Naumenko / Altenbach Modeling High Temperature Materials Behavior for Structural Analysis

Part II. Solution Procedures and Structural Analysis Examples
1. Auflage 2019
ISBN: 978-3-030-20381-8
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 224 Seiten

Reihe: Engineering (R0)

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.

Autoren/Hrsg.

Naumenko, Konstantin

Altenbach, Holm

Inhaltsverzeichnis

1;Preface;6
1.1;References;10
2;Contents;12
3;About the Authors;15
4;1 Bars and Bar Systems;17
4.1;1.1 Governing Equations for Two-bar System;17
4.2;1.2 Thermo-elasticity with Temperature Changes;20
4.3;1.3 Linear Viscous Behavior;21
4.3.1;1.3.1 Displacement-controlled Loading Paths;23
4.3.2;1.3.2 Force-controlled Loading Paths;24
4.3.3;1.3.3 Time-step Methods;26
4.3.3.1;1.3.3.1 Explicit Euler Method;26
4.3.3.2;1.3.3.2 Implicit Euler Method;30
4.3.3.3;1.3.3.3 Trapezoidal Rule;32
4.3.3.4;1.3.3.4 Reviewing the Solutions;34
4.4;1.4 Non-linear Inelastic Behavior;37
4.4.1;1.4.1 Constitutive Equations;37
4.4.1.1;1.4.1.1 Stress Functions for Creep and Relaxation;38
4.4.1.2;1.4.1.2 Power Law Breakdown and Monotonic Loading;41
4.4.2;1.4.2 Governing Equations for Two-bar System;42
4.4.3;1.4.3 Creep and Stress Redistribution;44
4.4.4;1.4.4 Creep Followed by Recovery;49
4.4.5;1.4.5 Stress Relaxation;52
4.4.6;1.4.6 Displacement-controlled Monotonic and Cyclic Loadings;55
4.4.7;1.4.7 Time-Step Methods;58
4.4.7.1;1.4.7.1 Explicit Euler Method;59
4.4.7.2;1.4.7.2 Implicit Euler Method;63
5;2 Initial-Boundary Value Problems and Solution Procedures;69
5.1;2.1 Governing Equations for Structural Analysis;69
5.1.1;2.1.1 Preliminary Remarks and Assumptions;69
5.1.2;2.1.2 Summary of Governing Equations;71
5.1.3;2.1.3 Steady-State Creep and Elastic Analogy;75
5.1.4;2.1.4 Matrix Representation;77
5.2;2.2 Numerical Solution Techniques;79
5.2.1;2.2.1 Time-Step Methods;81
5.2.1.1;2.2.1.1 Explicit Methods;82
5.2.1.2;2.2.1.2 Implicit Methods;84
5.2.2;2.2.2 Solution of Boundary Value Problems;87
5.2.3;2.2.3 Variational Formulations and Procedures;89
5.3;2.3 Temporal Scale Procedures;93
5.3.1;2.3.1 Inelastic Behavior with Temporal Scale Effects;93
5.3.2;2.3.2 Temporal Scale Approaches;95
5.3.3;2.3.3 Two-Time-Scales and Time Averaging Procedures;97
5.3.4;2.3.4 Analysis of Cyclic Creep;100
5.3.4.1;2.3.4.1 Constitutive Equations;100
5.3.4.2;2.3.4.2 Constitutive Equations for Slow Process;101
5.3.4.3;2.3.4.3 Examples;102
6;3 Beams;112
6.1;3.1 Classical Beam Theory;113
6.1.1;3.1.1 Governing Equations;113
6.1.2;3.1.2 Variational Formulation and the Ritz Method;118
6.1.3;3.1.3 Closed-Form Solutions for Steady-State Creep;120
6.1.3.1;3.1.3.1 Pure Bending with Norton-Bailey Creep Law;121
6.1.3.2;3.1.3.2 Pure Bending with Stress Regime Dependence;123
6.1.3.3;3.1.3.3 Bending Under Lateral Load;125
6.1.4;3.1.4 Solutions by Ritz Method;127
6.1.4.1;3.1.4.1 Norton-Bailey Creep Law;128
6.1.4.2;3.1.4.2 Kachanov-Rabotnov Creep-Damage Law;131
6.1.4.3;3.1.5 Solutions by Finite Element Method;132
6.1.4.3.1;3.1.5.1 Norton-Bailey Creep Law;132
6.1.4.3.2;3.1.5.2 Kachanov-Rabotnov Creep-Damage Law;134
6.2;3.2 Stress State Effects and Cross Section Assumptions;137
6.3;3.3 First Order Shear Deformation Theory;141
7;4 Plane Stress and Plane Strain Problems;152
7.1;4.1 Governing Equations;152
7.1.1;4.1.1 Assumptions and Preliminaries;152
7.1.2;4.1.2 Kinematical Equations;155
7.1.3;4.1.3 Equilibrium Conditions;156
7.1.4;4.1.4 Constitutive Equations;156
7.2;4.2 Pressurized Thick Cylinder;158
7.2.1;4.2.1 Governing Equations for Steady-State Flow;159
7.2.2;4.2.2 Solution with Norton-Bailey Creep law;160
7.2.3;4.2.3 Solution with Stress Regime Dependent Creep law;162
7.2.4;4.2.4 Finite Element Solution;165
7.3;4.3 Rotating Components;166
7.3.1;4.3.1 Rotating Rod;168
7.3.2;4.3.2 Rotating Disc;171
7.4;4.4 Plate with a Circular Hole;174
7.4.1;4.4.1 Plane Stress Solutions;176
7.4.2;4.4.2 Plane Strain Solutions;179
8;5 Plates and Shells;183
8.1;5.1 Approaches to the Analysis of Plates and Shells;183
8.2;5.2 Governing Equations of the FSDT Plate Theory;189
8.2.1;5.2.1 Equilibrium conditions;189
8.2.2;5.2.2 Constitutive equations;191
8.2.2.1;5.2.2.1 Linear-Elastic Behavior;191
8.2.2.2;5.2.2.2 Steady-State Flow;192
8.2.3;5.2.3 Shear-rigid Plates;195
8.3;5.3 Creep Bending of Circular Plates;196
8.4;5.4 Edge Effects in a Moderately Thick Rectangular Plate;201
8.5;5.5 Thin-walled Tube under Internal Pressure and Bending Moment;211
8.6;References;216
9;Index;221