Structure with Time Dependent Behavior
Open form approaches to the analysis of structural systems are usually complicated to a significant degree by the transition from a statics to a dynamics analysis; however, for a field approach the addition of D’Alembert inertial forces or time dependent
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LECTURES - No. 203
DONALD L. DEAN NORTH CAROLINA STATE UNIVERSITY RALEIGH, NORTH CAROLINA
DlSCRETE FIELD ANALYSIS OF
STRUCTURAL SYSTEMS
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright. AlI rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re·use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1976bySpringer-VerlagWien
Originally published by Springer-Verlag Wien-New York in 1976
ISBN 978-3-211-81377-5 DOI 10.1007/978-3-7091-4360-5
ISBN 978-3-7091-4360-5 (eBook)
LECTURE I INTRODUCTION TO DISCRETE FIELD MECHANICS Course Goals. - These lecture notes were prepared for publication prior to the lecture series and with limited knowledge as to the background of the typical participant. It was assumed, therefore, that the audience would have backgrounds in mathematics through differential equations, including introductory work in partial differential equations, and backgrounds in structural theory that include advanced frame analysis and introductory work in plate and shell theory. The course goals will be somewhat flexible depending upon the lecturer's observation of the rate at which the new material can be assimilated by the audience, but planning for the lecture series was based upon the ambitious goal of both introducing the fundamental concepts of discrete field mechanics and covering work at the frontiers of present knowledge of the subject as related to structural analysis.
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The term discrete field analysis denotes the body of concepts used to obtain field or functional solutions for systems most accurately represented as a lattice or a pattern of elements. The mathematical model for a lattice is characterized by the use of discrete (as opposed to continuous) variables for at least one of the coordinates required to cover the field. The application of discrete field methods to the analysis of structural systems is not new. Although there have been more recent 'publications(*), the best existing book on the subject(**) was written more than 45 years ago. It is somewhat surprising, therefore, to find that the state of the art is relatively undeveloped, especially as compared with continuum mechanics. To emphasize this point, one might observe that the student completing this short course should be able to derive formulas that could be duplicated by only a few dozen other structural analysts in the world today. It is the author's hope that the acquisition of this unique capability by the number of additional workers in the audienc~ will significantly increase the rate at which the state of the art of discrete field mechanics is being advanced. It is also his belief that a more wide-spread capability in discrete field methods will serve to advance structural design work by encouraging increased use of exotic lattice and composite lattice-continuum systems. The derivation of discrete field formulas for the design of complex structures often requires
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