Mathematical Analysis of Thin Plate Models / Edition 1

by Philippe Destuynder, Michel Salaun

Overview

Shells and plates have been widely studied by engineers during the last fifty years. As a matter of fact an important number of papers have been based on analytical calculations. More recently numerical simulations have been extensively used. for instance for large displacement analysis. for shape optimization or even -in linear analysis -for composite material understanding. But all these works lie on a choice of a finite element scheme which contains usually three kinds of approximations: 1. a plate or shell mndel including smnll parameters associated to the thickness, 2. an approximntion of the geometry (the medium sUrface of a shell and its boundary), 3. afinite element scheme in order to solve the mndel chosen. VI Obviously the conclusions that we can draw are very much depending on the quality of the three previous choices. For instance composite laminated plates with damage like a delamination is still an open problem even if interesting papers have already been published and based on numerical simulation using existing fmite element and even plate models. • In our opinion the understanding of plate modelling is still an area of interest. Furthermore the links between the various models have to be handled with care. The certainly best understood model is the Kirchhoff-Love model which was completely justified by P. O. Ciarlet and Ph. Destuynder in linear analysis using asymptotic method. But the conclusion is not so clear as far as large displacements are to be taken into account.

Product Details

ISBN-13:	9783540611677
Publisher:	Springer Berlin Heidelberg
Publication date:	08/29/1996
Series:	Math�matiques et Applications , #24
Edition description:	1996
Pages:	236
Product dimensions:	6.14(w) x 9.61(h) x 0.02(d)

Table of Contents

I — Plate models for thin structures.- I.0 — A short description of the chapter.- I.1 — The three dimensionnal elastic-model.- I.2 — The Kirchhoff-Love assumption.- I.3 — The Kirchhof f-Love plate model.- I.4 — The Naghdi model revisited using mixed variational formulation.- I.5 — About the rest of the book.- References of Chapter I.- II — Variational formulations for bending plates.- II.0 — A brief summary of the chapter.- II. 1 — Why a mixed formulation for plates.- II.2 — The primal variational formulation for Kirchhoff-Love model.- II.3 — The Reissner-Mindlin-Naghdi model for plates.- II.4 — Natural duality techniques for the bending plate model.- II.5 — A comparison between the mixed method and the one of section II.2.4.- References of Chapter II.- III — Finite element approximations for several plate models.- III.0 — A summary of the chapter.- III. 1 — Basic results in finite element approximation.- III.2 — C1 elements.- III.3 — Primal finite element methods for bending plates.- III.4 — The penalty-duality finite element method for the bending plate model.- III.5 — Numerical approximation of the mixed formulation for a bending plate.- References of Chapter III.- IV — Numerical tests for the mixed finite element schemes.- IV.0 — A brief description of the chapter.- IV. 1 — Precision tests for the mixed formulation.- IV.2 Vectorial and parallel algorithms for mixed elements.- IV.3 — Concluding remarks.- References of Chapter IV.- V — A Numerical model for delamination of composite plates.- V.O — A brief description of the chapter.- V. 1 — What is delamination of thin multilayered plates.- V.2 — The three-dimensional multilayered composite plate model with delamination.- V.3 — A plate model for largedelamination.- V.4 — The three-dimensional energy release rate.- V.5 — The mechanical example and the numerical method.- V.6 — Concluding remarks.- References of Chapter V.