Thèse présentée pour l'obtention du grade de Docteur de l'UTC

153 Pages·2014·15.31 MB·English

Par Jun LIN

Nonlinear transient analysis of isotropic and

composite shell structures under dynamic loading by

SPH method

Thèse présentée
pour l’obtention du grade
de Docteur de l’UTC

Soutenue le 02 avril 2014
Spécialité : Mécanique avancée
D2138
par Jun LIN
Nonlinear transient analysis of isotropic and composite
shell structures under dynamic loading by SPH method
Thèse présentée
pour l’obtention du grade
de Docteur de l’UTC.
Soutenue le : 02 avril 2014
Spécialité : Mécanique avancée

Nonlinear transient analysis of isotropic and composite
shell structures under dynamic loading by SPH method
Thèsesoutenuele02avril2014 devantlejurycomposéde:
Prof WUJianjun NorthwesternPolytechnicalUniversity,Xi’an (Rapporteur)
Prof IORDANOFFIvan ENSAMdeBordeaux (Rapporteur)
Prof RASSINEUXAlain UniversitédeTechnologiedeCompiègne
Prof COUTELLIERDaniel UniversitédeValenciennes
Prof LAKSIMIAbdelouahed UniversitédeTechnologiedeCompiègne (Directeurdethèse)
Prof NACEURHakim UniversitédeValenciennes (Co-directeurdethèse)
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I lovingly dedicate this thesis to my parents, my wife and my sister for
their understanding and encouragement
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Acknowledgements
First of all, I would like to express my profound gratitude to my supervisor Prof. Hakim
NACEUR, for his sincere and patient guidance and help along this academic journey. He
believed in me and encourages me constantly, keeping me motivated throughout this long
journey. He is not only a great supervisor, but also a very good friend. I believe that the
experience working with him will be of much benefit in my future scientific life.
I owe special gratitude to Prof. Abdelouahed LAKSIMI, for giving me the opportunity to
work in UTC. He allowed me all the freedom I wanted to follow my own steps and offered
me tremendous support and advice which are invaluable for this thesis.
Besides my supervisors, I feel very lucky to get precious suggestions and support from
Prof.DanielCOUTELLIERandDr.JamilaRAHMOUN.Iwouldliketoshowmyheartfelt
appreciation to you.
I would like to gratefully acknowledge Prof. WU Jianjun, Prof. IORDANNOF Ivan, Prof.
RASSINEUX Alain for their acceptance to participate in the evaluation committee of this
thesis.
IamindebtedtotheCSC(ChinaScholarshipCouncil)forthescholarshipandtheopportunity
of the study in France.
I would like to express my sincere gratitude to my colleagues, Thanh Loan NGUYEN,
Lukasz KURPASKA, Amira JAZIRI, Joseph HENRY, Ha Manh HUNG and Khanh-toan
TRAN who helped me a lot to habituate the work and life in France.
Special thanks would be paid to my lovely friends, Weiting TIAN & Weidong DANG,
XiaojuanJIA&BaochaoWANG,LeiQIN,ShengchengJi,ManyuXIAO,ErliangZHANG,
Yang XIA & Mengdi SONG, Jianquan LUO, Bin DONG, Fang WANG & Zhenzhou ZHU,
Dan LIU, Liguo ZHANG, Yingjuan ZHAO, Pengfei HUYAN, Peng CAO, Yang Song,
Dingfu ZHOU, Xiaodong WANG, Liang XIA in Compiègne, and Yingshuang XIE, Yufei
ZHANG, Guijin YAO, Yaojie SHI, Yuxi CUI, Sicong LIU, Amina LAOUIRA, Wassem
ARIF, and Jimin GUAN in Valenciennes, etc. Without you, my life would be dark in
France.
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I’d like to thank my parents and my sister, your unconditional love and understanding are
my lifeblood.
Finally,thisdissertationisdedicatedtomywife,JiaoLI,foryourendlesslove,neverending
support and long wait, making me never fear and move forward.
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Contents
Acknowledgements vii
Table of Contents ix
List of Tables xiii
List of Figures xv
1 General Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Meshless methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 SPH method and its applications . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Motivations and outline of the thesis . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 SPH formulation for 2D solids 11
2.1 Brief recall of basic continuum mechanics relations . . . . . . . . . . . . . . 11
2.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Constitutive relations . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Principle of mass conservation . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 Principle of conservation of linear momentum . . . . . . . . . . . . . 14
2.1.5 Principle of conservation of angular momentum . . . . . . . . . . . . 15
2.1.6 Principle of conservation of energy . . . . . . . . . . . . . . . . . . . 16
2.2 SPH foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Approximation of a field variable . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Smoothing function. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Approximation of field derivatives . . . . . . . . . . . . . . . . . . . 20
2.3 SPH discretization of the equilibrium equations of solids . . . . . . . . . . . 20
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