Part II
After a very short description of Pontryagin’s maximum principle and sensitivity analysis as applied to eigenvalue problems, a unified approach to column optimization has been presented. Particular attention has been paid to multimodal solutions obtained
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SCIENCES
COURSES AND LECTURES -No. 308
STRUCTURAL OPTIMIZATION UNDER STABILITY AND VIBRATION CONSTRAINTS
EDITED BY M. ZYCZKOWSKI TECHNICAL UNIVERSITY OF CRACOW
Springer-Verlag Wien GmbH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
This volume contains 111 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. e 1989 by Springer-Verlag Wien Originally published by CISM, Udine in 1989.
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82173-2 ISBN 978-3-7091-2969-2 (eBook) DOI 10.1007/978-3-7091-2969-2
PREFACE
Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints. Loading parameters corresponding to the loss of stability are, in most cases, expressed by eingenvalues of certain differential equations, and hence the problems under consideration reduce to minimization of a certain functional (volume) under eigenvalues (critical loadings) kept constant. Briefly, wa call such problems "optimization with respect to eigenvalues", though in many cases the eigenvalue problems are not visible explicitely. Optimal design under vibration constraints is related to that under stability constraints because of at least two reasons. First, the vibration frequencies are also expressed by eigenvalues of some differential equations, and hence the relevant problems belong also to optimization with respect to eigenvalues. Second, in nonconservative cases of structural stability we usually have to apply the kinetic criterion of stability, analyzing the stability of vibrations in the vicinity of the equilibrium state: hence both problems are directly interconnected in such cases. The course on structural optimization under stability and vibration constraints was given in Udine, 20-24 June 1988, by five researchers particularly active in this field, namely prof M. Zyczkowski (coordinator) and prof. A. Gajewski from the Technical University of Cracow, Poland, prof. N. Olhofffrom the University of Aalborg, Denmark, prof. J. Ronda/ from the University of Liege, Belgium, and prof A. P. Seyranian from the Institute of Problems of Mechanics in Moscow, U.S.S.R. Part I, by M. Zyczkowski, deals just with optimal structural design under stability constraints. It gives first a general introduction to structural optimization, discussing typical objectives, design variables, constraints and equations of state. Then a chapte
