vi CONTENTS 2.10 Strain Energy 55 2.10.1 The Ritz Method 5 2.11 Summary 56 2.11.1 Note on the Compliance and Stiffness Matrices 56 3 Laminated Composites 63 3.1 Laminate Code 63 3.2 Stiffness Matrices of Thin Laminates 65 3.2.1 The Significance of the [A],B],and [D]Stiffness Matrices 72 3.2.2 Stiffness Matrices for Selected Laminates 74 4 Thin Plates 89 4.1 Governing Equations 90 4.1.1 Boundary Conditions 92 4.1.2 Strain Energy 92 4.2 Deflection of Rectangular Plates 93 4.2.1 Pure Bending and In-Plane Loads 93 4.2.2 Long Plates 94 4.2.3 Simply Supported Plates-Symmetrical Layup 100 4.2.4 Plates with Built-In Edges-Orthotropic and Symmetrical Layup 107 4.3 Buckling of Rectangular Plates 112 4.3.1 Simply Supported Plates-Symmetrical Layup 112 4.3.2 Plates with Built-In and Simply Supported Edges-Orthotropic and Symmetrical Layup 118 4.3.3 Plates with One Free Edge-Orthotropic and Symmetrical Layup 124 4.3.4 Plates with Rotationally Restrained Edges-Orthotropic and Symmetrical Layup 127 4.3.5 Long Plates 132 4.4 Free Vibration of Rectangular Plates 141 4.4.1 Long Plates 141 4.4.2 Simply Supported Plates-Symmetrical Layup 144 4.4.3 Plates with Built-In and Simply Supported Edges-Orthotropic and Symmetrical Layup 149 4.5 Hygrothermal Effects 151 4.5.1 Change in Thickness Due to Hygrothermal Effects 161 4.6 Plates with a Circular or an Elliptical Hole 163 4.7 Interlaminar Stresses 166 5 Sandwich Plates 169 5.1 Governing Equations 170 5.1.1 Boundary Conditions 172 5.1.2 Strain Energy 173 5.1.3 Stiffness Matrices of Sandwich Plates 174 5.2 Deflection of Rectangular Sandwich Plates 178 5.2.1 Long Plates 178 5.2.2 Simply Supported Sandwich Plates-Orthotropic and Symmetrical Layup 182vi CONTENTS 2.10 Strain Energy 55 2.10.1 The Ritz Method 55 2.11 Summary 56 2.11.1 Note on the Compliance and Stiffness Matrices 56 3 Laminated Composites 63 3.1 Laminate Code 63 3.2 Stiffness Matrices of Thin Laminates 65 3.2.1 The Significance of the [A], [B], and [D] Stiffness Matrices 72 3.2.2 Stiffness Matrices for Selected Laminates 74 4 Thin Plates 89 4.1 Governing Equations 90 4.1.1 Boundary Conditions 92 4.1.2 Strain Energy 92 4.2 Deflection of Rectangular Plates 93 4.2.1 Pure Bending and In-Plane Loads 93 4.2.2 Long Plates 94 4.2.3 Simply Supported Plates – Symmetrical Layup 100 4.2.4 Plates with Built-In Edges – Orthotropic and Symmetrical Layup 107 4.3 Buckling of Rectangular Plates 112 4.3.1 Simply Supported Plates – Symmetrical Layup 112 4.3.2 Plates with Built-In and Simply Supported Edges – Orthotropic and Symmetrical Layup 118 4.3.3 Plates with One Free Edge – Orthotropic and Symmetrical Layup 124 4.3.4 Plates with Rotationally Restrained Edges – Orthotropic and Symmetrical Layup 127 4.3.5 Long Plates 132 4.4 Free Vibration of Rectangular Plates 141 4.4.1 Long Plates 141 4.4.2 Simply Supported Plates – Symmetrical Layup 144 4.4.3 Plates with Built-In and Simply Supported Edges – Orthotropic and Symmetrical Layup 149 4.5 Hygrothermal Effects 151 4.5.1 Change in Thickness Due to Hygrothermal Effects 161 4.6 Plates with a Circular or an Elliptical Hole 163 4.7 Interlaminar Stresses 166 5 Sandwich Plates 169 5.1 Governing Equations 170 5.1.1 Boundary Conditions 172 5.1.2 Strain Energy 173 5.1.3 Stiffness Matrices of Sandwich Plates 174 5.2 Deflection of Rectangular Sandwich Plates 178 5.2.1 Long Plates 178 5.2.2 Simply Supported Sandwich Plates – Orthotropic and Symmetrical Layup 182