Modeling High Temperature Materials Behavior for Structural Analysis (eBook)

Part II. Solution Procedures and Structural Analysis Examples

Konstantin Naumenko, Holm Altenbach (Autoren)

eBook Download: PDF

2019
210 Seiten
Springer International Publishing (Verlag)
978-3-030-20381-8 (ISBN)

Infos

This second part of the work on creep modeling offers readers essential guidance on practical computational simulation and analysis. Drawing on constitutive equations for creep in structural materials under multi-axial stress states, it applies these equations, which are developed in detail in part 1 of the work, to a diverse range of examples.

Inhalt

Preface 6
References 10
Contents 12
About the Authors 15
1 Bars and Bar Systems 17
1.1 Governing Equations for Two-bar System 17
1.2 Thermo-elasticity with Temperature Changes 20
1.3 Linear Viscous Behavior 21
1.3.1 Displacement-controlled Loading Paths 23
1.3.2 Force-controlled Loading Paths 24
1.3.3 Time-step Methods 26
1.3.3.1 Explicit Euler Method 26
1.3.3.2 Implicit Euler Method 30
1.3.3.3 Trapezoidal Rule 32
1.3.3.4 Reviewing the Solutions 34
1.4 Non-linear Inelastic Behavior 37
1.4.1 Constitutive Equations 37
1.4.1.1 Stress Functions for Creep and Relaxation 38
1.4.1.2 Power Law Breakdown and Monotonic Loading 41
1.4.2 Governing Equations for Two-bar System 42
1.4.3 Creep and Stress Redistribution 44
1.4.4 Creep Followed by Recovery 49
1.4.5 Stress Relaxation 52
1.4.6 Displacement-controlled Monotonic and Cyclic Loadings 55
1.4.7 Time-Step Methods 58
1.4.7.1 Explicit Euler Method 59
1.4.7.2 Implicit Euler Method 63
2 Initial-Boundary Value Problems and Solution Procedures 69
2.1 Governing Equations for Structural Analysis 69
2.1.1 Preliminary Remarks and Assumptions 69
2.1.2 Summary of Governing Equations 71
2.1.3 Steady-State Creep and Elastic Analogy 75
2.1.4 Matrix Representation 77
2.2 Numerical Solution Techniques 79
2.2.1 Time-Step Methods 81
2.2.1.1 Explicit Methods 82
2.2.1.2 Implicit Methods 84
2.2.2 Solution of Boundary Value Problems 87
2.2.3 Variational Formulations and Procedures 89
2.3 Temporal Scale Procedures 93
2.3.1 Inelastic Behavior with Temporal Scale Effects 93
2.3.2 Temporal Scale Approaches 95
2.3.3 Two-Time-Scales and Time Averaging Procedures 97
2.3.4 Analysis of Cyclic Creep 100
2.3.4.1 Constitutive Equations 100
2.3.4.2 Constitutive Equations for Slow Process 101
2.3.4.3 Examples 102
3 Beams 112
3.1 Classical Beam Theory 113
3.1.1 Governing Equations 113
3.1.2 Variational Formulation and the Ritz Method 118
3.1.3 Closed-Form Solutions for Steady-State Creep 120
3.1.3.1 Pure Bending with Norton-Bailey Creep Law 121
3.1.3.2 Pure Bending with Stress Regime Dependence 123
3.1.3.3 Bending Under Lateral Load 125
3.1.4 Solutions by Ritz Method 127
3.1.4.1 Norton-Bailey Creep Law 128
3.1.4.2 Kachanov-Rabotnov Creep-Damage Law 131
3.1.5 Solutions by Finite Element Method 132
3.1.5.1 Norton-Bailey Creep Law 132
3.1.5.2 Kachanov-Rabotnov Creep-Damage Law 134
3.2 Stress State Effects and Cross Section Assumptions 137
3.3 First Order Shear Deformation Theory 141
4 Plane Stress and Plane Strain Problems 152
4.1 Governing Equations 152
4.1.1 Assumptions and Preliminaries 152
4.1.2 Kinematical Equations 155
4.1.3 Equilibrium Conditions 156
4.1.4 Constitutive Equations 156
4.2 Pressurized Thick Cylinder 158
4.2.1 Governing Equations for Steady-State Flow 159
4.2.2 Solution with Norton-Bailey Creep law 160
4.2.3 Solution with Stress Regime Dependent Creep law 162
4.2.4 Finite Element Solution 165
4.3 Rotating Components 166
4.3.1 Rotating Rod 168
4.3.2 Rotating Disc 171
4.4 Plate with a Circular Hole 174
4.4.1 Plane Stress Solutions 176
4.4.2 Plane Strain Solutions 179
5 Plates and Shells 183
5.1 Approaches to the Analysis of Plates and Shells 183
5.2 Governing Equations of the FSDT Plate Theory 189
5.2.1 Equilibrium conditions 189
5.2.2 Constitutive equations 191
5.2.2.1 Linear-Elastic Behavior 191
5.2.2.2 Steady-State Flow 192
5.2.3 Shear-rigid Plates 195
5.3 Creep Bending of Circular Plates 196
5.4 Edge Effects in a Moderately Thick Rectangular Plate 201
5.5 Thin-walled Tube under Internal Pressure and Bending Moment 211
References 216
Index 221

Produkt-Details

• Erscheint lt. Verlag: 1.6.2019
• Reihe/Serie: Advanced Structured Materials
• Reihe/Serie: Advanced Structured Materials
• Zusatzinfo: XVI, 210 p. 1 illus.
• Sprache: englisch
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Creep-Fatigue • Kachanov-Rabotnov Model • Low Cycle Fatigue • non-linear initial-boundary value • Ritz Method • thermo-mechanical fatigue
• ISBN-10: 3-030-20381-6 / 3030203816
• ISBN-13: 978-3-030-20381-8 / 9783030203818