Doctoral thesis Engineering mechanics: Isogeometric finite element method for limit and shakedown analysis of structures

In this research, the isogeometric finite element method is used to discretise the displacement domain of strutures in the first step. The primal-dual algorithm based upon the von Mises yield criterion and a Newton-like iteration is used in the second step to solve optimization problem.
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Doctoral thesis Engineering mechanics: Isogeometric finite element method for limit and shakedown analysis of structures MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF TECHNOLOGY AND EDUCATION HO CHI MINH CITY DO VAN HIENISOGEOMETRIC FINITE ELEMENT METHODFOR LIMIT AND SHAKEDOWN ANALYSIS OF STRUCTURES DOCTORAL THESIS MAJOR: ENGINEERING MECHANICS Ho Chi Minh City, June 16, 2020 DeclarationI, Do Van Hien, declare that this thesis entitled, Isogeometric finite element methodfor limit and shakedown analysis of structures is a presentation of my original researchwork. I confirm that: • Wherever contributions of others are involved, every effort is made to indicate this clearly, with due reference to the literature,and acknowledgement of collaborative research and discussions. • The work was done under the guidance of Prof. Nguyen Xuan Hung at the Ho Chi Minh City University of Technology and Education. i AcknowledgementsThis thesis summarizes my research carried out during the past five years at the DoctoralProgram Engineering Mechanics at Ho Chi Minh City University of Technology andEducation in Ho Chi Minh City. This thesis would not have been possible without helpof many, and I would like to acknowledge their kind efforts and assistance. First of all I would like to express my deep gratitude to my supervisor Prof. NguyenXuan Hung, for his guidance, support and encouragement during the past five years. Iappreciate that he left a lot of freedom for me to pursue my own ideas, set the rightdirection when it was necessary and contributed valuable advice. I am also very grateful to Assoc.Prof. Van Huu Thinh, who has been my secondadvisor at HCMUTE for many years. I am indebted to Prof. Timon Rabczuk for giving me the chance to spend aone-year research visit at the Bauhaus-Universität Weimar, and I also want to thankProf. Tom Lahmer and Prof. Xiaoying Zhuang for the fruitful discussions and theirsupport. I also would like to thank the research group members at GACES (at HCMUTE),CIRTECH (at HUTECH) and ISM (at Bauhaus-Universität Weimar, Germany) fortheir helpful supports. I would like to thank from the bottom of my heart to Assoc.Prof. Nguyen HoaiSon, Assoc.Prof Nguyen Trung Kien, Assoc.Prof Chau Dinh Thanh and other colleaguesat HCMUTE for their kind supports and advice. I am immensely indebted to my father Do Tang, my mother Pham Thi Nghe andmy parents in-law who have been the source of love and discipline for their inspirationand encouragement throughout the course of my education including this DoctoralProgram. Last but not least, I am extremely grateful to my wife Mrs. Nguyen Thi Nhu Lanwho has been the source of love, companionship and encouragement, to my sons, DoQuang Khai and Do Minh Nhat, who has been the source of joy and love. ii AbstractThe structural safety such as nuclear power plants, chemical industry, pressure vesselindustry and so on can commonly be evaluated with the help of limit and shakedownanalysis. Nowadays, the limit and shakedown analysis plays a well-known role in notonly assessing the safety of engineering structures but also designing of the engineeringstructures. The limit load multipliers can be determinated by using lower or upperbound method. In order to ultilize the limit and shakedown analysis in many practicalengineering areas, the development of numerical tools which are sufficiently efficient androbust is a neccessary of current research in the field of limit and shakedown analysis.The numerical tools involve the two steps: finite element discretisation strategy andconstrained optimization. In this research, the isogeometric finite element method is used to discretise thedisplacement domain of strutures in the first step. The primal-dual algorithm basedupon the von Mises yield criterion and a Newton-like iteration is used in the second stepto solve optimization problem. Mathematically, the shakedown problem is consideredas a nonlinear programming problem. Starting from upper bound theorem, shakedownbound is the minimum of the plastic dissipation function, which is based on von Misesyield criterion, subjected to compatibility, incompressibility and normalized constraints.This constraint nonlinear optimization problem is solved by combined penalty functionand Lagrange multiplier methods. The isogeometric analysis (IGA) uses NURBS basis functions for both the repre-sentation of the geometry and the approximation of solutions. The main aim of theIGA was to integrate Finite Element Analysis (FEA) into NURBS based Computer AidDesign (CAD) design tools. The Bézier and Lagrange extraction of NURBS was usedin the analysis due to The computational aspects of the NURBS function increase thequestion of how to implement efficiently the NURBS function in the existing FEM codesdue to a significant differences between the NURBS basis function and the Lagrangefunction. The Bézier extraction is founded on the NURBS basis functions in terms of C 0Bernstein polynomials. Lagrange extraction is similar to Bézier extraction but it sets upa direct connection between NURBS and Lagrange polynomial basis functions instead iiiAbstract ivof using C 0 Bernstein polynomials as a new shape function in the Bézier extraction.Numerical results of structure problems are compared with analytical or other availablesolutions to pro ...