Limit and shakedown analysis of plates and shells including uncertainties [Elektronische Ressource] / von Thanh Ngọc Trân

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Informations

• Publié par: technische_universitat_chemnitz
• Publié le: 01 janvier 2008
• Nombre de lectures: 13
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

LIMIT AND SHAKEDOWN ANALYSIS OF PLATES
AND SHELLS INCLUDING UNCERTAINTIES


Von der Fakultät für Maschinenbau der
Technischen Universität Chemnitz
genehmigte

Dissertation

zur Erlangung des akademischen Grades
Doktoringenieur
(Dr.-Ing.)

vorgelegt
von MSc. Thanh Ng ọc Tr ần
geboren am 03. Februar 1975
in Nam Dinh, Vietnam

eingereicht am 12. Dezember 2007

Gutachter:
Prof. Dr.-Ing. Reiner Kreißig
Prof. Dr.-Ing. Manfred Staat
Prof. Dr.-Ing. Christos Bisbos

Tag der Verteidigung: 12. März 2008
Tr ần, Thanh Ng ọc

Limit and shakedown analysis of plates and shells including uncertainties

Dissertation an der Fakultät für Maschinenbau der Technischen Universität Chemnitz,
Institut für Mechanik und Thermodynamik, Chemnitz 2008

149 + vii Seiten
55 Abbildungen
28 Tabellen
162 Literaturzitate


Referat

The reliability analysis of plates and shells with respect to plastic collapse or to inadaptation is
formulated on the basis of limit and shakedown theorems. The loading, the material strength and
the shell thickness are considered as random variables. Based on a direct definition of the limit
state function, the nonlinear problems may be efficiently solved by using the First and Second
Order Reliability Methods (FORM/SORM). The sensitivity analyses in FORM/SORM can be
based on the sensitivities of the deterministic shakedown problem. The problem of the reliability
of structural systems is also handled by the application of a special barrier technique which
permits to find all the design points corresponding to all the failure modes. The direct plasticity
approach reduces considerably the necessary knowledge of uncertain input data, computing costs
and the numerical error.

Die Zuverlässigkeitsanalyse von Platten und Schalen in Bezug auf plastischen Kollaps oder
Nicht-Anpassung wird mit den Traglast- und Einspielsätzen formuliert. Die Lasten, die
Werkstofffestigkeit und die Schalendicke werden als Zufallsvariablen betrachtet. Auf der
Grundlage einer direkten Definition der Grenzzustandsfunktion kann die Berechnung der
Versagenswahrscheinlichkeit effektiv mit den Zuverlässigkeitsmethoden erster und zweiter
Ordnung (FROM/SORM) gelöst werden. Die Sensitivitätsanalysen in FORM/SORM lassen sich
auf der Basis der Sensitivitäten des deterministischen Einspielproblems berechnen. Die
Schwierigkeiten bei der Ermittlung der Zuverlässigkeit von strukturellen Systemen werden durch
Anwendung einer speziellen Barrieremethode behoben, die es erlaubt, alle Auslegungspunkte zu
allen Versagensmoden zu finden. Die Anwendung direkter Plastizitätsmethoden führt zu einer
beträchtlichen Verringerung der notwendigen Kenntnis der unsicheren Eingangsdaten, des
Berechnungsaufwandes und der numerischen Fehler.

Schlagworte:

Limit analysis, shakedown analysis, exact Ilyushin yield surface, nonlinear programming, first
order reliability method, second order reliability method, design point

Archivierungsort:

http://archiv.tu-chemnitz.de/pub/2008/0025





ACKNOWLEDGEMENTS



This work has been carried out at the Biomechanics Laboratory, Aachen University of
Applied Sciences, Campus Jülich. The author gratefully acknowledges the Deutscher
Akademischer Austausch Dienst (DAAD) for a research fellowship award under the grant
reference A/04/20207.

The author is indebted to Prof. Dr.-Ing. M. Staat who has been the constant source of
caring and inspiration for his helpful guidance and encouragement. His commitment and
assistance were limitless and this is greatly appreciated.

The author would like to express his deep gratitude to Prof. Dr.-Ing. R. Kreißig for giving
him the permission to complete Doctorate of Engineering at the Chemnitz University of
Technology and for kindly assistance and supervision.

The author would like to thank Prof. Dr.-Ing. C. Bisbos, Aristotle University of
Thessalonoki, Greece for having kindly accepted to review this thesis.

The author is thankful to Dr.-Ing. V ũ Đức Khôi for help and advice, to Ms Wierskowski
and Ms Dronia for their programming as part of their diploma theses in some parts of FEM
source code. The author’s thanks are also extended to Prof. Dr. rer. nat. Dr.-Ing.
S. Sponagel and to the other colleagues at the Biomechanics Laboratory for their helpful
assistance.

The author is immensely indebted to his father Tr ần Thanh Xuân and his mother Nguy ễn
Th ị Hòa who have been the source of love and discipline for their inspiration and
encouragement throughout the course of his education including this Doctorate.

Last but not least, the author is extremely grateful to his wife Mrs. Nguy ễn Thị Thu Hà
who has been the source of love, companionship and encouragement, to his daughters My
and Ly who have been the source of joy and love.
iii
ivTABLE OF CONTENTS

INTRODUCTION ........................................................................................................ 1

1. FUNDAMENTALS.................................................................................................. 3
1.1 Basic concepts of plasticity................................................................................. 3
1.1.1 Elastic and rigid perfectly plastic materials................................................. 3
1.1.2 Fundamental principles in plasticity............................................................ 4
1.1.3 Drucker’s postulate...................................................................................... 6
1.1.4 Yield criteria ................................................................................................ 7
1.1.5 Plastic dissipation function in local variables.............................................. 8
1.2 Normalized shell quantities ................................................................................ 9
1.2.1 Reference quantities..................................................................................... 9
1.2.2 Stress quantities ........................................................................................... 9
1.2.3 Strain quantities ......................................................................................... 10
1.2.4 Stress-Strain relation.................................................................................. 11
1.3 Exact Ilyushin yield surface.............................................................................. 12
1.3.1 Derivation .................................................................................................. 12
1.3.2 Description of the exact Ilyushin yield surface ......................................... 14
1.3.3 Reparameterization .................................................................................... 16
1.3.4 Plastic dissipation function ........................................................................ 18
1.3.5 Reformulation ............................................................................................ 19

2. MATHEMATICAL FORMULATIONS OF LIMIT AND SHAKEDOWN
ANALYSIS IN GENERALIZED VARIABLES ....................................................... 21
2.1 Theory of limit analysis .................................................................................... 22
2.1.1 Introduction................................................................................................ 22
2.1.2 General theorems of limit analysis ............................................................ 23
2.2 Theory of shakedown analysis.......................................................................... 24
2.2.1 Introduction 24
2.2.2 Definition of load domain 25
2.2.3 Fundamental of shakedown theorems........................................................ 27
2.2.4 Separated shakedown limit ........................................................................ 30
2.2.5 Unified shakedown limit............................................................................ 33

v Table of Contents
3. DETERMINISTIC LIMIT AND SHAKEDOWN PROGRAMMING.................. 38
3.1 Finite element discretization............................................................................. 39
3.2 Kinematic algorithm ......................................................................................... 41

4. PROBABILISTIC LIMIT AND SHAKEDOWN PROGRAMMING................... 49
4.1 Basic concepts of probability theory ................................................................ 50
4.1.1 Sample space.............................................................................................. 50
4.1.2 Random variables ...................................................................................... 50
4.1.3 Moments .................................................................................................... 51
4.2 Reliability analysis............................................................................................ 53
4.2.1 Failure function and probability