Mathematical Analysis of Thin Plate Models

1. Front Matter

   Pages I-X

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2. Plate Models for Thin Structures

   • Philippe Destuynder, Michel Salaun

   Pages 1-27

3. Variational Formulations for Bending Plates

   • Philippe Destuynder, Michel Salaun

   Pages 29-104

4. Finite Element Approximations for Several Plate Models

   • Philippe Destuynder, Michel Salaun

   Pages 105-182

5. Numerical Tests for the Mixed Finite Element Schemes for Bending Plates

   • Philippe Destuynder, Michel Salaun

   Pages 183-205

6. A Numerical Model for Delamination of Composite Multilayered Plates

   • Philippe Destuynder, Michel Salaun

   Pages 207-234

7. Back Matter

   Pages 235-238

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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.

• Plaques
• delaminage
• elements-finis
• formulations variationnelles
• vectoriel et parallel
• algorithms
• calculus
• composite material
• Extension
• finite element method
• geometry
• kinematics
• mathematical analysis
• model
• modeling
• numerical model
• numerical simulation
• optimization
• simulation
• stability

• C. N. A. M. - I. A. T., St. Cyr-L’Ecole, France

  Philippe Destuynder, Michel Salaun

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