1 Fundamental Equations of Laminated Beams，Plates and Shells. 1
1.1 Three-Dimensional Elasticity Theory in Curvilinear Coordinates 1
1.2 Fundamental Equations of Thin Laminated Shells 3
1.2.1 Kinematic Relations 3
1.2.2 Stress-Strain Relations and Stress Resultants 5
1.2.3 Energy Functions 9
1.2.4 Governing Equations and Boundary Conditions 11
1.3 Fundamental Equations of Thick Laminated Shells 16
1.3.1 Kinematic Relations 17
1.3.2 Stress-Strain Relations and Stress Resultants 18
1.3.3 Energy Functions 23
1.3.4 Governing Equations and Boundary Conditions 26
1.4 Lamé Parameters for Plates and Shells. 29
2 Modified Fourier Series and Rayleigh-Ritz Method 37
2.1 Modified Fourier Series 38
2.1.1 Traditional Fourier Series Solutions. 39
2.1.2 One-Dimensional Modified Fourier Series Solutions 43
2.1.3 Two-Dimensional Modified Fourier Series Solutions 48
2.2 Strong Form Solution Procedure 53
2.3 Rayleigh-Ritz Method (Weak Form Solution Procedure) 58
3 Straight and Curved Beams 63
3.1 Fundamental Equations of Thin Laminated Beams 64
3.1.1 Kinematic Relations 64
3.1.2 Stress-Strain Relations and Stress Resultants 65
3.1.3 Energy Functions 66
3.1.4 Governing Equations and Boundary Conditions 68
3.2 Fundamental Equations of Thick Laminated Beams. 71
3.2.1 Kinematic Relations 71
3.2.2 Stress-Strain Relations and Stress Resultants 72
3.2.3 Energy Functions 73
3.2.4 Governing Equations and Boundary Conditions 74
3.3 Solution Procedures 76
3.3.1 Strong Form Solution Procedure 77
3.3.2 Weak Form Solution Procedure (Rayleigh-Ritz Procedure) 80
3.4 Laminated Beams with General Boundary Conditions 83
3.4.1 Convergence Studies and Result Verification 83
3.4.2 Effects of Shear Deformation and Rotary Inertia 85
3.4.3 Effects of the Deepness Term (1+z/R). 87
3.4.4 Isotropic and Laminated Beams with General Boundary Conditions. 90
4 Plates 99
4.1 Fundamental Equations of Thin Laminated Rectangular Plates. 100
4.1.1 Kinematic Relations 100
4.1.2 Stress-Strain Relations and Stress Resultants 102
4.1.3 Energy Functions 103
4.1.4 Governing Equations and Boundary Conditions 105
4.2 Fundamental Equations of Thick Laminated Rectangular Plates. 107
4.2.1 Kinematic Relations 108
4.2.2 Stress-Strain Relations and Stress Resultants 108
4.2.3 Energy Functions 109
4.2.4 Governing Equations and Boundary Conditions 111
4.3 Vibration of Laminated Rectangular Plates 113
4.3.1 Convergence Studies and Result Verification 116
4.3.2 Laminated Rectangular Plates with Arbitrary Classical Boundary Conditions 117
4.3.3 Laminated Rectangular Plates with Elastic Boundary Conditions. 122
4.3.4 Laminated Rectangular Plates with Internal Line Supports. 125
4.4 Fundamental Equations of Laminated Sectorial， Annular and Circular Plates 131
4.4.1 Fundamental Equations of Thin Laminated Sectorial， Annular and Circular Plates 134
4.4.2 Fundamental Equations of Thick Laminated Sectorial， Annular and Circular Plates 137
4.5 Vibration of Laminated Sectorial， Annular and Circular Plates 139
4.5.1 Vibration of Laminated Annular and Circular Plates 139
4.5.2 Vibration of Laminated Sectorial Plates 144
5 Cylindrical Shells 153
5.1 Fundamental Equations of Thin Laminated Cylindrical Shells 156
5.1.1 Kinematic Relations 156
5.1.2 Stress-Strain Relations and Stress Resultants 157
5.1.3 Energy Functions 158
5.1.4 Governing Equations and Boundary Conditions 159
5.2 Fundamental Equations of Thick Laminated Cylindrical Shells 162
5.2.1 Kinematic Relations 162
5.2.2 Stress-Strain Relations and Stress Resultants 163
5.2.3 Energy Functions 165
5.2.4 Governing Equations and Boundary Conditions 167
5.3 Vibration of Laminated Closed Cylindrical Shells 169
5.3.1 Convergence Studies and Result Verification 172
5.3.2 Effects of Shear Deformation and Rotary Inertia 175
5.3.3 Laminated Closed Cylindrical Shells with General End Conditions 177
5.3.4 Laminated Closed Cylindrical Shells with Intermediate Ring Supports 184
5.4 Vibration of Laminated Open Cylindrical Shells 188
5.4.1 Convergence Studies and Result Verification 192
5.4.2 Laminated Open Cylindrical Shells with General End Conditions 193
6 Conical Shells. 199
6.1 Fundamental Equations of Thin Laminated Conical Shells 200
6.1.1 Kinematic Relations 201
6.1.2 Stress-Strain Relations and Stress Resultants 201
6.1.3 Energy Functions 202
6.1.4 Governing Equations and Boundary Conditions 202
6.2 Fundamental Equations of Thick Laminated Conical Shells 207
6.2.1 Kinematic Relations 208
6.2.2 Stress-Strain Relations and Stress Resultants 209
6.2.3 Energy Functions 210
6.2.4 Governing Equations and Boundary Conditions 211
6.3 Vibration of Laminated Closed Conical Shells 215
6.3.1 Convergence Studies and Result Verification 217
6.3.2 Laminated Closed Conical Shells with General Boundary Conditions. 219
6.4 Vibration of Laminated Open Conical Shells 225
6.4.1 Convergence Studies and Result Verification 227
6.4.2 Laminated Open Conical Shells with General Boundary Conditions. 228
7 Spherical Shells 235
7.1 Fundamental Equations of Thin Laminated
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