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© 2014

Mathematical Methods for Elastic Plates

Book

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

  1. 1.Department of MathematicsThe University of TulsaTulsaUSA

About the authors

Christian Constanda, BS, PhD, DSc, is the Charles W. Oliphant Professor of Mathematical Sciences at the University of Tulsa, USA, Emeritus Professor of Mathematics at the University of Strathclyde, UK, and Chairman of the International Consortium on Integral Methods in Science and Engineering. He has authored, edited, and translated 25 mathematical books and has published over 135 research papers in scholarly journals.

Bibliographic information

  • Book Title Mathematical Methods for Elastic Plates
  • Authors Christian Constanda
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4471-6433-3
  • Softcover ISBN 978-1-4471-7265-9
  • eBook ISBN 978-1-4471-6434-0
  • Series ISSN 1439-7382
  • Series E-ISSN 2196-9922
  • Edition Number 1
  • Number of Pages X, 209
  • Number of Illustrations 12 b/w illustrations, 3 illustrations in colour
  • Topics Analysis
    Integral Equations
    Solid Mechanics
  • Buy this book on publisher's site
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Reviews

From the book reviews:

“This is a nice short and self-contained book on mathematical methods in the linear theory of plates. … The book is strongly recommended to those who are interested in mathematical problems of elasticity and applications of the theory of potentials in mathematical physics.” (Leonid P. Lebedev, zbMATH, Vol. 1301, 2015)