Introduction to Boundary Elements: Theory and Applications

ISBN-13: 9783642488757 / Angielski / Miękka / 2012 / 418 str.

Friedel Hartmann

Opis

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: 10.1007/978-3-642-48873-3 Library of Congress Cataloging-in-Publication Data Hartmann, F. (Friedel) Introduction to boundary elements: theory and applications/Friedel Hartmann. ISBN-13: 978-3-642-48875-7 1. Boundary value problems. I. Title. TA347.B69H371989 515.3'5--dc19 89-4160 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. 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 be paid. Violations fall under the prosecution act of the German Copyright Law. (c) Springer-Verlag Berlin Heidelberg 1989 Softcover reprint of the hardcover 1 st edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Spis treści

1 Fundamentals.- 1.1 Notation.- 1.2 The basic idea.- 1.2.1 The basic idea from a mathematical point of view.- 1.2.2 The basic idea from an engineering point of view.- 1.3 Influence functions.- 1.3.1 Betti’s principle.- 1.3.2 Betti data.- 1.3.3 Fundamental solutions.- 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.- 3.9.1 Shear and torsion.- 3.9.2 Temperature distribution.- 3.9.3 Brownian motion.- 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.- 4.10.1 Beam with openings.- 4.10.2 Spring element.- 4.10.3 The search for cavities an inverse problem.- 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.- 5.4.1 Initial strain algorithm.- 5.4.2 Initial stress algorithm.- 5.4.3 Examples.- 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.- 6.16.1 Plates on elastic foundations.- 6.16.2 Plate buckling.- 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).- 8.6.1 The radiation resistance of a rotating engine.- 8.7 Algebraization of the eigenvalue problem.- 9 Transient problems.- 9.1 Finite elements and boundary elements.- 9.1.1 Finite elements.- 9.1.2 Boundary elements.- 9.1.3 Summary.- 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.