1 Traditional Perturbation Method 1
1.1 Introduction 1
1.2 Load-type Perturbation Method 2
1.3 Deflection-type Perturbation Method 3
1.4 Multi-parameter Perturbation Method 4
1.5 Limitations of the Traditional Perturbation Method 5
References 6
2 Nonlinear Analysis of Beams 9
2.1 Introduction 9
2.2 Nonlinear Motion Equations of Euler-Bernoulli Beams 10
2.3 Postbuckling Analysis of Euler-Bernoulli Beams 13
2.4 Nonlinear Bending Analysis of Euler-Bernoulli Beams 17
2.5 Large Amplitude Vibration Analysis of Euler-Bernoulli Beams 21
References 25
3 Nonlinear Vibration Analysis of Plates 27
3.1 Introduction 27
3.2 Reddy's Higher Order Shear Deformation Plate Theory 29
3.3 Generalized Kármán-type Motion Equations 35
3.4 Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Plates 42
3.5 Hygrothermal Effects on the Nonlinear Vibration of Shear Deformable Laminated Plate 63
3.6 Nonlinear Vibration of Shear Deformable Laminated Plates with PFRC Actuators 69
References 74
4 Nonlinear Bending Analysis of Plates 79
4.1 Introduction 79
4.2 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and In-plane Loads and Resting on Two-parameter Elastic Foundations 80
4.3 Nonlinear Bending of Rectangular Plates with Free Edges under Transverse and Thermal Loading and Resting on Two-parameter Elastic Foundations 91
4.4 Nonlinear Bending of Rectangular Plates with Free Edges Resting on Tensionless Elastic Foundations 94
4.5 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and In-plane Loads 97
4.6 Nonlinear Bending of Shear Deformable Laminated Plates under Transverse and Thermal Loading 109
4.7 Nonlinear Bending of Functionally Graded Fiber Reinforced Composite Plates 116
Appendix 4.A 126
Appendix 4.B 131
Appendix 4.C 132
Appendix 4.D 133
Appendix 4.E 136
Appendix 4.F 137
References 141
5 Postbuckling Analysis of Plates 145
5.1 Introduction 145
5.2 Postbuckling of Thin Plates Resting on Tensionless Elastic Foundation 147
5.3 Postbuckling of Shear Deformable Laminated Plates under Compression and Resting on Tensionless Elastic Foundations 163
5.4 Thermal Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations 171
5.5 Thermomechanical Postbuckling of Shear Deformable Laminated Plates Resting on Tensionless Elastic Foundations 178
5.6 Postbuckling of Functionally Graded Fiber Reinforced Composite Plates under Compression 185
5.7 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Plates 194
5.8 Postbuckling of Shear Deformable Hybrid Laminated Plates with PFRC Actuators 200
References 211
6 Nonlinear Vibration Analysis of Cylindrical Shells 215
6.1 Introduction 215
6.2 Reddy's Higher Order Shear Deformation Shell Theory and Generalized Kármán-type Motion Equations 216
6.3 Nonlinear Vibration of Shear Deformable Cross-ply Laminated Cylindrical Shells 219
6.4 Nonlinear Vibration of Shear Deformable Anisotropic Cylindrical Shells 233
6.5 Hygrothermal Effects on the Nonlinear Vibration of Functionally Graded Fiber Reinforced Composite Cylindrical Shells 252
6.6 Nonlinear Vibration of Shear Deformable Laminated Cylindrical Shells with PFRC Actuators 257
Appendix 6.G 263
References 269
7 Postbuckling Analysis of Cylindrical Shells 273
7.1 Introduction 273
7.2 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under Axial Compression 274
7.3 Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells under External Pressure 295
7.4 Thermal Postbuckling of Functionally Graded Fiber Reinforced Composite Cylindrical Shells 312
7.5 Postbuckling of Axially Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium 320
7.6 Postbuckling of Internal Pressure Loaded Anisotropic Cylindrical Shells Surrounded by an Elastic Medium 325
Appendix 7.H 331
Appendix 7.I 339
Appendix 7.J 341
References 344
Index 349