## 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 – INTRODUCTION

• SCOPE AND LAYOUT OF THE BOOK
• CLASSIFICATION OF NON-LINEARITIES
• NON-LINEAR FE PROCEDURES

### CHAPTER 2 – PLASTICITY (TIME-INDEPENDENT MATERIAL NON-LINEARITY)

• INTRODUCTION
• STRESS-STRAIN RELATIONSHIPS
• REVIEW OF ELASTO-PLASTICITY THEORY
• FUNDAMENTAL 2D PLASTICITY BENCHMARK
• 3D PLASTICITY BENCHMARK
• KINEMATIC HARDENING BENCHMARK
• PRESSURISED CYLINDER PLASTICITY BENCHMARK
• CYCLIC PLASTICITY BENCHMARK
• RIGID PUNCH PLASTICITY BENCHMARK

### CHAPTER 3 – CREEP (TIME-INDEPENDENT MATERIAL NON-LINEARITY)

• INTRODUCTION
• REVIEW OF CREEP THEORY
• STRESS RELAXATION CREEP BENCHMARKS
• PRESSURISED CYLINDER CREEP BENCHMARK
• TORSIONAL CREEP BENCHMARKS
• THERMALLY-INDUCED CREEP BENCHMARK

### CHAPTER 4 – GEOMETRIC NON-LINEARITY

• INTRODUCTION
• REVIEW OF GEOMATRIC NON-LINEARITY THEORY
• SNAP-THROUGH GNL BENCHMARK
• BIFURCATION BENCHMARK
• SNAP-BACK BENCHMARK
• RIGID-BODY ROTATION BENCHMARK
• STRAIGHT CANTILEVER BENCHMARK
• CURVED CANTILEVER BENCHMARK
• Z-SHAPED 3D CANTILEVER BENCHMARK
• TORSIONAL BUCKLING 3D BENCHMARK
• PIPE COLLAPSE BENCHMARK
• STIFFENED CYLINDRICAL PANEL BENCHMARK

### CHAPTER 5 – PRACTICAL GUIDELINES

• QUESTIONS TO BE ADDRESSED BY THE USER
• DIFFICULTIES ASSOCIATED WITH NON-LINEAR PROBLEMS
• NON-LINEAR BENCHMARKS

### Document Details

Reference R0080 Becker. A English Analyst Student Publication 1st January 2001 Global