Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis

The first objective of this monograph is to show that the method of asymptotic expansions, with the thickness as the parameter, provides a very effective tool for justifying two-dimensional plate theories, in both the nonlinear and the linear case. Without resorting to any a priori assumption of a geometrical or mechanical nature, it is shown that, the displacements and stresses corresponding to the leading term of the expansion of the 3-dimensional solution do indeed solve the classical equations of 2-dimensional nonlinear plate theories such as the von Karman equations. The second objective is to extend this analysis to the mathematical modelling of junctions in elastic multi-structures, e.g. typically a structure comprising a "3-dimensional" part, and a "2-dimensional" part. These can be folded plates, H-shaped beams, plates with stiffeners, plates held by rods as in a solar panel, etc. A similar asymptotic analysis provides a systematic way of finding the models for such multi-structures, as the "thin" part approach.