THEORY AND ANALYSIS OF LAMINATED COMPOSITE AND FUNCTINALLY GRADED BEAMS, PLATES, AND SHELLS

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1 THEORY AND ANALYSIS OF LAMINATED COMPOSITE AND FUNCTINALLY GRADED BEAMS, PLATES, AND SHELLS J. N. Reddy Texas A&M University College Station, TX USA * This document contains a copy of the overheads used in the course. Much of the material used in the course comes from the instructor s book, Mechanics of Laminated Composite Plates and Shells (2 nd ed., CRC Press, 2004); other material comes from the researchpublications of the lecturer.

2 THEORY AND ANALYSIS OF LAMINATED COMPOSITE AND FUNCTINALLY GRADED BEAMS AND PLATES CONTENTS Composite Materials: General Introduction Laminate Theories (CLPT and FSDT) Finite Element Models FGM Beams and Plates Nonlocal Elasticity of Eringen for Beams Modified Couple Stress Theory of Beams and Plates Strain Gradient Theory of Srinivasa and Reddy Summary of the Course and Closing Comments Preliminaries: - 2

3 COMPOSITE MATERIALS: General Introduction Composite Materials - Definition The Big Picture The Role of Stress Analysis Classification of Composites Advantages and Disadvantages of Composites Use of Composite Materials in Aerospace Structures Study Areas in Composites Structural Analysis of Composite Structures Mechanical Characterization NOTE: Minor changes are made here and there to the viewgraphs without adding any major new material. J N Reddy General Introduction 3

4 PRIMARY REFERENCE on mechanics of composite materials J. N. Reddy, Mechanics of Laminated Composite Plates and Shells, 2 nd ed., CRC Press, 2004 (introduction to the theory and analysis - analytical as well as FEM - of laminated composite plates and shells) A list of papers authored by is provided at the end of this lecture notes. References to the works of many other authors can be found in References cited in the author s papers. General Introduction 4

5 COMPOSITE MATERIALS-Definition Definition: Two or more materials combined on a macroscopic scale to form a useful third material Properties to be Improved: Strength, stiffness, weight, fatigue life, wear resistance, thermal insulation, thermal conductivity, corrosion resistance, acoustical insulation, etc. General Introduction 5

6 THE BIG PICTURE Manufacturing Process Modeling & Simulation Tooling, Machining, Assembly Materials Characterization Stiffness, Strength, Toughness Cost Analysis Cost/Performance, Trade-offs Performance Evaluation Durability, Damage Tolerance General Introduction 6

7 THE ROLE OF STRESS ANALYSIS Initial Deformation Models Stress Analysis Stress/strain/Temp at Critical Sites Service Loading Damage Mechanisms Matrix Cracking, Delamination, Viscoelasticity/aging, etc. Stiffness Degradation Damage Mechanics Micro/Meso/Macro Models Strength Degradation Life Prediction General Introduction 7

8 CLASSIFICATION OF COMPOSITE MATERIALS Fibrous composites: Fibers in a matrix Particulate composites: Particles in a matrix Combinations of above: Reinforced fiber-reinforced composites Woven composites Braided composites Laminated composites: Layers of various materials (nano-composites) General Introduction 8

9 Fiber-reinforced Composite Materials: Constituents P Fiber P Fiber: Load-carrying agent Matrix: Supports and protects fibers, and transfers load between broken fibers τ Fiber (a) characteristic distance springs represent the lateral restraint provided by the matrix τ Matrix material Lamina: Basic building block; flat or curved arrangement of unidirectional or woven fibers in a matrix (b) broken fiber 1.5 τ (c)

10 Classification of Composite Materials θ = 90 +θ θ= 0 θ y (a) Unidirectional (b) Bi directional z x (c) Discontinuous fiber (d) Woven

11 Woven Composites General Introduction 11

12 Nanocomposites: Carbon Nanotubes Carbon nanotubes can be viewed as a sheet of graphite that has been rolled in to a single tube. Carbon nanotubes can be single- or multi-walled. General Introduction 12

13 Advantages/Disadvantages of Composites Advantages Weight reduction High strength or stiffness to weight ratio Tailorable properties Can tailor strength or stiffness in the load direction Longer life (no corrosion) Lower manufacturing costs because of less part count. Inherent damping. Increased (or decreased) thermal or electrical conductivity Disadvantages Cost of raw material and fabrication Transverse properties may be weak. Matrix is weak, low toughness Reuse and disposal may be difficult Difficult to attach. Analysis is difficult. Matrix subjected to environment degradation. General Introduction 13

14 Composites in Aerospace Structures Boeing 787 more than 50% structure is made of composites Composite components are approximately 15% of structural weight for civil aircraft. For military aircrafts and helicopters, it is 40% of structural weight. Earlier use of fibrous composites in aerospace are because of the potential for lighter structures as it affects fuel consumption, performance, and payload General Introduction 14

15 Design requirements and objective for aerospace vehicles Product Structural item Primary structural requirements Primary design Objectives Aircraft Airframe Rotor blades Helicopter Understructure Compressive strength Damage tolerance Joint strength Durability Tensile strength Stiffness Fatigue life Stiffness Energy absorption Minimum weight Maximum service Minimum weight Maximum service life Minimum weight Crashworthiness General Introduction 15

16 Rocket motor Design requirements and objective for aerospace and underwater vehicles Product Structural item Motor cases nozzles Primary structural requirements Tensile strength Resistance to elevated temperature Primary design Objectives Minimum weight Survivability at 2000 C Satellite Rotor blades Stiffness Low thermal expansion Minimum weight Dimensional stability Marine (submercibles) Understructure Compression strength and stability Joint integrity Minimum weight Maximum depth General Introduction 16

17 CHOICE OF COMPOSITE MATERIALS Reason for use Lower inertia, less deflection Light weight, damage tolerance Material selected High strength carbon/graphiteepoxy High strength carbon/graphite, hybrids, epoxy Application/driver Industrial rolls Trucks and buses to reduce environment pollutions More reproducible complex surface High strength or high modulus carbon, graphite epoxy High special aircraft General Introduction 17

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