Mathematical analysis of thin plate models
The title of this book is not quite correct in so far as only one special method of solving plate problems is handled. The authors develop a finite element code which enables one to evaluate precisely what happens near free or loaded edges, and to have both triangles and quadrangles facilities with very low order polynomials. In the first chapter, the Kirchhoff-Love model and the Reissner-Mindlin-Naghdi-model are derived from the three-dimensional theory, using the Hellinger-Reissner mixed formulation. The goal of the next chapters is to give a description, a mathematical analysis and numerical results concerning mixed finite elements for plates. Chapter 2 gives several variational formulations of the plate model under special regard of boundary conditions. After a brief reminder of the finite element method (FEM) in chapter 3, the natural duality technique is used to construct a new kind of structural finite element. In the next chapter, the new elements are compared with QUAD 4, and vector and parallel optimization are used to deliver the best computational time. Finally, in chapter 5 the laminated plate theory is discussed and a computational model for studying delamination is presented together with an example including experiments. The comparison between numerical and test results is quite satisfying. This book is written by mathematicians and therefore contains a lot of lemmas and existence and uniqueness proofs which aggravates the study of the book for engineers. Nevertheless, it may be of interest for all scientists who solve plate problems by FEM.
scientific article; zbMATH DE number 921447