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Understanding Non-linear Finite Element Analysis Through Illustrative Benchmarks

The use of Finite Element software has become very widespread in engineering and its range of applicable has greatly increased. Indeed, it is nowadays difficult to find many engineering applications for which the Finite Element method has not been used or at least attempted. With this rapid increase in the use of the Finite Element  method, it’s increasingly automated procedures, and its user-friendly graphical interfaces, the expectations of FE users have risen, sometimes unrealistically. Inexperienced Finite Element users may be under the impression that they can easily tackle non-linear problems without having to gain a good understanding of the background theory.

NAFEMS has published many benchmarks on non-linear problems, usually devised to address a particular type of non-linearity, such as plasticity, geometric non-linearity, etc. Non-linear FE theory has been included in many FE textbooks.

This book is written to fill the gap between the benchmark reports and the textbooks of Finite Element theory, by presenting a carefully selected set of non-linear benchmarks and providing a brief coverage of the background non-linear theory covered in the benchmarks.

Contents

CHAPTER 1 - INTRODUCTION1
1.1 SCOPE AND LAYOUT OF THE BOOK1
1.2 CLASSIFICATION OF NON-LINEARITIES2
1.3 NON-LINEAR FE PROCEDURES7
CHAPTER 2 - PLASTICITY (TIME-INDEPENDENT MATERIAL NON-LINEARITY)13
2.1 INTRODUCTION13
2.2 STRESS-STRAIN RELATIONSHIPS14
2.3 REVIEW OF ELASTO-PLASTICITY THEORY21
2.4 FUNDAMENTAL 2D PLASTICITY BENCHMARK31
2.5 3D PLASTICITY BENCHMARK39
2.6 KINEMATIC HARDENING BENCHMARK45
2.7 PRESSURISED CYLINDER PLASTICITY BENCHMARK51
2.8 CYCLIC PLASTICITY BENCHMARK57
2.9 RIGID PUNCH PLASTICITY BENCHMARK66
CHAPTER 3 - CREEP (TIME-DEPENDENT MATERIAL NON-LINEARITY)71
3.1 INTRODUCTION71
3.2 REVIEW OF CREEP THEORY72
3.3 CONSTANT-LOAD CREEP BENCHMARKS83
3.4 STRESS RELAXATION CREEP BENCHMARKS87
3.5 VARIABLE-LOAD CREEP BENCHMARKS92
3.6 PRESSURISED CYLINDER CREEP BENCHMARK96
3.7 TORSIONAL CREEP BENCHMARK98
3.8 THERMALLY-INDUCED CREEP BENCHMARK102
CHAPTER 4 - GEOMETRIC NON-LINEARITY105
4.1 INTRODUCTION105
4.2 REVIEW OF GEOMETRIC NON-LINEARITY THEORY106
4.3 SNAP-THROUGH GNL BENCHMARK116
4.4 BIFURCATION BENCHMARK124
4.5 SNAP-BACK BENCHMARK134
4.6 RIGID-BODY ROTATION BENCHMARK138
4.7 STRAIGHT CANTILEVER BENCHMARK140
4.8 CURVED CANTILEVER BENCHMARK146
4.9 Z-SHAPED 3D CANTILEVER BENCHMARK149
4.10 TORSIONAL BUCKLING 3D BENCHMARK151
4.11 PIPE COLLAPSE BENCHMARK154
4.12 STIFFENED CYLINDRICAL PANEL BENCHMARK158
CHAPTER 5 - PRACTICAL GUIDELINES161
5.1 QUESTIONS TO BE ADDRESSED BY THE USER161
5.2 DIFFICULTIES ASSOCIATED WITH NON-LINEAR PROBLEMS162
5.3 NON-LINEAR BENCHMARKS163
REFERENCES165
GLOSSARY167

Document Details

ReferenceR0080
AuthorBecker. A
LanguageEnglish
AudiencesAnalyst Student
TypePublication
Date 1st January 2001
RegionGlobal

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