The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulations

1. Front Matter

   Pages i-x

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2. Numerical Analysis of a Linear Thin Shell Model

   1. Front Matter

      Pages 1-4

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   2. The Continuous Problem

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 5-25

   3. The Discrete Problem

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 27-63

   4. Implementation

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 65-88

3. Application to Arch Dam Simulations

   1. Front Matter

      Pages 89-90

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   2. Geometrical Definition of the Dam

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 91-107

   3. Variational Formulation of the Arch Dam Problem

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 109-122

   4. Implementation — Presentation of Results

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 123-149

   5. Numerical Experiments

      • Michel Bernadou, Jean-Marie Boisserie

      Pages 150-166

4. Back Matter

   Pages 167-199

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~his Monograph has two objectives : to analyze a f inite e l e m en t m e th o d useful for solving a large class of t hi n shell prob l e ms, and to show in practice how to use this method to simulate an arch dam prob lem. The first objective is developed in Part I. We record the defi- tion of a general thin shell model corresponding to the W.T. KOlTER linear equations and we show the existence and the uniqueness for a solution. By using a co nform ing fi nite e l e m ent me t hod , we associate a family of discrete problems to the continuous problem ; prove the convergence of the method ; and obtain error estimates between exact and approximate solutions. We then describe the impl em enta t ion of some specific conforming methods. The second objective is developed in Part 2. It consists of applying these finite element methods in the case of a representative practical situation that is an arc h dam pro b le m. This kind of problem is still of great interest, since hydroelectric plants permit the rapid increase of electricity production during the day hours of heavy consumption. This regulation requires construction of new hydroelectric plants on suitable sites, as well as permanent control of existing dams that may be enlightened by numerical stress analysis .

• Finite
• calculus
• class
• construction
• control
• convergence
• eXist
• equation
• finite element method
• form
• implementation
• numerical analysis
• object
• presentation
• simulation

• INRIA, Le Chesnay Cedex, France

  Michel Bernadou

• E.D.F.-D.E.R., Chatou, France

  Jean-Marie Boisserie

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