Michell Structures
The book covers the theory of Michell structures being the lightest and fully stressed systems of bars, designed within a given domain, possibly within the whole space, transmitting a given load towards a given support. Discovered already in 1904 by A.G.M
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Structures
Michell Structures
Tomasz Lewiński Tomasz Sokół Cezary Graczykowski •
Michell Structures
123
Tomasz Lewiński Faculty of Civil Engineering Warsaw University of Technology Warsaw, Poland
Cezary Graczykowski Institute of Fundamental Technological Research Polish Academy of Sciences Warsaw, Poland
Tomasz Sokół Faculty of Civil Engineering Warsaw University of Technology Warsaw, Poland
ISBN 978-3-319-95179-9 ISBN 978-3-319-95180-5 https://doi.org/10.1007/978-3-319-95180-5
(eBook)
Library of Congress Control Number: 2018949872 © Springer International Publishing AG, part of Springer Nature 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
In memory of Professor George Rozvany
Preface
The publication written by Anthony George Maldon Michell (1904) was far ahead of its time. This remarkable paper has posed and solved selected optimum design problems in which a structure as a whole is treated as the design variable, contrary to the traditional setting in which only some selected dimensions or parameters may be chosen to play this role. Michell has raised the question of a safe and economic way of transmitting the given loading to the prescribed zone of the support, without imposing a priori assumptions on the layout of the bars (i.e. on the structural topology concerning the position of nodes and members connections) designed to make this load transmission possible. The adopted safety conditions require keeping the uniaxial stress in members between the lower bound rC and the upper bound rT . The cost of the structure is assumed as proportional to its volume. Forty years later, Leonid Kantorovich (1942) has shed a new light on the mass transport problem of Gaspard Monge
