MECHANICS OF FUNCTIONALLY GRADED MATERIAL STRUCTURES

by Isaac E Elishakoff, Demetris Pentaras, Cristina Gentilini

Overview

Mechanics of Functionally Graded Material Structures is an authoritative and fresh look at various functionally graded materials, customizing them with various structures. The book is devoted to tailoring material properties to the needed structural performance. The authors pair materials with the appropriate structures based upon their purpose and use.Material grading of structures depending upon thickness, axial and polar directions are discussed. Three dimensional analysis of rectangular plates made of functional graded materials and vibrational tailoring of inhomogeneous beams and circular plates are both covered in great detail. The authors derive novel closed form solutions that can serve as benchmarks that numerical solutions can be compared to. These are published for the first time in the literature. This is a unique book that gives the first exposition of the effects of various grading mechanisms on the structural behavior as well as taking into account vibrations and buckling.

Product Details

ISBN-13:	9789814656603
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/29/2015
Sold by:	Barnes & Noble
Format:	eBook
Pages:	340
File size:	22 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface vii

Part I Three-Dimensional Analysis of Rectangular Plates Made of Functionally Graded Materials 1

Introduction 1

1 Elastic Plates 3

1.1 Bi-dimensional theories 4

1.1.1 The CPT 4

1.1.2 Shear deformation theories: First-order deformation theory 7

1.1.3 Shear deformation theories: Third-order deformation theory 8

1.2 Three-dimensional theory 9

1.3 Some remarks 12

2 Introduction to Functionally Graded Materials 13

2.1 Fabrication methods 15

2.2 Modelling of the effective material properties 15

2.2.1 The rule of mixtures 16

2.2.2 The Mori-Tanaka model 17

2.2.3 Self-consistent model 21

2.3 Some remarks 22

3 Dynamic Analysis of Plates Made of Functionally Graded Materials 23

3.1 Statement of the problem 25

3.1.1 Basic definitions 25

3.2 Three-dimensional analysis 27

3.2.1 Strain energy 27

3.2.2 Kinetic energy 28

3.2.3 Dissipation functional 28

3.2.4 Work done by the external forces 29

3.3 Ritz method: Displacement representation 29

3.3.1 Chebyshev polynomials 31

3.3.2 Boundary functions 32

3.4 Solution methodology 33

3.5 Numerical results 37

3.5.1 Free vibrations 37

3.5.2 Forced vibrations 57

3.6 Some remarks 71

4 Static Analysis of Plates Made of Functionally Graded Materials 73

4.1 Statement of the problem and solution methodology 74

4.2 Numerical results 77

4.3 Some remarks 85

Part II Vibration Tailoring of Inhomogeneous Beams and Circular Plates 87

5 Beams Made of Functionally Graded Material 89

5.1 Euler-Bernoulli beam equation 90

5.2 Method of solution of uniform beam vibrations 90

5.2.1 Determination of natural frequencies and mode shapes 92

6 Vibration Tailoring of Inhomogeneous Elastically Restrained Vibrating Beams 97

6.1 Background 97

6.2 Analysis 99

6.3 Comparison between closed-form solutions of inhomogeneous vibrating beam and homogeneous beam 105

6.4 Vibration tailoring: Numerical example 106

7 Some Intriguing Results Pertaining to Functionally Graded Columns 107

7.1 Background 107

7.2 Formulation of the problem 108

7.3 Dependence between Q2 and P 118

7.4 Numerical example 125

7.5 Conclusion 127

8 Design of Heterogeneous Polar-Orthotropic Clamped Circular Plates with Specified Fundamental Natural Frequency 129

8.1 Background 129

8.2 Derivation of governing differential equation 130

8.3 Semi-inverse method of solution 132

8.3.1 Parabolic mode shape 134

8.3.2 Two cubic mode shapes 138

8.3.3 Two alternative quartic mode shapes 145

8.4 Discussion 152

8.5 Vibration tailoring: Numerical example 153

9 Vibration Tailoring of Simply-Supported Polar Orthotropic Inhomogeneous Circular Plates 155

9.1 Introduction 155

9.2 Analysis 156

9.2.1 Semi-inverse method of solution associated with m = 1 157

9.2.2 Semi-inverse method of solution associated with m = 2 159

9.2.3 Semi-inverse method of solution associated with m = 3 163

9.2.4 Semi-inverse method of solution associated with m = 4 167

9.3 Vibration tailoring: Numerical example 174

10 Vibration Tailoring of Clamped-Clamped Polar Orthotropic Inhomogeneous Circular Plates 177

10.1 Analysis 177

10.1.1 Semi-inverse method of solution associated with m = 1 178

10.1.2 Semi-inverse method of solution associated with m = 2 180

10.1.3 Semi-inverse method of solution associated with m = 3 184

10.1.4 Semi-inverse method of solution associated with m = 4 186

10.2 Vibration tailoring: Numerical example 192

11 Vibration Tailoring of a Polar Orthotropic Circular Plate with Translational Spring 193

11.1 Analysis 193

11.1.1 Boundary conditions 194

11.1.2 Method of solution 194

11.1.3 Vibration tailoring: Numerical example 210

12 Conclusion 213

Appendix A A Novel Formulation Leading to Closed-Form Solutions for Buckling of Circular Plates 215

Appendix B Inverse Vibration Problem for Inhomogeneous Circular Plate with Translational Spring 227

Appendix C Apparently First Closed-Form Solutions for Non-Symmetric Vibrations of Inhomogeneous Circular Plates 241

Appendix D Closed-Form Solution for Axisymmetric Vibration of Inhomogeneous Simply- Supported Circular Plates 251

References 265

Author Index 309

Subject Index 319