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.

CHAPTER 1 - INTRODUCTION	1
1.1 SCOPE AND LAYOUT OF THE BOOK	1
1.2 CLASSIFICATION OF NON-LINEARITIES	2
1.3 NON-LINEAR FE PROCEDURES	7
CHAPTER 2 - PLASTICITY (TIME-INDEPENDENT MATERIAL NON-LINEARITY)	13
2.1 INTRODUCTION	13
2.2 STRESS-STRAIN RELATIONSHIPS	14
2.3 REVIEW OF ELASTO-PLASTICITY THEORY	21
2.4 FUNDAMENTAL 2D PLASTICITY BENCHMARK	31
2.5 3D PLASTICITY BENCHMARK	39
2.6 KINEMATIC HARDENING BENCHMARK	45
2.7 PRESSURISED CYLINDER PLASTICITY BENCHMARK	51
2.8 CYCLIC PLASTICITY BENCHMARK	57
2.9 RIGID PUNCH PLASTICITY BENCHMARK	66
CHAPTER 3 - CREEP (TIME-DEPENDENT MATERIAL NON-LINEARITY)	71
3.1 INTRODUCTION	71
3.2 REVIEW OF CREEP THEORY	72
3.3 CONSTANT-LOAD CREEP BENCHMARKS	83
3.4 STRESS RELAXATION CREEP BENCHMARKS	87
3.5 VARIABLE-LOAD CREEP BENCHMARKS	92
3.6 PRESSURISED CYLINDER CREEP BENCHMARK	96
3.7 TORSIONAL CREEP BENCHMARK	98
3.8 THERMALLY-INDUCED CREEP BENCHMARK	102
CHAPTER 4 - GEOMETRIC NON-LINEARITY	105
4.1 INTRODUCTION	105
4.2 REVIEW OF GEOMETRIC NON-LINEARITY THEORY	106
4.3 SNAP-THROUGH GNL BENCHMARK	116
4.4 BIFURCATION BENCHMARK	124
4.5 SNAP-BACK BENCHMARK	134
4.6 RIGID-BODY ROTATION BENCHMARK	138
4.7 STRAIGHT CANTILEVER BENCHMARK	140
4.8 CURVED CANTILEVER BENCHMARK	146
4.9 Z-SHAPED 3D CANTILEVER BENCHMARK	149
4.10 TORSIONAL BUCKLING 3D BENCHMARK	151
4.11 PIPE COLLAPSE BENCHMARK	154
4.12 STIFFENED CYLINDRICAL PANEL BENCHMARK	158
CHAPTER 5 - PRACTICAL GUIDELINES	161
5.1 QUESTIONS TO BE ADDRESSED BY THE USER	161
5.2 DIFFICULTIES ASSOCIATED WITH NON-LINEAR PROBLEMS	162
5.3 NON-LINEAR BENCHMARKS	163
REFERENCES	165
GLOSSARY	167

Document Details

Reference	R0080
Author	Becker. A
Language	English
Audiences	Analyst Student
Type	Publication
Date	1st January 2001
Region	Global

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