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Boundary Integral Equation Methods and Numerical Solutions

Thin Plates on an Elastic Foundation

  • Christian Constanda
  • Dale Doty
  • William Hamill

Part of the Developments in Mathematics book series (DEVM, volume 35)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Christian Constanda, Dale Doty, William Hamill
    Pages 1-8
  3. Christian Constanda, Dale Doty, William Hamill
    Pages 9-24
  4. Christian Constanda, Dale Doty, William Hamill
    Pages 25-33
  5. Christian Constanda, Dale Doty, William Hamill
    Pages 35-91
  6. Christian Constanda, Dale Doty, William Hamill
    Pages 93-228
  7. Back Matter
    Pages 229-232

About this book

Introduction

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique.  The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients.  The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy.

The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems. 

Keywords

Dirichlet boundary value problems Galerkin technique Neumann boundary value problems Robin boundary value problems boundary integral equation methods mechanics of deformable solids piecewise constant spline Neumann problem Robin problem piecewise cubic spline

Authors and affiliations

  • Christian Constanda
    • 1
  • Dale Doty
    • 2
  • William Hamill
    • 3
  1. 1.Department of MathematicsUniversity of TulsaTulsaUSA
  2. 2.The University of TulsaTulsaUSA
  3. 3.Department of MathematicsThe University of TulsaTulsaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26309-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-26307-6
  • Online ISBN 978-3-319-26309-0
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • Buy this book on publisher's site