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The Boundary Element Method for Plate Analysis

Book Description

Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design.

Aiming to fill in the knowledge gaps left by contributed volumes on the topic and increase the accessibility of the extensive journal literature covering BEM applied to plates, author John T. Katsikadelis draws heavily on his pioneering work in the field to provide a complete introduction to theory and application.

Beginning with a chapter of preliminary mathematical background to make the book a self-contained resource, Katsikadelis moves on to cover the application of BEM to basic thin plate problems and more advanced problems. Each chapter contains several examples described in detail and closes with problems to solve. Presenting the BEM as an efficient computational method for practical plate analysis and design, Boundary Element Method for Plate Analysis is a valuable reference for researchers, students and engineers working with BEM and plate challenges within mechanical, civil, aerospace and marine engineering.

  • One of the first resources dedicated to boundary element analysis of plates, offering a systematic and accessible introductory to theory and application
  • Authored by a leading figure in the field whose pioneering work has led to the development of BEM as an efficient computational method for practical plate analysis and design
  • Includes mathematical background, examples and problems in one self-contained resource

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Foreword
  7. Preface
  8. Chapter one: Preliminary Mathematical Knowledge
    1. Abstract
    2. 1.1 Introduction
    3. 1.2 Gauss-green theorem
    4. 1.3 Divergence theorem of gauss
    5. 1.4 Green’s second identity
    6. 1.5 Adjoint operator
    7. 1.6 Dirac delta function
    8. 1.7 Calculus of variations; Euler-Lagrange equation
    9. Problems
  9. Chapter two: BEM for Plate Bending Analysis
    1. Abstract
    2. 2.1 Introduction
    3. 2.2 Thin plate theory
    4. 2.3 Direct BEM for the plate equation
    5. 2.4 Numerical solution of the boundary integral equations
    6. 2.5 PLBECON Program for solving the plate equation with constant boundary elements
    7. 2.6 Examples
    8. Problems
  10. Chapter three: BEM for Other Plate Problems
    1. Abstract
    2. 3.1 Introduction
    3. 3.2 Principle of the analog equation
    4. 3.3 Plate bending under combined transverse and membrane loads; buckling
    5. 3.4 Plates on elastic foundation
    6. 3.5 Large deflections of thin plates
    7. 3.6 Plates with variable thickness
    8. 3.7 Thick plates
    9. 3.8 Anisotropic plates
    10. 3.9 Thick anisotropic plates
    11. Problems
  11. Chapter Four: BEM for Dynamic Analysis of Plates
    1. Abstract
    2. 4.1 Direct BEM for the dynamic plate problem
    3. 4.2 AEM for the dynamic plate problem
    4. 4.3 Vibrations of thin anisotropic plates
    5. 4.4 Viscoelastic plates
    6. Problems
  12. Chapter five: BEM for Large Deflection Analysis of Membranes
    1. Abstract
    2. 5.1 Introduction
    3. 5.2 Static analysis of elastic membranes
    4. 5.3 Dynamic analysis of elastic membranes
    5. 5.4 Viscoelastic membranes
    6. Problems
  13. Appendix A: Derivatives of r and Kernels, Particular Solutions and Tangential Derivatives
    1. A.1 Derivatives of r
    2. A.2 Derivatives of kernels
    3. A.3 Particular solutions of the Poisson equation (3.57)
    4. A.4 Tangential derivatives , , and their different approximations
  14. Appendix B: Gauss Integration
    1. B.1 Gauss integration of a regular function
    2. B.2 Integrals with a logarithmic singularity
    3. B.3 Double integrals of a regular function
  15. Appendix C: Numerical Integration of the Equations of Motion
    1. C.1 Introduction
    2. C.2 Linear systems
    3. C.3 Nonlinear equations of motion
    4. C.4 Variable coefficients
  16. Index