Viscoplasticity formulation
Here we shall take a law defining the plastic//creep strain rate as a function of the distance from the yield surface. Thus if .
- PDF / 4,163,906 Bytes
- 99 Pages / 481.89 x 691.654 pts Page_size
- 34 Downloads / 180 Views
1/!!fi
v
OLGIERD C. ZI.ENKIEWICZ UNIVI-:RSITY OF W:\l.ES, SWANSEA
INTRODUCTORY LECTURES ON THE FINITE ELEMENT METHO D
COURSE HELD AT THE DEPARTMENT OF MECHANICS OF SOLIDS JULY 1972
UDINE 1972
Springer-Verlag Wien GmbH
This wodt is suiject to copyright
AU rights are reserved. whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illuatrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1972 by Springer-Verlag Wien
Originally published by Springer Verlag Vien New York in 1972
ISBN 978-3-211-81202-0 DOI 10.1007/978-3-7091-2973-9
ISBN 978-3-7091-2973-9 (eBook)
PREFACE
In presenting the introductory lectures to an audience of engineers of a "mixed kind" including some for whom the subject is new and others already well versed in its application an obvious difficulty occurs. For the first, a complete coverage of essentials is necessary at the same time touching on a vari ety of problems of practical interest. For the latter, an expectation of some novelty beyond that available in texts and published papers is necessary to indicate some recent lines of thought. Further the whole presentation has to be compact and limited in space and time. It is within this framework that the present notes were prepared. As many of the fundamentals and also some quite complex applications are presented in the author's text (which is referred to as reference A), a "telegraphic" style is adopted condensing some of the essentials to the types of notes that can be taken by a student in a lecture course. Frequent reference is made to "reference A" and indeed further explanation, elaboration and proof is often presented there. While the larger part of the notes covers standard material, several points are made which give material either not available in the text
4
Prefaae
or which is still subject of current research. While "reference A" contains a wide bibliography, specific reffl'l'ences are extracted at the end of these lectures either to draw attention to classic papers or for an elaboration of some recent researches. Olgierd C. Zinkiewicz Udine, July 1972
Historical Note-Discrete Analysis
Basis of discrete engineering analysis
(~
structural mechanics) is:
1.
Isolation of individual members (elements)
2.
Establishment of two sets of quantities ~e and
fe
associ-
ated with each element which have the property a) that if
U
stands for global values
u~ u. - ..,,
""~
b) that ~
f ~ • 0, gives
the second physical requirement
c) that for each element we can determine the relation
These three relations (together with appropriate physical constraints) allow a set of equations for u to be "" found from which this can be determined. In context of linear structures we have for example displacement of nodes forces exerted by each element
6
Historical development and discrete analysis
and (a) and (b) ensure interelement continuity and equilibrium respectively, (c) is a linear relation
Fe
-
= ke ...
Data Loading...
