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Introduction to Boundary Elements : Theory and Applications

Author: Friedel Hartmann
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1989.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is an introduction to the Boundary Element Method. It offers both an elementary and advanced exposition of the Boundary Element Method. It deals with the application of the BEM to elastostatics, elastodynamics, plasticity, acoustics and heat conduction. The book contains the complete influence matrices for plate-bending problems, for membrane and plate problems and for problems in three-dimensional  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Friedel Hartmann
ISBN: 9783642488733 3642488730
OCLC Number: 851800477
Description: 1 online resource (xii, 416 pages 194 illustrations)
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.
Responsibility: by Friedel Hartmann.

Abstract:

Duplication of this publication or parts thereof is only permitted under the provision of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always  Read more...

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