ORIGINALITY STATEMENT I, Nguyen Thi Bich Lieu, hereby assure that this dissertation is my own work, done under the guidance of Prof. Nguyen Xuan Hung and Assoc. Dang Thien Ngon with the best of my knowledge. The data and results stated in the dissertation are honest and were not been published by any works.
Ho Chi Minh City, 2019 Nguyen Thi Bich Lieu i ACKNOWLEDGEMENTS This dissertation has been carried out in the Faculty of Civil Engineering, HCM City University of Technology and Education, Viet Nam. The process of conducting this thesis brings excitement but has quite a few challenges and difficulties. And I can say without hesitation that it has been finished thanks to the encouragement, support and help of my professors and colleagues. First of all, I would like to express my deepest gratitude to Prof.
Nguyen Xuan Hung and Assoc. Dang Thien Ngon, especially Prof. Nguyen Xuan Hung from CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), Vietnam for having accepted me as their PhD student and for the enthusiastic guidance and mobilization during my research. Also, I would like to sincerely thank Dr.
Thai Hoang Chien, a close brother, for his helpful guidance at first step of doing research and his support for my overcoming of the hardest time. Secondly, I would like also to acknowledge Msc. Nguyen Van Nam, Faculty of Mechanical Technology, Industrial University of Ho Chi Minh City, Vietnam for their troubleshooting and the cooperation in my study. Furthermore, I am grateful to Chau Nguyen Khanh and the staffs at CIRTech Institute, HUTECH, Vietnam for their professional knowledge, interactive discussion, and immediate support.
Thirdly, I take this chance to thank all my nice colleagues at the Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, for their professional advice and friendly support. Finally, this dissertation is dedicated to my family, especially my beloved husband, who has always given me valuable encouragement and assistance. Nguyen Thi Bich Lieu ii CONTENTS ORIGINALITY STATEMENT. vii LIST OF TABLES.
xi LIST OF FIGURES.2 An overview of isogeometric analysis .3 Literature review about materials used in this dissertation. Laminated composite plate. Piezoelectric laminated composite plate. Piezoelectric functionally graded porous plates reinforced by graphene platelets (PFGP-GPLs).
Functionally graded piezoelectric material porous plates (FGPMP) .4 Goal of the dissertation .5 The novelty of dissertation .16 ISOGEOMETRIC ANALYSIS FRAMEWORK .2 Advantages of IGA compared to FEM .3 Some disadvantages of IGA .6 NURBS basis function .1 Introduction of Bézier extraction .2 Bézier decomposition and Bézier extraction [97-98] .2 An overview of plate theories .1 The higher-order shear deformation theory .2 The generalized unconstrained higher-order shear deformation theory (UHSDT) .3 The C0-type higher-order shear deformation theory (C0-type HSDT) .3 Laminated composite plate .1 Definition of laminated composite plate .2 Constitutive equations of laminated composite plate .1 Introduce to piezoelectric material .2 The basic equation of piezoelectric material .5 Piezoelectric functionally graded porous plates reinforced by graphene platelets (PFGP-GPLs) .6 Functionally graded piezoelectric material porous plates (FGPMP) .60 ANALYZE AND CONTROL THE LINEAR RESPONSES OF THE PIEZOELECTRIC LAMINATED COMPOSITE PLATES .2 Laminated composite plate formulation based on Bézier extraction for NURBS .1 The weak form for laminated composite plates .2 Approximated formulation based on Bézier extraction for NURBS .3 Theory and formulation of the piezoelectric laminated composite plates.1 Variational forms of piezoelectric composite plates .2 Approximated formulation of electric potential field .3 Governing equations of motion .4 Active control analysis .5 Results and discussions. Static analysis of the four-layer [00/900/900/00] square laminated plate .2 Static analysis of laminated circular plate subjected to a uniform distributed load .3 Free vibration of laminated composite square plate .4 Free vibration of laminated circular plate .6 Static analysis of the square piezoelectric laminated composite plate .7 Free vibration analysis of an elliptic piezoelectric composite plate .8 Dynamic control of piezoelectric laminated composite plate .97 ANALYSIS AND CONTROL THE RESPONSES OF PIEZOELECTRIC FUNCTIONALLY GRADED POROUS PLATES REINFORCED BY GRAPHENE PLATELETS .2 Theory and formulation of PFGP-GPLs plate .1 Approximation of mechanical displacement .2 Governing equations of motion .1 Convergence and verification studies .2 Geometrically nonlinear static analysis.3 Geometrically nonlinear dynamic analysis .4 Static and dynamic responses active control .136 FREE VIBRATION ANALYSIS OF THE FUNCTIONALLY GRADED PIEZOELECTRIC MATERIAL POROUS PLATES .2 Functionally graded piezoelectric material plate formulation based on Bézier extraction for NURBS .1 Kinematics of FGPMP plates .3 Numerical examples and discussions. 167 CONCLUSIONS AND RECOMMENDATIONS .173 LIST OF PUBLICATIONS .191 vi NOMENCLATURE Latin Symbols C Global damping matrix D Matrix of material K Global stiffness matrix M Global mass matrix Ni,p B-splines basis functions J Jacobian matrix P Control points R Rational basic function u Displacement field u Velocity u Acceleration f Global force vector k Dielectric constant matrix e Piezoelectric constant matrix qs The surface charges Qp The point charges E The gradient of the electric potential E Young’s modulus h The thickness w Weights Gd The constant displacement feedback control gain Gv The constant velocity feedback control gain t Time Vm The volume fraction of the metal vii Vc The volume fraction of the ceramic V0 Electric voltage Greek Symbols Poisson’s ratio Natural frequency Mass density Stress field xx Normal stress in x direction yy Normal stress in y direction xy Shear stress in xy direction yz Shear stress in yz direction xz Shear stress in xz direction Strain field xx Normal strain in x direction yy Normal strain in y direction xy Shear strain in xy direction yz Shear strain in yz direction xz Shear strain in xz direction ; Parametric coordinates The electric potential field Abbreviations 2D Two dimensional 3D Three dimensional CAD Computer Aided Design viii CAE Computer Aided Engineering CFS Closed form solution CLPT Classical laminate plate theory CPT Classical plate theory DQM Differential quadrature method EFG Element-free Galerkin ESDT Exponential shear deformation theory ESL Equivalent single layer FEA Finite Element Analysis FEM Finite Element Method IGA Isogeometric Analysis FGM Functionally graded material FSDT First-order shear deformation theory FSM Finite strip method GLHOT Global-local higher-order theory GSDT Generalized shear deformation theory HSDT Higher-order shear deformation theory ITSDT Inverse tangent shear deformation theory LHOT Local higher-order theory LWT Layer-wise theory NURBS Non-Uniform Rational B-splines RBF Radial Basis Function RPIM Radial point interpolation method RPT Refined plate theory SCFs Shear correction factors SSDT Sinusoidal shear deformation theory TrSDT Trigonometric shear deformation theory TSDT Third-order shear deformation theory UTSDT Unconstrained third-order shear deformation theory ix UISDT Unconstrained inverse trigonometric shear deformation theory USSDT Unconstrained sinousoidal shear deformation theory DOF Degree of Freedom C, S, F Clamped, simply supported, and free boundary conditions FGPM Functionally graded piezoelectric material FGPMP Functionally graded piezoelectric material with porosity ES-DSG3 Edge-based smoothed and discrete shear gap plate element GDQ Generalized differential quadrature GPLs Graphene platelets CNTs Carbon nanotubes PFGP Piezoelectric functionally graded porous plate NL Nonlinear DKQ Discrete Kirchhoff quadrilateral FGP Functionally graded porous PFGP Piezoelectric functionally graded porous GPLs Graphene platelets PFGP-GPLs Piezoelectric functionally graded porous reinforced by graphene platelets FGPM Functionally graded piezoelectric material FGPMP Functionally graded piezoelectric material porous x LIST OF TABLES Table 3. 1: The various forms of shape function.
2: Three used forms of distributed functions and their derivatives. 1: Convergence of the normalized displacement and stresses of a four-layer [00/900/900/00] laminated composite square plate (a/h = 4). 2: Normalized displacement and stresses of a simply supported [00/900/900/00] square laminated plate under a sinusoidally distributed load. 3: Control points and weights for a circular plate with a radius of R = 0.
4: The transverse displacement w(0,0,0) and in-plane stress x of isotropic circular plate with various R/H ratios. 5: The deflection w(0,0,0)x102 (mm) of three-layer symmetrical isotropic and laminated composite circular plates. 6: The first non-dimensional frequency parameter of a four-layer [00/900/900/00] laminated composite square plate (a/h = 5). 7: The non-dimensional frequency parameter of a four-layer [00/900/900/00] simply supported laminated square plate ( E1 / E2 = 40 ).
8: First non-dimensional frequency parameters of a four-layer [ 0 / − 0 / − 0 / 0 ] laminated circular plate (R/h = 5). 9: First six non-dimensional frequency parameters of a four-layer [ 0 / − 0 / − 0 / 0 ] clamped laminated circular plate (R/h = 5). 10: The properties of the piezoelectric composite plates. 11: Central control point/node deflection of the simply supported piezoelectric composite plate subjected to a uniform load and different input voltages (10-4 m).
The first ten natural frequencies of the CCCC elliptical piezoelectric composite plate. The first ten natural frequencies of the SSSS elliptical piezoelectric composite plate. 2: Comparison of convergence of the natural frequency (rad/s) for a sandwich simply supported FGP square plater reinforced by GPLs with different Bézier control meshes. 3: Tip node deflection of the cantilevered piezoelectric FGM plate subjected to a uniform load and different input voltages (10-3 m).
4: Tip node deflection w.10−3 (m) of a cantilever PFGP-GPLs plate for various porosity coefficients with GPL = 0 under a uniform loading and different input voltages. 5: Tip node deflection w.10−3 (m) of a cantilever PFGP-GPLs plate for three GPL patterns with GPL = 1wt % and e0 =0.2 under a uniform loading and different input voltages. 6: Normalized central deflection w of CCCC isotropic square plate under the uniform load with a/h = 100. 7: Tip node deflection of the cantilever piezoelectric FGM plate subjected to the uniform load and various input voltages (x 10-4 m).
Comparison of convergence of the first non-dimensional frequency of a perfect FGPM plate ( = 0 ) with different electric voltages for the simply supported boundary condition. 3: Comparison of the first dimensionless frequency of an imperfect FGPM plate ( = 0.2 ) with different electric voltages for the simply supported boundary conditions. 4: Comparison of non-dimensional frequency of a perfect FGPM plate with different boundary conditions ( = 0 ). 5: Non-dimensional frequency of an imperfect FGPM plate ( = 0.2 ) with different boundary conditions.
6: Comparisons of non-dimensional frequencies = c / Ec of the h FG square plate with a hole of complicated shape (a=b=10, a/h=20). 7: The first dimensionless frequency = b2 / h ( / c11 ) of a FGPMP PZT − 4 square plate with a complicated cutout ( = 0 ) with different electric voltages (a=b=10, a/h=20). 8: The first dimensionless frequency of a square FGPMP plate with a complicated cutout ( = 0.2 ) with different electric voltages (a=b=10, a/h=20). 9: The first dimensionless frequency of a square FGPMP plate with a complicated cutout with various side-to-thickness ratios (a=b=10, = 0.
10: First six non-dimensional frequencies = R2 ( h / Dm )1/2 of the fully clamped isotropic circular plate (R/h=5). 11: The first dimensionless frequency = 4 R 2 / h ( / c11 ) of a perfect PZT − 4 FGPMP circular plate ( = 0 ) with different electric voltages and power index parameters for SSSS and CCCC BCs (R/h=5). 12: The first dimensionless frequency = 4 R 2 / h ( / c11 ) of an PZT − 4 imperfect FGPM circular plate ( = 0.5 ) with different electric voltages and power index parameters for SSSS and CCCC BCs (R/h=5). 13: The first dimensionless frequency = 4 R 2 / h ( / c11 ) of a PZT − 4 circular FGPMP plate with various side-to-thickness ratios ( = 0.
14: Comparisons of the frequencies (Hz) of the FG annular plate (R/h=20). 15: The first natural frequency (Hz) of a FGPMP annular plate with different electric voltages and power index values (R=2m; r=0.