Buckling analysis of inflatable composite beams

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITYUNIVERSITY OF TECHNOLOGY AND EDUCATION Ph. THESIS PHAN THI DANG THU BUCKLING ANALYSIS OF INFLATABLE COMPOSITE BEAMS MAJOR: MECHANICAL ENGINEERING S K A0 0 0 0 3 5 Ho Chi Minh City, December 2021 MINISTRY OF EDUCATION AND TRAINING HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION ---oo0oo--- PHAN THI DANG THU BUCKLING ANALYSIS OF INFLATABLE COMPOSITE BEAMS PH. THESIS MAJOR: MECHANICAL ENGINEERING CODE: 9520103 HCM City, December 2021 MINISTRY OF EDUCATION AND TRAINING HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION --- oOo --- PHAN THI DANG THU BUCKLING ANALYSIS OF INFLATABLE COMPOSITE BEAMS MAJOR: MECHANICAL ENGINEERING CODE: 9520103 Supervisor one: Assoc. Phan Dinh Huan Supervisor two: Assoc.

Le Hieu Giang Reviewer 1: Reviewer 2: Reviewer 3: HCM City, December 2021 LÝ LỊCH CÁ NHÂN I. LÝ LỊCH SƠ LƯỢC Họ và tên: PHAN THỊ ĐĂNG THƯ Giới tính: Nữ Ngày, tháng, năm sinh: 05/11/1977 Nơi sinh: Tiền Giang Quên quán: Tiền Giang Dân tộc: Kinh Học vị cao nhất: Thạc Sỹ Kỹ thuật Đơn vị công tác: Trường Cao Đẳng Công Nghệ Thủ Đức Chỗ ở riêng hoặc địa chỉ liên lạc: B2-14/09 c/c Lê Thành, Phường An Lạc, Quận Bình Tân, TP.HCM Điện thoại liên hệ: 0903373645 Email: dangthu0511@yahoo. QUÁ TRÌNH ĐÀO TẠO 1. Đại học: - Hệ đào tạo: Chính qui - Nơi đào tạo: Trường Đại học Sư phạm Kỹ thuật TP.

HCM - Ngành học: Kỹ thuật công nghiệp - Năm tốt nghiệp: 2000 2. Sau đại học - Hệ đào tạo: Chính qui - Nơi đào tạo: trường Đại học Sư phạm Kỹ thuật Tp. HCM - Việt Nam - Thạc sĩ chuyên ngành: Kỹ thuật cơ khí - Năm tốt nghiệp: 2004 III. QUÁ TRÌNH CÔNG TÁC - 2000-2005: Giảng viên - Trường Cao đẳng Bán công Công nghệ và quản trị doanh nghiệp.

- 2005-2019: Giảng viên, Trưởng khoa Cơ khí - Trường Cao đẳng nghề TPHCM - 2019-2020: Giảng viên, Giám đốc trung tâm - Viện khoa học An toàn vệ sinh lao động TPHCM i - 2020 đến nay: Giảng viên - Trường Cao đẳng Công nghệ Thủ Đức TPHCM IV. LĨNH VỰC CHUYÊN MÔN - CAD/CAM/CNC - Gia công CNC - Thiết kế kỹ thuật cơ khí V. CÁC CÔNG TRÌNH ĐÃ CÔNG BỐ Số NỘI DUNG TT 1 T. Huynh-Van, Thu D.

Nguyen-Xuan “Isogeometric nonlinear bending and buckling analysis of variable thickness composite plate structures”; Composite Structures 1 January 2017, Pages 818-826. 2 Phan Thi Dang Thu, Phan Dinh Huan and Nguyen Thanh Truong “Effect parametric to properties of a 2D orthogonal plain classical woven fabric composite”; ISBN: 978-604-913-367-1, pages 509-517. 3 Phan Thi Dang Thu, Phan Dinh Huan, and Nguyen Thanh Truong “Biaxial beam inflation test on orthotropic fabric beam”; ISBN: 978-604-913-213-1, pages 1169-1176. 4 Nguyen Thanh Truong, Phan Dinh Huan, Phan Thi Dang Thu “Discretizing an analytical inflating beam model by the shell membrane finite element”; ISBN: 978-604-913-213-1, pages 1221-1228.

5 Phan Thi Dang Thu, Le Manh Tuan, Nguyen Xuan Hung, Nguyen Thanh Truong “Geometrically nonlinear behavior of composite beams of variable fiber volume fraction in isogeometric analysis”; ISBN: 978-604-82-2028-0, Pages: 1404-1409. 6 Thu Phan-Thi-Dang, Tuan Le-Manh, Giang Le-Hieu, Truong Nguyen- Thanh “Buckling of cylindrical inflating composite beams using isogeometric analysis”; ISBN: 978-604-73-3691-3, Pages 821-826. ii Số NỘI DUNG TT 7 Phan Thi Dang Thu, Nguyen Thanh Truong, Phan Dinh Huan “Mô hình dầm hơi composite phi tuyến chịu uốn”; ISBN: 976-604-82-2026-6, Page 697-704. 8 Phan Thi Dang Thu, Nguyen Thanh Truong, Phan Dinh Huan, Le Dinh Tuan “Biaxial experiments for determining material properties and joint strength of textile plain-woven fabric composites”; ISBN: 978-604-913-722- 8, Page 1174-1181.

HCM, ngày 03 tháng 12 năm 2021 Nghiên cứu sinh Phan Thị Đăng Thư iii ORIGINALITY STATEMENT I, Phan Thị Đăng Thư, hereby assure that this dissertation is my work, done under the guidance of Assoc. Phan Dinh Huan and Assoc. Le Hieu Giang to the best of my knowledge. All results and data that are stated and presented in this dissertation are honest.

And they have not been published by any previous works. Ho Chi Minh City, December 2021 Phan Thi Dang Thu iv ACKNOWLEDGEMENTS The dissertation is implemented at the Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology and Education, Viet Nam. The conducting process of this thesis not only brings motivation but also takes several challenges and difficulties. Without any support and cooperation from my professors, colleagues as well as students, this thesis would not be achieved completely and fluently.

That is why, first of all, I would like to express my appreciation to Assoc. Phan Dinh Huan and Assoc. Le Hieu Giang, for accepting me as a Ph. student and for their enthusiastic guidance during my research.

Moreover, I would like to kindly thank Dr. Nguyen Thanh Truong, Dr. Le Manh Tuan, Mr. Duong Chi Hung (a young brother), for their helpful support in every first step of doing research.

They conscientiously helped me to overcome my hardest time. Secondly, I would like to acknowledge Assoc. Le Dinh Tuan, Faculty of Transportation Engineering, Ho Chi Minh City University of Technology, Vietnam, troubleshot my troubles and helped to solve problems incidentally occurring in my study. Thirdly, I also take this chance to thank all my talented colleagues for their professional instruction and advice, as well as to my lovely students for their nice support.

Last but not least, the family’s love and encouragement are my biggest motivation. They gave me plenty of valuable assistance with their love and affection. Phan Thi Dang Thu v ABSTRACT This thesis presents a numerical modeling and an experimental program approach to investigate the buckling behavior of inflatable beams made from woven fabric composite materials. In the numerical study, the Isogeometric Analysis (IGA) is utilized to analyze the bucking response of inflatable beams subject to axial compressive load and predict the critical load at which the first wrinkle occurs.

In the numerical model, Timoshenko’s kinematics principle is used to build a 3D model of inflating orthotropic beams. In this modeling process, geometrical nonlinearity is considered by using the energy concept that accounts for the change in membrane and strain energies when the beams are bent. By using Lagrangian and virtual work principles, nonlinear equilibrium equations were derived. These equations are then discretized by using NURBS basis functions inherited from the IGA approach to derive the global nonlinear equation.

The well-known Newton-Raphson algorithm is then used to solve the nonlinear equation. The numerical results are then calibrated with the experimental one. It was found that a good agreement between IGA predictions and test results is achieved. The numerical model could be used for other parametric studies to investigate the influences of material and geometrical parameters on the buckling behavior of inflatable beams.

In the experiment study, the mechanical properties of the woven fabric composite material used in the fabrication of inflatable beams are determined and the biaxial buckling test is carried out. The experimental studies are performed under various inflation pressures to characterize the orthotropic mechanical properties and the nonlinear buckling behaviors. Load versus deflection curve of inflating beams beam with different air pressures obtained from the experiments are illustrated., and the first wrinkles of the beams when buckling happens are also monitored. Therefore, the maximum load-carrying capacity of the inflating beam with respect to the appearance of the first wrinkle is totally found.

In addition, the critical buckling load is determined through distinct load cases. Then, the discrepancy is evaluated among the proposed orthotropic and isotropic models in the literature. vi Contents BIOGRAPHY .VII NOTATIONS AND CONVENTIONS. X LIST OF FIGURE.

XVI LIST OF TABLE. XX CHAPTER 1: INTRODUCTION .2 The motivation of the thesis .3 The objectives and scope of the study .5 Outline of the thesis .6 Original contributions of the thesis .7 Significances of the thesis .5 CHAPTER 2: OVERVIEW OF FIBROUS COMPOSITE MATERIALS AND LITERATURE REVIEW .1 An overview of fibrous composite materials and practical applications of inflating composite structures .2 Literature review on the analysis of inflatable beams.22 CHAPTER 3: THEORETICAL FORMULATIONS .1 Continuum-based governing equations of stability problems of inflating beams .1 Mathematical description of inflating beams .3 Virtual work principle .38 CHAPTER 4: IGA-BASED BUCKLING ANALYSIS OF INFLATING COMPOSITE BEAMS .1 A brief review on isogeometric analysis .1 The concept of isogeometric analysis .2 Disadvantages of IGA .2 B-Spline Basis Functions .5 NURBS-based IGA.6 NURBS-based elements for IGA.7 Isogeometric analysis versus classical finite element in the analysis .2 IGA-based formulations for the buckling problems of inflating composite beams .1 Linear eigen buckling .3 Implementation of an iterative algorithm in solving nonlinear model .1 Linear buckling analysis .1 Simply-supported beam .2 Fixed – Free beam .1 Simply-supported beam .2 Fixed-free beam .76 CHAPTER 5: BUCKLING EXPERIMENTS OF INFLATING BEAMS .2 Material properties and selection of fabrics .1 The woven fabric materials .2 Mechanical properties of woven fabric composites .3 Test of joint’s durable strength .1 Glued joint PVC 1 cm .2 Glued joint PVC 1cm thermal .3 Glued joint PVC 2 cm thermal .4 Glued joint PVC 2.5 cm with thermal attachment .4 Inflatable beam specimens .5 Buckling test set-up .6 Experimental results and discussion .1 Load vs displacement u relation of the beam at pressure .1 Beams inflated with different air pressures .2 Comparison of 3 beams at pressure p = 80 kPa .2 Load vs displacement v relation of the beam at pressure .1 Beams inflated with different air pressures .2 Comparison of 3 beams at pressure p = 80 kPa .7 Comparison between experimental and IGA numerical methods .138 CHAPTER 6: CONCLUSIONS AND FURTHER STUDIES .143 LIST OF PUBLICATIONS .