Laminated Composite Plates and Shells

Transcription

1 Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer

2 Table of Contents 1. Introduction to Composite Materials Introduction Classification of Composite Materials Fibre Composites Particle Composites Laminated Composites Characterisation of Unidirectional Fibre Composite Materials Mechanics of Material Approach to the Moduli Elasticity Approach to the Moduli Three-dimensional Modelling of Laminated Composite Materials Three-dimensional Analytical Modelling of Laminated Composite Plates and Shells Three-dimensional Numerical Modelling of Laminated Composite Plates and Shells Fundamental Equations of Three-dimensional Elasticity Introduction Equilibrium Equations of Stresses Strain-Displacement Relations Stress-Strain Relations Hooke's Law of Elasticity Engineering Constants for Stress-Strain Relations of Orthotropic Materials Engineering Constants for Stress-Strain Relations of a Lamina State Variable Equation of a Continuous System Introduction Concept of State and State Variables Solutions for a Linear Time-invariant System The Eigenvalue Problem Diagonalisation of Square Matrices Calculation of e A " by Series Expansions 41

3 xii Table of Contents Calculation of e A ' by Matrix Transformation Calculation of e 1 A ' by the Cayley-Hamilton Method Calculation of e A " by the Time Step Integration Method Solutions for a Time-varying System The Successive Approximation Method for Homogeneous Equations The Successive Approximation Method for Non-homogeneous Equations State Variable Equation of Elasticity Bending, Vibration and Buckling of Laminated Rectangular Plates Introduction Free Vibration of Cross-ply Laminated Plates Free Vibration of Simply Supported Plates Free Vibration of Single-layered Plates Free Vibration of Laminated Plates Free Vibration of Plates with Clamped Edges Buckling of Cross-ply Laminated Plates Bending of Cross-ply Laminated Plates ; Bending of Simply Supported Laminated Plates Bending of Laminated Plates with Clamped Edges Bending of Laminated Plates with Free Edges Other Topics on Plate Bending Bending of Laminated Continuous Plates Bending of Laminated Piezoelectric Plates Asymptotic Three-dimensional Solution Axisymmetric Vibration, Buckling and Bending of Laminated Plates with Transversely Isotropic Layers Introduction Axisymmetric Free Vibration of Laminated Plates Axisymmetric Vibration of Laminated Circular Plates Axisymmetric Vibration of Laminated Annular Plates State Space Solution State Space with Hankel Transform Method Axisymmetric Buckling of Laminated Plates Axisymmetric Buckling of Laminated Circular Plates Axisymmetric Buckling of Laminated Annular Plates Axisymmetric Bending of Laminated Circular Plates Axisymmetric Bending of Circular Plates Under Uniformly Distributed Transverse Pressure Axisymmetric Bending of Circular Plates on Winkler's Foundation Vibration, Buckling and Bending of Laminated Cylindrical Shells Introduction 127

4 Table of Contents xiii 6.2 Vibration of Laminated Cylindrical Shells Vibration of Simply Supported Laminated Cylindrical Shells Free Vibration of Simply Supported Laminated Cylindrical shells Forced Vibration of Simply Supported Laminated Cylindrical Shells Axisymmetric Vibration of Simply Supported Laminated Cylinders Composed of Monoclinic Material Layers Free Vibration of Cross-ply Laminated Cylindrical Shells with Clamped Edges Free Vibration of Cross-ply Laminated Cylindrical Shells with Interior Point Supports Axisymmetric Vibration of Cross-ply Laminated Cylinders with Ring Stiffeners Buckling of Laminated Cross-ply Cylindrical Shells Pre-buckling State in a Thin Orthotropic Layer Perturbed State in a Thin Orthotropic Layer Solution for Thick or Laminated Cylindrical Shells Buckling of Multi-laminated Angle-ply Cylindrical Shells Bending of Laminated Cylindrical Shells Bending of Simply Supported Cylindrical Shells Bending of Cross-ply Laminated Cylindrical Shells Axisymmetric Bending of Angle-ply Laminated Cylinders Bending of Cross-ply Laminated Cylinders with Clamped Edges Bending of Cross-ply Laminated Cylinders with Free Edges Bending of Laminated Continuous Cylinders Generalized Plane Strain, Torsion and Bending of Laminated Cylinders Stationary Thermo-elastic Bending of Laminated Cylinders 186 7, Analysis of Laminated Shells of Various Shapes Introduction Free Vibration of Transversely Isotropic Spheres Free Axisymmetric Vibration of Transversely Isotropic Thin Spheres Free Axisymmetric Vibration of a Laminated Thick Sphere Composed of Transversely Isotropic Layers Static Analysis of Piezoelectric Hollow Spheres Free Vibration of Doubly-curved Shells Bending of Anisotropic Inhomogeneous, Non-circular Cylinders Decay of Edge Effects in Laminated Composites Introduction 207

5 xiv Table of Contents 8.2 Decay Rate of Stresses in Hollow Cylinders with Cross-ply Lay-ups Decay Rate of Stresses in Hollow Cylinders with Angle-ply Lay-ups Decay of Stresses in Laminated Strips Semi-analytical State Equation Method Introduction Semi-analytical State Space Finite Element Method for Laminated Plates Matrix Representation of the Three-dimensional Equations of Elasticity The Principle of Virtual Displacements The Principle of Virtual Forces Finite Element Approximation in the Plane of a Plate State Equation of the Semi-analytical FE Solution Semi-analytical Finite Difference State Equation Method for Laminated Plates and Shells General Formulation Finite Difference Approximation State Space Boundary Element Method Derivation of the Fundamental Solution The Boundary Element Method Semi-analytical Variational State Space Method for Laminated Plates and Shells Galerkin Weighting and State Space Method Weighted Form of State Equation 255 References 257 Index 269