Stability of Discrete Systems
This paper describes the general features of structural stability problems and pays particular attention to eigen-analysis. Both non-linear eigen solutions are presented and linear eigen solutions which arise out of minimum total potential energy formulat
- PDF / 35,178,521 Bytes
- 225 Pages / 481.96 x 691.64 pts Page_size
- 102 Downloads / 257 Views
Series Editors: The Rectors of CISM Sandor Kaliszky - Budapest Mahir Sayir - Zurich Wilhelm Schneider - Wien The Secretary General of CISM Giovanni Bianchi - Milan Executive Editor Carlo Tasso - Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series in to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 354
e It
• •
~
SUMMATION THEOREMS IN STRUCTURAL STABILITY
EDITED BY
T. TARNAI TECHNICAL UNIVERSITY OF BUDAPEST
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 106 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. © 1995 by Springer-Verlag Wien Originally published by ClSM, Udine in 1995.
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 978-3-211-82704-8 ISBN 978-3-7091-2912-8 (eBook) DOI 10.1007/978-3-7091-2912-8
PREFACE
Summation formulae are used in the theory of elastic stability so that approximate estimates of the critical load factors of a complex problem are obtained by combining the load factors of subproblems in different ways. That is, the subproblems are solved and an approximate value of the load factor of the original problem is given by the load factors of subproblems by addition. If the critical load factors are directly added, then a formula is called a Southwell type formula. If the reciprocals of the critical load factors are added, then the formula is called a Dunkerley type. The practical advantage of the summation formulae is that, for the subproblems, there are usually solutions available, or easy to determine, while for the original problem the solution would be difficult to obtain. This book is a published form of the lecture notes prepared by lecturers for an advanced course entitled "Summation and Bounding Theorems and their Applications to Structural Stability Problems". The aim of the course was to present the basic mathematical principles, the main theorems and formulae, and their applications to practical problems. The course presented the basic mathematical background of elastic buckling, based on relationships for eigenvalues of linear operators in Hilbert space, and the basic principles like monotonicity, convexity principles (H.F. Weinberger). The main relationship
