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.
- ISBN10 3540529179
- ISBN13 9783540529170
- Publish Date 8 November 1990 (first published 1 November 1990)
- Publish Status Out of Print
- Out of Print 11 November 2010
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Format Paperback
- Pages 215
- Language English