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
SCOPE AND LAYOUT OF THE BOOK
CLASSIFICATION OF NON-LINEARITIES
NON-LINEAR FE PROCEDURES
CHAPTER 2 – PLASTICITY (TIME-INDEPENDENT MATERIAL NON-LINEARITY)
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)