Luận án tiến sĩ: Ứng xử tĩnh ổn định và dao động dầm composite tiết diện khác nhau - Nguyễn Ngọc Dương

Declaration I declare that this thesis is all my own work based on instruction of Associate Professor Dr. Trung-Kien Nguyen and Dr. The work contained in this thesis has not been submitted for any other award. Name: Ngoc-Duong Nguyen Signature: ii Acknowledgement Firstly, I wish to express my deep gratitude to my advisor, Associate Professor Dr.

Trung-Kien Nguyen, for his warm guidance, suggestions and support during my study. He has influenced my career by coaching me the work ethics and responsibilities, along with research skills, which are required of a good researcher. The completion of this work would not have been possible without his detailed advice, constructive criticism and constant encouragement and patience. I am also extremely grateful to Dr.

Vo at Northumbria University who generously spent a great deal of time providing me with alternative viewpoints to my ideas through many helpful discussions. His invaluable knowledge, experience and moral support proved to be of inestimable value to the revision and completion of this thesis. In addtion, I am grateful to Dr. Huu-Tai Thai for his comments in my publications, and Mr.

Thien-Nhan Nguyen for sharing his Matlab code. My special thanks are extended to my colleagues at Department of Structural Engineering in Falcuty of Civil Engineering, HCMC University Technology and Education, who have offered me intellectual stimulation, friendship and provided a warm and inspiring environment. Finally, I wish to express my deep appreciation to my family and wife for their continued encouragement and support during my study. Without their presence, this work would have never been possible.

Ngoc-Duong Nguyen iii Abstract Composite materials are widely used in many engineering fields owing to their high stiffness-to-weight, strength-to-weight ratios, low thermal expansion, enhanced fatigue life and good corrosive resistance. Among them, laminated composite beams are popular in application and attract a huge attention from reseacher to study their structural behaviours. Many theories are proposed for the bending, buckling and vibration analysis. They can be divided into classical beam theory (CBT), first-order beam theory (FOBT), higher-order beam theory (HOBT) and quasi-three dimension (quasi-3D) beam theory.

It should be noted that classical continuum mechanics theories are just suitable for macro beams. For analysing microbeams, researchers proposed many non-classical theories. Among them, the modified couple stress theory (MCST) is the most popular and commonly applied owing to its simplicity in formulation and programming. In order to accurately predict behaviours of beams, a large number of methods are developed.

Numerical approaches are used increasingly, however, analytical methods are also used by researchers owing to their accuracy and efficiency. Among analytical approaches, Ritz method is the most general one, which accounts for various boundary conditions, however, it has seldom been used to analyse the bending, buckling and free vibration behaviours of beams. This is also the main motivation of this study. This dissertation focuses on propsing new approximation functions to analyse laminated composite beams with various cross-sections and boundary conditions.

The displacement field is based on the FOBT, HOBT and quasi-3D theories. Size- dependent effect for microbeams is investigated using the MCST. Poisson’s effect is considered by integrating in the constitutive equations. The governing equations of motion are derived from Lagrange’s equations.

Numerical results for beam with various boundary conditions are presented and compared with existing ones available in the literature. The effects of fiber angle, length-to-height ratio, material anisotropy, shear and normal strains on the displacements, stresses, natural frequencies, mode shape and buckling loads of the composite beams are investigated. Some of numerical iv results are presented at the first time and can be used as the benchmark results for numerical methods. Besides, a study on efficacy of approximation functions for analysis of laminated composite beams with simply-supported boundary conditions is carried out.

v List of Publications ISI papers with peer-reviews: 1. Lee, Vibration and buckling behaviours of thin-walled composite and functionally graded sandwich I-beams, Composites Part B: Engineering. Thai, Ritz-based analytical solutions for bending, buckling and vibration behavior of laminated composite beams, International Journal of Structural Stability and Dynamics. Vo, A Ritz type solution with exponential trial functions for laminated composite beams based on the modified couple stress theory, Composite Structures.

Thai, New Ritz- solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams, Composite Structures. Thai, Trigonometric-series solution for analysis of laminated composite beams, Composite Structures. Domestic papers with peer-reviews: 6. Nguyen, Effects of transverse normal strain on bending of laminated composite beams, Vietnam Journal of Mechanics.

Nguyen, Dynamic analysis of composite beams resting on winkler foundation, Vietnam Journal of Construction (8-2017) 123- 129. Nguyen, Ritz solution for buckling analysis of thin-walled composite channel beams based on a classical beam theory, Journal of Science and Technology in Civil Engineering (STCE)-NUCE. vi Conference papers: 9. Vo, Bending Analysis of Laminated Composite Beams Using Hybrid Shape Functions, International Conference on Advances in Computational Mechanics.

Nguyen, Free vibration analysis of laminated composite beams based on higher – order shear deformation theory. Proceeding of National Conference-Composite Material and Structure (2016) 157-164. Vo, Hybrid-shape-functions for free vibration analysis of thin-walled laminated composite I-beams with different boundary conditions, Proceeding of National Mechanical Conference (2017) 424- 433 vii Table of content Lý lịch cá nhân. iv List of Publications.

vi Table of content.viii List of Figures .xii List of Tables. Necessity of the thesis. Composite material - Fiber and matrix. Composite material - Lamina and laminate.

Objectives and scopes of the thesis. ANALYSIS OF LAMINATED COMPOSITE BEAMS BASED ON A HIGH-ORDER BEAM THEORY. Beam model based on the HOBT. Kinetic, strain and stress relations.

Vibration and buckling analysis. VIBRATION AND BUCKLING ANALYSIS OF LAMINATED COMPOSITE BEAMS UNDER THERMO-MECHANICAL LOAD. Beam model based on the HOBT. EFFECT OF TRANSVERSE NORMAL STRAIN ON BEHAVIOURS OF LAMINATED COMPOSITE BEAMS.

Kinetic, strain and stress relations. Cross-ply beams. Angle-ply beams. Arbitrary-ply beams.

SIZE DEPENDENT BEHAVIOURS OF MICRO GENERAL LAMINATED COMPOSITE BEAMS BASED ON MODIFIED COUPLE STRESS THEORY. Convergence and accuracy studies. Vibration and buckling analysis. ANALYSIS OF THIN-WALLED LAMINATED COMPOSITE BEAMS BASED ON FIRST-ORDER BEAM THEORY.

Functionally graded sandwich I-beams. Composite channel-beams. CONVERGENCY, ACCURARY AND NUMERICAL STABILITY OF RITZ METHOD. Results of comparative study.

CONCLUSIONS AND RECOMMENDATIONS. Disadvantages and recommendations. 157 The coefficients in Eq. 157 The coefficients in Eq.

157 The coefficients in Eqs. 157 The coefficients in Eq. 157 The coefficients in Eq. 158 The coefficients in Eq.

158 The coefficients in Eq. 159 The coefficients in Eq. 159 The coefficients in Eq. 161 xi List of Figures Figure 1.

Composite material classification [1]. Various types of fiber-reinforced composite lamina [1]. A laminate made up of laminae with different fiber orientations [1]. Composite material applied in engineering field.

Material used in Boeing 787. Geometry and coordinate of a rectangular laminated composite beam. Geometry and coordinate of a laminated composite beam. Distribution of the normalized stresses (  xx ,  xz ) through the beam depth of (00/900/00) and (00/900) composite beams with simply-supported boundary conditions (MAT II.

Effects of the fibre angle change on the normalized transverse displacement of  /  s composite beams ( L / h  10 , MAT II.The first three mode shapes of (00/900/00) and (00/900) composite beams with simply-supported boundary conditions (L/h = 10, MAT I. Effects of material anisotropy on the normalized fundamental frequencies and critical buckling loads of (00/900/00) and (00/900) composite beams with simply-supported boundary conditions ( L / h  10 , MAT I. Effects of the fibre angle change on the normalized fundamental frequencies and critical buckling loads of  /   s composite beams ( L / h  15 , MAT III. Effects of the length-to-height ratio on the normalized fundamental frequencies and critical buckling loads of  30 / 30 s composite beams ( L / h  15 , MAT III.

Variation of fundamental frequency of (00/900/00) and (00/900) beams (MAT II.3) with respect to uniform temperature rise ∆T. Effect of 2 / 1 ratio on nondimensional critical buckling temperature of (00/900/00) composite beams (MAT I. Distribution of nondimensional transverse displacement through the thickness of (00/900) and (00/900/00) composite beams with S-S boundary condition (MAT II. Distribution of nondimensional transverse displacement through the thickness of (00/900) and (00/900/00) composite beams with C-F boundary condition (MAT II.

Distribution of nondimensional transverse displacement through the thickness of (00/900) and (00/900/00) composite beams with C-C boundary condition (MAT II. The nondimensional mid-span transverse displacement with respect to the fiber angle change of composite beams with S-S boundary condition ( L / h  3 , MAT II. The nondimensional mid-span transverse displacement with respect to the fiber angle change of composite beams with C-F boundary condition ( L / h  3 , MAT II. The nondimensional mid-span transverse displacement with respect to the fiber angle change of composite beams with C-C boundary condition ( L / h  3 , MAT II.

Effects of the fiber angle change on the nondimensional fundamental frequency of  /   s composite beams (MAT IV. Geometry and coordinate of a laminated composite beam. Rotation displacement about the x’-, y’-axes. Comparison of critical buckling loads of S-S beams (MAT I.

Comparison of fundamental frequencies of S-S beams (MAT I. Comparison of displacement and normal stress of  900 / 00 / 900  S-S beams (MAT II. Effect of MLSP on displacements of S-S beams (MAT II. Effect of MLSP on displacements of C-F beams (MAT II.

Effect of MLSP on displacements of C-C beams (MAT II, L / h  4 ). Effect of MLSP on displacements of beams with various BCs (MAT II. Effect of MLSP on through-thickness distribution of stresses of. Effect of MLSP on through-thickness distribution of stresses of.

Effect of MLSP on frequencies of beams with various BC (MAT III. Effect of MLSP on buckling loads of beams with various BCs (MAT III. Thin-walled coordinate systems. Geometry of thin-walled I-beams.

Variation of the fundamental frequencies (Hz) of thin-walled C-C I-beams with respect to fiber angle. Variation of the critical buckling loads (N) of thin-walled C-C I-beams with respect to fiber angle. Shear effect on the fundamental frequency for various BCs. Shear effect on the critical buckling loads for various BCs.

Shear effect on first three natural frequencies of thin-walled C-C I-beams. Variation of E33 / E77 ratio with respect to . Mode shape 1 of thin-walled C-C I-beams. Mode shape 2 of thin-walled C-C I-beams.

Mode shape 3 of thin-walled C-C I-beams. Non-dimensional fundamental frequency for various BCs. Non-dimensional critical buckling load for various BCs. Non-dimensional fundamental frequency of thin-walled FG sandwich I- beams.

Non-dimensional fundamental frequency with respect to 1, 2 ( 1  2 ,   0. Non-dimensional critical buckling load with respect to 1, 2 (   0. Non-dimensional fundamental frequency with respect to . Non-dimensional critical buckling load with respect to .

Shear effect on fundamental frequency for various BCs. Shear effect on critical buckling load for various BCs. Shear effect on first three frequency of C-C I-beams with respect to material parameter. Geometry of thin-walled composite channel beams.

Shear effect on fundamental frequency for various BCs. Shear effect on critical buckling load for various BCs. Distance of fundamental frequency. Distance of critical buckling load.

Distance of deflection. Elapsed time to compute frequency. Elapsed time to compute critical buckling load. Elapsed time to compute deflection.

Maximun eigen value-to-Minimun eigen value ratio. 152 xv List of Tables Table 1. Shear variation functions f ( z ). Approximation functions of the beams.

Kinematic BCs of the beams. Convergence studies for the non-dimensional fundamental frequencies, critical buckling loads and mid-span displacements of (00/900/00) composite beams (MAT I. Normalized mid-span displacements of (00/900/00) composite beam under a uniformly distributed load (MAT II.