Plates and Junctions in Elastic Multi-Structures

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 Kármán equations. The second objective is to extend this analysis to the mathematical modeling 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. Interestingly, the limit problems found in this way are coupled, multi-dimensional, problems of a new type providing new instances of stiff problems. The book written by one of the leading experts internationally in the field of numerical methods applied to solid mechanics presents an up-to-date report on an active research topic, and will be a useful reference for applied mathematicians and engineers working with elastic multi-structures.