Structural optimization is currently attracting considerable attention. Interest in - search in optimal design has grown in connection with the rapid development of aeronautical and space technologies, shipbuilding, and design of precision mach- ery. A special ?eld in these investigations is devoted to structural optimization with incomplete information (incomplete data). The importance of these investigations is explained as follows. The conventional theory of optimal structural design - sumes precise knowledge of material parameters, including damage characteristics and loadings applied to the structure. In practice such precise knowledge is seldom available. Thus, it is important to be able to predict the sensitivity of a designed structure to random ?uctuations in the environment and to variations in the material properties. To design reliable structures it is necessary to apply the so-called gu- anteed approach, based on a "worst case scenario" or a more optimistic probabilistic approach, if we have additional statistical data. Problems of optimal design with incomplete information also have consid- able theoretical importance. The introduction and investigations into new types of mathematical problems are interesting in themselves. Note that some ga- theoretical optimization problems arise for which there are no systematic techniques of investigation. This monograph is devoted to the exposition of new ways of formulating and solving problems of structural optimization with incomplete information. We recall some research results concerning the optimum shape and structural properties of bodies subjected to external loadings.

The International Union of Theoretical and Applied Mechanics (IUTAM) initiated and supported an International Symposium on Dynamical Problems for Rigid-elastic Systems and Structures held in 1990 in Moscow, USSR. The Symposium was intended to bring together scientists working in the fields of multibody system dynamics and finite element systems with special emphasis to modeling, simulation, optimization and control. A Scientific Committee was appointed by the Bureau of IUTAM with following members: N.V. Banichuk (USSR). E.J. Haug (USA). Y. Hori (Japan). S. Kaliszky (Hungary), D.M. Klimov (USSR). Chairman, L. Lilov (Bulgaria), F. Niordson (Denmark), B. Roth (USA), W. Schiehlen (Germany), G. Schmidt (Germany), J. Wittenburg (Germany). The chairman invited the participants on recommendation by the Scientific Committee. As a result 48 active scientific participants from 11 countries followed the invitation, and 32 papers were presented in lecture sessions. The available manuscripts were reviewed by the Scientific Committee after the Symposium, and 24 of them are collected in this volume. At the Symposium a tour to the Institute for Problems of Mechanics, USSR Academy of Sciences, was arranged. The scientific lectures were devoted to the following topics: o Modeling and Optimization, o Dynamics of Systems with Elastic Constraints, o Vibrations, o Multibody Systems.

to Optimization of Structures With 66 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong N.V. Banichuk Institute for Problems in Mechanics USSR Academy of ScienCes 117526 Moscow Soviet Union Translator Vadim Komkov Mathematics and Computer Science Department Air Force Institute of Technology Wright Patterson Air Force Base, OH 45433 USA Original Russian edition Vvedenie v Optimizatsiyu Konstruktsiy published (c) 1986 by Nauka Moscow. Library of Congress Cataloging-in-Publication Data Banichuk, Nikolai Vladimirovich. [Vvedenie v optimizatsiiii konstruktsii. English] Introduction to optimization of structuresfN.V. Banichuk. p. cm. Translation of: Vvedenie v optimizaiSiiu konstrukiSii. Includes bibliographical references. ISBN-13:978-1-4612-7988-4 (aIk. paper) 1. Structures, Theory of. I. Title. TA645.B3513 1990 624. 1 '7-dc20 89-26165 Printed on acid-free paper. (c) 1990 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1990 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, Ne\l York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis Use in connection with any form of information storage and retrieval, electronic adaptation computer software, or by similar or dissimilar methodology now known or hereafter developec is forbidden.

Structural optimization is currently attracting considerable attention. Interest in - search in optimal design has grown in connection with the rapid development of aeronautical and space technologies, shipbuilding, and design of precision mach- ery. A special ?eld in these investigations is devoted to structural optimization with incomplete information (incomplete data). The importance of these investigations is explained as follows. The conventional theory of optimal structural design - sumes precise knowledge of material parameters, including damage characteristics and loadings applied to the structure. In practice such precise knowledge is seldom available. Thus, it is important to be able to predict the sensitivity of a designed structure to random ?uctuations in the environment and to variations in the material properties. To design reliable structures it is necessary to apply the so-called gu- anteed approach, based on a "worst case scenario" or a more optimistic probabilistic approach, if we have additional statistical data. Problems of optimal design with incomplete information also have consid- able theoretical importance. The introduction and investigations into new types of mathematical problems are interesting in themselves. Note that some ga- theoretical optimization problems arise for which there are no systematic techniques of investigation. This monograph is devoted to the exposition of new ways of formulating and solving problems of structural optimization with incomplete information. We recall some research results concerning the optimum shape and structural properties of bodies subjected to external loadings.