Contents Preface page xi List of Symbols xiii 1 Introduction 1 2 Displacements, Strains, a n Stresses 3 2.1 Slra in-Di splacement Relations 4 2. 2 Equilibrium Equations 6 2.3 Stress-Strain Relationships 8 2.3.1 Generally Anisotropic Mate ria l 8 2.3.2 Monoclinic Material 11 2.3.3 Orthotropic Material 14 2.3.4 Transversel y Isotropic Material 19 2. 3. 5 Isotropic Mat erial 20 2.4 Plane-Strain Con di tion 22 2.4.1 Frce E n d - Generally Anisotropic Material 28 2.4.2 Free End -Monoclinic Material 30 2.4.3 Free End - Orthotropic, Transversely Isotropic. or Isotropic Material 34 2.4.4 Built-In Ends - Generally Anisotropic Material 35 2.4.5 Built-Tn Ends - Monoclinic Material 36 2.4.6 Built-In Ends - Orth otro pic, Transversely Isotropic, or Isotropic Material 38 2.5 Plane-Stress Condition 38 2.6 Hygrothermal Strains and Stresses 44 2.6.1 Planc-Strain Condition 47 2.6.2 Plane-Strcss Condition 47 2.7 Boundary Conditions 47 2.8 Con tinuity Condit ions 48 2.9 Stress and Strain Transformations 49 2.9.1 Stress Transformaron 50 2.9.2 Strain Transf orm aron 52 2.9.3 Transformation of the Stiffness and Compl iance Matrices 53
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8/3/2019 In Dice 001
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Contents
Preface page x i
List of Symbols x i i i
1 Introduction 1
2 Displacements, Strains, and Stresses 3
2.1 Slra in-Di splacement Relations 4
2.2 Eq ui li br iu m Equations 6
2.3 Stress-Strain Relationships 8
2.3.1 Generally Anis otrop ic Mate ria l 8
2.3.2 Monoc lin ic Mate ria l 11
2.3.3 Ortho tropi c Mate ria l 14
2.3.4 Transversely Isotr opic Mat er ia l 19
2.3.5 Isotropic Mat er ial 20
2.4 Plane-S train Con di ti on 22
2.4.1 Frce E n d - Generally Anisotropic Materia l 28
2.4.2 Free End -Mo noc li ni c Material 30
2.4.3 Free En d - Ortho trop ic, Transversely Isotropic.
or Isotropic Mate ria l 34
2.4.4 B u i l t - I n Ends - Generally Anisot ropic Mate ria l 35
2.4.5 Bu i l t - T n Ends - Monocl inic Mate ria l 36
2.4.6 B u i l t - I n Ends - Orth otro pic, Transversely Isotropic,
or Isotropic Mate rial 382.5 Plane-Stress Condition 38
2.6 Hygrothermal Strains and Stresses 44
2.6.1 Planc-Stra in Con dit ion 47
2.6.2 Plane-Strcss Condition 47
2.7 Boundary Condit ions 47
2.8 Con tinuit y Condit ions 48
2.9 Stress and Strain Transformat ions 49
2.9.1 Stress Transformaron 50
2.9.2 Strain Tra nsf ormaro n 52
2.9.3 Transformation of the Stiffness and Compl iance Matrices 53
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vi CONTENTS
2.10 Strain Ener gy 55
2.10.1 The Ri tz Me th od 55
2.11 Summary 56
2.11.1 Not e on the Compliance and Stiffness Matr ices 56
3 Laminated Gomposites 63
3.1Lamína t e
Code 633.2 Stiffness Matrices of T h i n Lamína l e s 65
3.2.1 The Significance of the [A], [ B ] , and [D] Stiffness Matr ices 72
3.2.2 Stiffness Matrices for Selected Laminares 74
4 ThinPlates 89
4.1 Gover ning Equations 90
4.1.1 Boundary Condi tions 92
4.1.2 Strain Energy 92
4.2 Deñec t i on of Rectangular Plates 93
4.2.1 Puré Ben ding and In-Plane Loads 93
4.2.2 Long Plates 944.2.3 Simpl y Suppor ted Plates - Symmetrical Layu p 100
4.2.4 Plates w i t h B u i l t - I n Edges - Orthotropic and