Mathematical Methods for Elastic Plates

  • Christian Constanda
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Christian Constanda
    Pages 1-36
  3. Christian Constanda
    Pages 37-66
  4. Christian Constanda
    Pages 67-81
  5. Christian Constanda
    Pages 83-101
  6. Christian Constanda
    Pages 103-129
  7. Christian Constanda
    Pages 131-145
  8. Christian Constanda
    Pages 147-162
  9. Christian Constanda
    Pages 163-201
  10. Back Matter
    Pages 203-209

About this book

Introduction

Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one.
 
The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.
 
The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials.
 
The last chapter develops a generalized Fourier series method closely connected with the structure of the system, which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure.
 
The presentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students with a basic knowledge of advanced calculus.

Keywords

Boundary Integral Equation Methods Complex Potentials Elastic Plates Generalized Fourier Series Layer Potentials

Authors and affiliations

  • Christian Constanda
    • 1
  1. 1.Department of MathematicsThe University of TulsaTulsaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-6434-0
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-6433-3
  • Online ISBN 978-1-4471-6434-0
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book