optimum design of 3-d irregular steel frames using ant colony optimization and harmony search ...

205 Pages·2010·1.95 MB·English

OPTIMUM DESIGN OF 3-D IRREGULAR STEEL FRAMES USING ANT
COLONY OPTIMIZATION AND HARMONY SEARCH ALGORITHMS

A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY

BY

İBRAHİM AYDOĞDU

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY
IN
ENGINEERING SCIENCES

AUGUST 2010
Approval of the thesis:
OPTIMUM DESIGN OF IRREGULAR 3-D STEEL FRAMES USING ANT
COLONY OPTIMIZATION AND HARMONY SEARCH ALGORITHMS
Submitted by İBRAHİM AYDOĞDU in partial fulfillment of the requirements
for the degree of doctor of philosophy in Engineering Sciences Department,
Middle East Technical University by,
Prof. Dr. Canan Özgen ________________
Dean, Graduate School of Natural and Applied Sciences

Prof. Dr. Turgut Tokdemir ________________
Head of Department, Engineering Sciences

Prof. Dr. Mehmet Polat Saka ________________
Supervisor, Engineering Sciences Dept., METU

Prof. Dr. Turgut Tokdemir ________________
Co-Supervisor, Engineering Sciences Dept., METU

Examining Committee Members:
Prof. Dr. Mehmet Polat Saka ________________
Engineering Sciences Dept., METU

Prof. Dr. Gülin Ayşe Birlik ________________
Engineering Sciences Dept., METU

Prof. Dr. Mehmet ÜLKER ________________
Civil Engineering Dept., Fırat University

Assoc. Prof. Dr. Oğuzhan Hasançebi ________________
Civil Engineering Dept., METU

Assoc. Prof. Dr. Ömer Civalek ________________
Civil Engineering Dept., Ákdeniz University

Date:
ii
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also
declare that, as required by these rules and conduct, I have fully cited and
referenced all material and results that are not original to this work.

Name, Last name:
Signature:
iii
ABSTRACT
OPTIMUM DESIGN OF IRREGULAR 3-D STEEL FRAMES USING ANT
COLONY OPTIMIZATION AND HARMONY SEARCH ALGORITHMS

Aydoğdu, İbrahim
Ph.D, Department of Engineering Sciences
Supervisor : Prof. Dr. Mehmet Polat Saka
Co-Supervisor: Prof. Dr. Turgut Tokdemir

August 2010, 185 pages

Steel space frames having irregular shapes when subjected to lateral loads caused
by wind or earthquakes undergo twisting as a result of their unsymmetrical
topology. As a result, torsional moment comes out which is required to be resisted
by the three dimensional frame system. The members of such frame are generally
made out of steel I sections which are thin walled open sections. The simple beam
theory is not adequate to predict behavior of such thin-walled sections under
torsional moments due to the fact that the large warping deformations occur in the
cross section of the member. Therefore, it is necessary to consider the effect of
warping in the design of the steel space frames having members of thin walled
steel sections is significant. In this study the optimum design problem of steel
space frames is formulated according to the provisions of LRFD-AISC (Load and
Resistance factor design of American Institute of Steel Construction) in which the
effect of warping is also taken into account. Ant colony optimization and harmony
search techniques two of the recent methods in stochastic search techniques are
used to obtain the solution of the design problem. Number of space frame
iv
examples is designed by the algorithms developed in order to demonstrate the
effect of warping in the optimum design.
Keywords: optimum structural design, combinatorial optimization, stochastic
search techniques, ant colony optimization, minimum weight, steel space frame,
warping effect
v
ÖZ
DÜZENSİZ ÜÇ BOYUTLU ÇELİK ÇERÇEVELERİN KARINCA KOLONİ
OPTİMİZASYONU VE HARMONİ ARAMA YÖNTEMLERİ İLE OPTİMUM
BOYUTLANDIRILMASI

Aydoğdu, İbrahim
Doktora, Mühendislik Bilimleri Bölümü
Tez Yöneticisi : Prof. Dr. Mehmet Polat Saka
Ortak Tez Yöneticisi: Prof. Dr. Turgut Tokdemir

Ağustos 2010, 185 sayfa

Düzensiz şekle sahip çelik uzay çerçeveler rüzgar veya depremden oluşan yatay
yüklerin etkisinde kaldıklarında simetrik olmayan topolojilerinden dolayı burulma
dönmesine maruz kalırlar. Bunun sonucunda oluşan burulma momentlerine üç
boyutlu çerçevenin karşı koyması gerekir. Genel olarak bu tür çerçevelerin
elemanları I şeklinde, açık ve ince cidarlı kesitlerden yapılır. Basit kiriş teorisi
burulma momentine maruz ince cidarlı kesitlerin davranışını elemanların
kesitlerinde çarpılmadan dolayı oluşan büyük şekil değiştirmeleri nedeniyle
belirlemeye yeterli değildir. Bundan dolayı ince cidarlı kesitlerden oluşan çelik
uzay çerçevelerin boyutlandırılmasında çarpılmanın göz önüne alınması gerekir.
Bu çalışmada çelik uzay çerçevelerin optimum boyutlandırılması problemi LRFD-
AISC (Yük ve Direnç Faktörü Tasarımı - Amerikan Çelik Konstrüksiyon
Enstitüsü) kurallarına göre çarpılma etkisi göz önüne alınarak formüle edilmiştir.
Optimum boyutlandırma probleminin çözümü de stokastik arama yöntemlerinin
yeni iki metodu olan karınca kolonisi ve harmoni arama teknikleri ile elde
edilmiştir. Çarpılmanın optimum boyutlandırmadaki etkisini göstermek
vi
için geliştirilen algoritma ile uzay çerçeve sistemleri boyutlandırılmıştır.
Anahtar kelimeler: Optimum yapı tasarımı, kombinasyönel optimizasyon,
stokastik arama teknikleri, karınca kolonisi optimizasyonu, harmoni arama
minimum ağırlık, uzay çelik çerçeve, çarpılma etkisi
vii
To My Family,
For your endless support and love

viii
ACKNOWLEDGEMENTS
I wish to express his deepest gratitude to his supervisor Prof. Dr. Mehmet Polat
SAKA for his guidance, advice, criticism, encouragements and insight throughout
the research.
Grateful thanks also extended to Assoc. Prof. Dr. Ömer CİVALEK and
Assoc. Prof. Dr. Oğuzhan HASANÇEBİ for not only serving as members of my
thesis committee but also for offering their invaluable guidance and help.
I should remark that without the sincere friendship of my roommate Alper Akın,
this work would not have been come to conclusion. I aprreciate him for his amity.
And strongly thanks to Zeynep Özdamar, Erkan Doğan, Serdar Çarbaş, and
Ferhat Erdal for their excellent understanding and great help at every stage of my
thesis study.

I would also like to appreciate to my friends, especially Semih Erhan,
Hakan Bayrak, Refik Burak Taymuş, Fuat Korkut, Özlem Aydın, Hüseyin Çelik,
Cihan Yıldırım, Serap Güngör Geridönmez and Kaveh Hassanzehtap for their
friendship and encouragement during my thesis.
I owe appreciate to most special person in my life Gülşah Sürekli for her
boundless moral support giving me joy of living.

Words cannot describe my gratitude towards the people dearest to me Havvana,
Halil, Ömer and Özkan my family; my mother, my father and my brothers. Their
belief in me, although at times irrational, has been vital for this work. I dedicate
this thesis to them.
ix
TABLE OF CONTENTS
ABSTRACT.......................................................................................................iv
ÖZ......................................................................................................................vi
ACKNOWLEDGEMENTS................................................................................ix
TABLE OF CONTENTS.....................................................................................x
LIST OF FIGURES..........................................................................................xvi
LIST OF TABLES...........................................................................................xix
CHAPTERS
1. INTRODUCTION...........................................................................................1
1.1 Optimization..............................................................................................1
1.2.1 Design variables..................................................................................2
1.2.2 Objective function...............................................................................2
1.2.3 Constraints..........................................................................................3
1.2.4 Mathematical modeling of the optimization problem...........................3
1.3 Structural optimization...............................................................................6
1.3.1 Mathematical modeling of structural optimization...............................6
1.3.2 Methods of Structural optimization......................................................7
1.4 Stochastic search methods..........................................................................9
x