Introduction to Boundary Elements Theory and Applications

Introduction to Boundary Elements Theory and Applications / by Friedel Hartmann.

to Boundary Elements Theory and Applications With 194 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Dr.-Ing. Friedel Hartmann University of Dortmund Department of Civil Engineering 4600 Dortmund 50 FRG ISBN-13: 978-3-642-48875-7 e-ISBN-13: 978-3-642-48873-3 001: 10....

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Bibliographic Details
Main Author: Hartmann, Friedel (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.
Edition:1st ed. 1989.
Series:Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Mechanics.
Mechanics, Applied.
Mechanical engineering.
Civil engineering.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Fundamentals
  • 1.1 Notation
  • 1.2 The basic idea
  • 1.3 Influence functions
  • 1.4 Coupling on the boundary
  • 1.5 Boundary elements
  • 1.6 Conforming and non-conforming solutions
  • 1.7 The interpretation of the solution
  • 1.8 Symmetric formulations
  • 1.9 The integral operators and their shifts
  • 1.10 Galerkin, collocation and least square
  • 1.11 Potentials
  • 1.12 The indirect method
  • 1.13 Weighted residuals
  • 1.14 Influence functions and finite elements
  • 1.15 The scale
  • 1.16 Trefftz’s method
  • 1.17 Construction of fundamental solutions
  • 1.18 Mixed methods
  • 1.19 Shells
  • Exercises
  • 2 One-dimensional problems
  • 2.1 Rods
  • 2.2 Beams
  • 2.3.Transfer matrices
  • 2.4 Matrix-displacement method
  • 2.5 The general principle
  • Exercises
  • 3 Membranes
  • 3.1 The influence function for the deflection u(x)
  • 3.2 Discretization
  • 3.3 Element matrices
  • 3.4 The master element
  • 3.5 Singular integrals
  • 3.6 The treatment of the system of equations
  • 3.7 The domain integral
  • 3.8 Internal actions
  • 3.9 Examples
  • 3.10 The maximum principle
  • 3.11 The influence function for the normal derivative
  • 3.12 Substructures
  • 3.13 Alternatives to substructures
  • 3.14 Singularities
  • 3.15 Three-dimensional problems
  • Exercises
  • 4 Elastic plates and bodies
  • 4.1 Introduction
  • 4.2 The influence functions
  • 4.3 Discretization
  • 4.4 Element matrices for plates
  • 4.5 Boundary conditions
  • 4.6 Stresses
  • 4.7 The domain integrals
  • 4.8 Double nodes
  • 4.9 Infinite domains
  • 4.10 Examples
  • 4.11 Singularities
  • 4.12 Concentrated forces
  • 4.13 Three-dimensional problems
  • 4.14 Axisymmetric problems
  • 4.15 Examples
  • Exercises
  • 5 Nonlinear problems
  • 5.1 The principle of virtual forces
  • 5.2 The calculation of the singular integrals
  • 5.3 The system of differential equations
  • 5.4 Numerical treatment
  • 6 Plates
  • 6.1 Introduction
  • 6.2 Fundamentals
  • 6.3 Influence functions for ? and ??/?n
  • 6.4 Coupling on the boundary
  • 6.5 Discretization
  • 6.6 Singular integrals
  • 6.7 Element matrices
  • 6.8 Degrees-of-freedom
  • 6.9 The domain integrals
  • 6.10 Actions on the boundary
  • 6.11 Internal actions
  • 6.12 Internal supports and subdomain loads
  • 6.13 Examples
  • 6.14 Singularities
  • 6.15 Influence surfaces
  • 6.16 Special problems
  • Exercises
  • 7 Boundary elements and finite elements
  • 7.1 Theory
  • 7.2 Practice
  • 7.3 Experience
  • 8 Harmonic oscillations
  • 8.1 Rods
  • 8.2 Beams
  • 8.3 Elastic plates and bodies
  • 8.4 Kirchhoff plates
  • 8.5 Natural frequencies
  • 8.6 Helmholtz equation (membrane)
  • 8.7 Algebraization of the eigenvalue problem
  • 9 Transient problems
  • 9.1 Finite elements and boundary elements
  • 9.2 The wave equation
  • 9.3 The heat equation
  • 9.4 Dynamic displacement fields
  • 9.5 Numerical treatment
  • 9.6 Fourier-and Laplace transforms
  • 9.7 Dynamic stiffness matrices
  • 10 Computer programs
  • 10.1 BE-LAPLACE
  • 10.2 BE-PLATES
  • 10.3 BE-PLATE-BENDING
  • 10.4 Service
  • Appendix A
  • Appendix B
  • Literature.

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