina Cioranescu
  • Jeannine Saint Jean Paulin
Part of the Applied Mathematical Sciences book series (AMS, volume 136)


We now consider a particular case of three-dimensional lattice structures, the gridworks (or networks) that consist in regular arrays of thin wires.

The specific feature of such structures is that the periodicity occurs only in two directions. In the third direction their dimension e, in fact their thickness when considering these structures as thin plates, is small (see Figures 3.1, 3.2, 3.3). Consequently, in the asymptotic description of these structures we have this new small parameter to take into consideration, the other two being, of course, the period ε of the wires and their cross-section δ. In this chapter we consider thermal problems, and our aim is to study what happens when these three parameters tend to zero. Let us mention that in Chapter 4 we will study the linearized elasticity system for these structures.


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Copyright information

© Springer-Verlag New York, Inc. 1999

Authors and Affiliations

  • Doina Cioranescu
    • 1
  • Jeannine Saint Jean Paulin
    • 2
  1. 1.Laboratoire d’Analyse NumériqueUniversité Paris VI et CNRSParis Cedex 05France
  2. 2.Départment de MathèmatiqueUniversité de MetzMetz Cedex 01France

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