1. Full name: Vu Thi Thuy Anh                                        2. Sex: Female

3. Date of birth: 20 June 1986                                                    4. Place of birth: Thai Binh city

5. Admission decision number: 1138/QD-CTSV Dated: 18 December 2013 by the Rector of UET.

6. Changes in academic process:

7. Official thesis title: Nonlinear analysis of functionally graded shells.

8. Major: Engineering mechanics                                                9. Code: 62520101

10. Supervisors: Professor Dr.Sci. Nguyen Dinh Duc

11. Summary of the new findings of the thesis:

For the FGM shallow spherical shells, the thesis aimed to propose an analytical approach to study the nonlinear static analysis of F-FGM, S-FGM shallow spherical shells by using the classical shell theory and the first-order shear deformation theory.

For the FGM annular spherical shells, thesis is studied the nonlinear stability according to analytical methods. An approximate solution was proposed to give analytical solutions of nonlinear stability of the shells. Classical thin shell theory in terms of the shell deflection and the stress function is used to determine the buckling loads and nonlinear response of the FGM annular spherical shells. Galerkin method is applied to obtain closed - form of load - deflection paths. An analysis is carried out to show the effects of material, geometrical properties, elastic foundations and combination of external pressure and temperature on the nonlinear stability of the annular spherical shells.

For the eccentrically stiffened FGM annular spherical shell, the thesis has solved the general case when the shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or ceramic depending on situation of stiffeners at metal-rich or ceramic-rich side of the shell respectively. From that the thesis deals with the formulation of governing equations of linear stability of eccentrically stiffened FGM annular spherical shells resting on elastic foundations. Numerical results are given to evaluate effects of inhomogeneous, dimensional parameters, outside stiffeners, elastic foundations to the buckling of structures.

For the FGM annular spherical segment, by using approximate solution which has been proposed for the nonlinear stability of FGM annular spherical shell, to analyzed the nonlinear stability of FGM annular spherical segment. Galerkin method has applied to obtain closed-form relations of bifurcation type of buckling loads. Simultaneously, the thesis has solved the problems of the nonlinear stability of eccentrically stiffened FGM annular spherical segment.

To validate the proposed approach, the research results of the thesis was conducted comparing with the results of other authors. Results in the numerical form, so easy evaluation and testing, can be the reference for designers to consider using techniques in practice.

12. Practical applicability, if any: The significance remarks of this thesis may be used as important references for engineering designs.          

13. Further research directions, if any:

Research on the nonlinear static and dynamic of eccentrically stiffened FGM, S-FGM spherical shells subjected thermal loads and thermo-mechanic combination loads.

Research on the nonlinear dynamic and vibration of FGM annular spherical shells and segments.

Research on the nonlinear static and dynamic of eccentrically stiffened or non-eccentrically stiffened FGM special shaped shell by using the first-order or hight-order shear deformation theory.

Consideration to different types of loads acting on the nonlinear static and dynamic stability of FGM shell structure….

14. Thesis-related publications:

Vu Thi Thuy Anh, Nguyen Dinh Duc (2016). “Nonlinear response of shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on elastic foundation in thermal environment”. J. Mechanics of Advanced Materials and Structures, Vol. 23 (8), pp.926-934.

Dinh Duc Nguyen, Huy Bich Dao, Thi Thuy Anh Vu (2016). “On the nonlinear stability of eccentrically stiffened functionally graded annular spherical segment shells.” J. Thin-Walled Structures. Vol. 106, pp. 258-267.

Vu Thi Thuy Anh, Pham Hong Cong, Dao Huy Bich, Nguyen Dinh Duc (2016). “On the linear stability of eccentrically stiffened functionally graded annular spherical shell on elastic foundations”. J. of Advanced Composite Materials, DOI: 10.1080/09243046.2016.1187819.

Vu Thi Thuy Anh, Nguyen Dinh Duc (2015). “The nonlinear stability of axisymmetric FGM annular spherical shells under thermo-mechanical load.” J. Mechanics of Advanced Materials and Structures, Vol.23 (12), pp.1421-1429.

Vu Thi Thuy Anh, Dao Huy Bich, Nguyen Dinh Duc (2015). “Nonlinear buckling analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads.” European Journal of Mechanics – A/Solids, Vol. 50, pp 28-38.

Vu Thi Thuy Anh, Dao Huy Bich, Nguyen Dinh Duc (2015). “Nonlinear stability of thin FGM annular spherical segment in thermal environment”. Vietnam Journal of Mechanics, Vol.37, N4, pp.285-302.

Nguyen Dinh Duc, Vu Thi Thuy Anh, Pham Hong Cong (2014). “Nonlinear axisymmetric response of FGM shallow spherical shells on elastic foundations under uniform external pressure and temperature”. J. European Journal of Mechanics – A/Solids, Vol.45, pp.80-89.

Vu Thi Thuy Anh, Dao Huy Bich, Nguyen Dinh Duc (2014). “Nonlinear post-buckling analysis of thin Sigmoid FGM annular spherical shells surrounded on elastic foundations under uniform external pressure including temperature effects”. Proceeding of The Third International Conference on Engineering Mechanics and Automation (ICEMA 2014), Hanoi, October- 2014,

Vu Van Dung, Vu Thi Thuy Anh, Nguyen Dinh Duc (2014). “Nonlinear response of axisymmetric shear deformable Sigmoid FGM shallow spherical shells resting on elastic foundations under external pressure”. Proceeding of The Third International Conference on Engineering Mechanics and Automation (ICEMA 2014), Hanoi, October- 2014, ISBN: 978-604-913-367-1, pp. 622

Nguyen Dinh Duc, Vu Thi Thuy Anh, Dao Huy Bich (2014), “The nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations”. Vietnam Journal of Mechanics, Vol.36, N4, pp. 283-290

Vu Thi Thuy Anh, Pham Hong Cong, Nguyen Dinh Duc (2013). “Nonlinear stability of axisymmetric spherical shell with ceramic-metal-ceramic layers (S-FGM) and temperature-dependent properties on elastic foundation”. Proceedings of XI National Conference on Mechanics of Deformed Solid, Ho Chi Minh City, Nov. 2013.

Nguyen Dinh Duc, Vu Thi Thuy Anh (2013). “Nonlinear axisymmetric response of thin FGM shallow spherical shells with ceramic-metal-ceramic layers under uniform external pressure and temperature”. Journal of Science, Mathematics- Physics, Vietnam National University, Hanoi, Vol.29, No.2, 2013, pp. 1-15.