Introduction to Boundary Elements: Theory and Applications by Friedel Hartmann

By Friedel Hartmann

to Boundary components thought and functions With 194 Figures Springer-Verlag Berlin Heidelberg big apple London Paris Tokyo Hong Kong Dr.-Ing. Friedel Hartmann collage of Dortmund division 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 info Hartmann, F. (Friedel) creation to boundary components: concept and applications/Friedel Hartmann. ISBN-13: 978-3-642-48875-7 1. Boundary worth difficulties. I. identify. TA347.B69H371989 515.3'5--dc19 89-4160 This paintings is topic to copyright. All rights are reserved, no matter if the full or a part of the cloth is anxious, particularly the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, replica on microfilms or in alternative routes, and garage in information banks. Duplication of this book or elements thereof is barely approved lower than the availability of the German Copyright legislations of September 9,1965, in its model of June 24,1985, and a copyright price should always be paid. Violations fall lower than the prosecution act of the German Copyright legislation. © Springer-Verlag Berlin Heidelberg 1989 Softcover reprint of the hardcover 1 st variation 1989 using registered names, logos, and so forth. during this e-book doesn't mean, even within the absence of a selected assertion, that such names are exempt from the appropriate protecting legislation and rules and for that reason loose for basic use.

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The coefficient Gki is the work done by the unit traction tPi on the edge of the membrane acting through the deflection U = go(y,zk) of the boundary of the subregion il, if the concentrated force P = 1 is located at the node zk. ) In more general terms we may state: the coefficient G ki or H ki represents the influence which the boundary layer tPi or "Pi, respectively, exerts on the collocation point zk. The influence depends on the two kernels go(y,zk) and Nogo(y,z)/ov, respectively. 28 Because each boundary layer (wherever it is located) influences each collocation point each row of the matrices G and H is fully populated.

If it is sitting on the boundary r of n then its work will be 8W = 1/2 or if it is sitting at a 90°-corner then its work will be 8W = 1/4. So the function c(z) is the work done by a point force of magnitude 1. 5 a-c. The three possible positions of J 8i (y - z)u(y) dily P = Cj(Z)aiu(z) n Note that this differential equation has only a symbolic meaning. You cannot verify it by differentiating the left side and comparing the result with the right side, but rather you must verify this equation indirectly by testing the action of the solution on' a certain class of functions, the virtual displacements.

This is the approach of the indirect method which either uses a single-layer potential or a double-layer potential. 9) In r p( y) dDy , [} is a sum of a single-layer potential, a double-layer potential and a volume potential the indirect method is, so to speak, a shortened variant of the direct method, the method we applied up to now. The difference between the two methods becomes manifest in the interpretation of what is or what are the source points. In the direct method the free point z is the source point while in the indirect method the integration points yare the source points.

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