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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.

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 <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="italic">r</span> and Kernels, Particular Solutions and Tangential Derivatives and Kernels, Particular Solutions and Tangential Derivatives
    1. A.1 Derivatives of <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="italic">r</span>
    2. A.2 Derivatives of kernels
    3. A.3 Particular solutions of the Poisson equation (3.57)
    4. A.4 Tangential derivatives <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780124167391099893/si98_e.gif" alt="si98_e"></img>, , <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780124167391099893/si99_e.gif" alt="si99_e"></img>, , <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780124167391099893/si100_e.gif" alt="si100_e"></img> and their different approximations 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