Computational Treatment of Transient Problems in Nonlinear Structural Mechanics
Nonlinear transient problems are often encountered in structural dynamics. While vibration induced problems are usually linear or at most weakly nonlinear and can, therefore, be suitably solved in the frequency domain by applicatition of mode superpositio
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ADVANCES IN COMPUTATIONAL NONLINEAR MECHANICS
EDITEDBY
I. St. DOLTSINIS UNIVERSITY OF STUTTGART
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da
contributi del Consiglio Nazianale delle Ricerche.
This volume contains 59 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. C 1989 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York 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 978-3-211-82113-8 DOI 10.10071978-3-7091-2828-2
ISBN 978-3-7091-2828-2 (eBook)
PREFACE
The demand for computational methods in the :field of nonlinear mechanics is evident. Whereas in linear problems of practical importance the use of the computer is justified by the complexity of the domain, in the nonlinear case complicated tasks may originate from the nonlinearity itself and necessitate a computational treatment. The communication of the physical phenomenon to the computer has to be considered an essential part of the numerical solution of nonlinear problems and may have a signi:ficant effect on the relevance of the results of the calculation. Due to the subtle interaction between physics and numerics, computational nonlinear mechanics still require both a clear understanding of the physical principles underlying the system under consideration and a profound knowledge of the appropriate numerical methodologies. It is only natural that the introduction of nonlinear computer techniques evolved from a suitable extension of linear algorithms to the analysis of moderate deviations from linear behaviour. The keyword in this context was incrementation. Subsequent developments are mainly characterised by the efforts undertaken towards a compensation of linearisation errors associated with incremental procedures. The current stage of algorithmic research and development is driven by the recognition that a numerical treatment of strongly nonlinear problems in mechanics requires specific computer models and solution techniques adjusted to the system under investigation. Also, efficiency requirements demand an adequate consideration of the architecture of the available hardware. The progress made in the development of nonlinear computer methods in conjunction with concurrent hardware developments today allows the treatment of problems in mechanics of a degree of complexity which makes remarkable nonlinearities of the initial period appear negligible. An illustrative example in this context may be the early elastoplastic analysis of structures and continua compared to current numerical simulations of comp
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