Elasto-Plastic and Damage Analysis of Plates and Shells

von: George Z. Voyiadjis, Pawel Woelke

Springer-Verlag, 2008

ISBN: 9783540793519 , 208 Seiten

2. Auflage

Format: PDF, OL

Kopierschutz: DRM

Windows PC,Mac OSX Apple iPad, Android Tablet PC's Online-Lesen für: Windows PC,Mac OSX,Linux

Preis: 139,09 EUR

Mehr zum Inhalt

Elasto-Plastic and Damage Analysis of Plates and Shells


 

Professor Maciej Bieniek

7

Preface

9

Contents

11

Introduction

15

1.1 Shell Structures

15

1.2 Motivation and Scope

18

1.3 Basic Assumptions

19

References

20

Shell Constitutive Equations

21

2.1 Introduction

21

2.1.1 Thickness of the Shell

22

2.1.2 Initial Curvature and Radial (Transverse Normal) Stresses

24

2.2 Plate Constitutive Equations

25

2.2.1 Stresses and Stress Resultants in a Thin Plate

25

2.2.2 Equilibrium Equations and Governing Differential Equation of Plate

27

2.2.3 Transverse Shear and Transverse Normal Stresses in a Plate

29

2.3 Coordinate Transformation Ò Strains in Spherical Coordinates

31

2.4 Theoretical Formulation of the Shell Equations

36

2.4.1 Assumed Out-of-Plane Stress Components

36

2.4.2 Displacement Field

39

2.4.3 Stress Components

42

2.4.4 Stress Couples and Stress Resultants on the Middle Surface

44

2.4.5 Average Displacements

48

2.4.6 Equilibrium Equations and Boundary Conditions

52

2.4.7 The Non-Linear Nature of the Stress Distribution

53

2.4.8 The Equivalent Formulation for Thick Plates

55

2.5 Examples

55

2.5.1 Thick Sphere Subjected to Uniform Pressures

56

2.5.2 Thick Cylinder Subjected to Uniform Pressures

58

2.6 Summary

59

References

60

Shell Element Based on the Refined Theory of Thick Spherical Shells

63

3.1 Introduction

63

3.1.1 Shear Locking

63

3.1.2 Membrane Locking

66

3.1.3 Mesh Instabilities

67

3.2 Finite Element Formulation

68

3.2.1 Shell Constitutive Equations

68

3.2.2 Displacements and Boundary Conditions

69

3.2.3 Element Displacement and Strain Fields – Quasi- Conforming Method

71

3.2.4 Strain Energy and Stiffness Matrix

76

3.3 Numerical Examples

78

3.3.1 The Patch Test

79

3.3.2 Cantilevered Beam

79

3.3.3 Morley’s Hemispherical Shell (Morley and Moris, 1978)

80

3.3.4 Pinched Cylinder with Diaphragms

83

3.3.5 Scordellis-Lo Roof

84

3.3.6 Pinched Cylinder

85

3.4 Summary

87

References

88

Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells

91

4.1 Introduction

91

4.2 Updated Lagrangian Description

92

4.3 Shell Kinematics

93

4.3.1 Local Coordinates

93

4.3.2 Surface Coordinates

94

4.3.3 Base Coordinates

95

4.4 Explicit Tangent Stiffness Matrix

96

4.5 Numerical Example

101

4.6 Summary

103

References

103

Elasto-Plastic Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells

105

5.1 Introduction

105

5.2 Yield Criterion and Hardening Rule

106

5.2.1 Iliushin’s Yield Function (Iliushin, 1956)

106

5.2.2 Influence of the Shear Forces

107

5.2.3 Development of the Plastic Hinge

108

5.2.4 Bauschinger Effect and Kinematic Hardening Rule

108

5.3 Explicit Elasto-Plastic Tangent Stiffness Matrix with Large Displacements

113

5.4 Numerical Examples

120

5.4.1 Simply Supported Elasto-Plastic Beam

121

5.4.2 Simply Supported Plate

122

5.4.3 Cylindrical Shell Subjected to Ring of Pressure

126

5.4.4 Spherical Dome Subjected to Ring of Pressure

128

5.5 Summary

129

References

130

Elasto-Plastic Geometrically Non-linear Finite Element Analysis of Thick Plates and Shells With Damage Due to Microvoids

133

6.1 Introduction

133

6.2 Yield and Damage Criterion

135

6.3 Explicit Tangent Stiffness Matrix

142

6.4 Numerical Examples

149

6.4.1 Clamped Square Plate Subjected to a Central Point Load

150

6.4.2 Spherical Dome Subjected to Ring of Pressure

151

6.5 Summary

153

References

155

Non-linear Post Buckling Finite Element Analysis of Plates and Shells

159

7.1 Introduction

159

7.2 Element Tangent Stiffness Matrix

160

7.2.1 Element Stiffness in Local Coordinates

160

7.2.2 Initial Surface Coordinates for Large Deformation Analysis

164

7.2.3 Transformation of Element Stiffness Matrix

165

7.3 Solution Algorithm

166

7.4 Numerical Examples

167

7.4.1 The Williams’ Toggle Frame

167

7.4.2 Simply Supported Circular Plate Subjected to Edge Pressure

168

7.4.3 Rectangular Plate Subjected to In-Plane Load

169

7.4.4 Cylindrical Shell Under a Central Load

171

7.4.5 Spherical Shell Subjected to Central Load

173

7.5 Summary

174

References

174

Determination of Transverse Shear Stresses and Delamination in Composite Laminates Using Finite Elements

177

8.1 Introduction

177

8.2 Kinematics of the Shell

178

8.3 Lamina Constitutive Equations

180

8.4 Failure Criteria for Composite Laminates

185

8.5 Implementation and Numerical Examples

186

8.5.1 Laminated Composite Strip under Three-Point Bending

187

8.5.2 Composite Cylinder under Internal Pressure

192

8.5.3 Cylindrical Shell Subjected to Ring of Pressure

194

8.6 Summary

196

References

197

Numerical Methods and Computational Algorithms

199

9.1 Introduction

199

9.2 Linear Elastic Analysis Ò System of Linear Algebraic Equations

199

9.3 Non-linear Analysis Ò System of Non-linear Algebraic Equations

201

9.3.1 Modified Newton-Raphson Method – Combined Incremental/ Iterative Solutions

202

9.3.2 The Arc-Length Technique

204

9.3.3 Integrating the Rate Equations – Return to the Yield Surface

208

References

210

Appendix

213

Interpolation Formulas for Displacement Field

213

Index

215