This report is written to provide a background to the theory of geometric non-linearity and how finite element analysis deals with such non-linearities through a specially selected set of benchmarks.
A theoretical background to geometric non-linearities is presented with emphasis on practical applications.
Practical examples are used to demonstrate important features of non-linear geometric behaviour such as bifurcation and snap-through. A number of two-dimensional and three-dimensional geometric non-linearity FE benchmarks are presented with discussions of their attributes and reference solutions.
1 | INTRODUCTION | 3 |
1.1 | Scope | 3 |
1.2 | Report Format | 3 |
1.3 | Classification of Non-Linearities | 4 |
1.4 | Geometric Non-Linearity FE Benchmarks | 5 |
2 | THEORETICAL BACKGROUND TO GEOMETRIC NON-LINEARITY | 6 |
2.1 | Some Features of GNL Problems | 6 |
2.2 | Uniaxial GNL Strains and Stresses | 12 |
2.3 | Example of Limit Points and Snap-Through Behaviour | 14 |
2.4 | Example of Tangent Stiffness Matrix | 18 |
2.5 | Example of Bifurcation and Buckling Behaviour | 20 |
2.6 | Multi-Axial GNL Strains and Stresses in a Continuum | 29 |
3 | FINITE ELEMENT TREATMENT OF GEOMETRIC NON-LINEARITY | 31 |
3.1 | Load and displacement control | 32 |
3.2 | Line Search Techniques | 32 |
3.3 | Arc Length Methods | 33 |
3.4 | Buckling and Instability Analysis | 35 |
4 | FUNDAMENTAL BENCHMARKS FOR GEOMETRIC NON-LINEARITY | 37 |
4.1 | Limit Load Fundamental GNL Benchmark (Test GNL-1) | 37 |
4.2 | Bifurcation Fundamental GNL Benchmark (Test GNL-2) | 40 |
4.3 | Snap-Back Fundamental GNL Benchmark (Test GNL-3) | 46 |
5 | 2D ASSEMBLY BENCHMARKS FOR GEOMETRIC NON-LINEARITY | 50 |
5.1 | Rigid-Body Rotation GNL Benchmark (Test GNL-4) | 50 |
5.2 | Straight Cantilever GNL Benchmark (Test GNL-5) | 52 |
5.3 | Curved Cantilever GNL Benchmark (Test GNL-6) | 57 |
6 | 3D ASSEMBLY BENCHMARKS FOR GEOMETRIC NON-LINEARITY | 60 |
6.1 | Z-Shaped 3D Cantilever GNL Benchmark (Test GNL-7) | 60 |
6.2 | Torsional Buckling 3D GNL Benchmark (Test GNL-8) | 63 |
REFERENCES | 66 |
Reference | R0065 |
---|---|
Author | Becker. A |
Language | English |
Audiences | Analyst Developer |
Type | Publication |
Date | 1st January 1999 |
Region | Global |
Order Ref | R0065 Book |
---|---|
Member Price | £25.00 | $32.76 | €29.68 |
Non-member Price | £75.00 | $98.27 | €89.02 |
Order Ref | R0065 Download |
---|---|
Member Price | £25.00 | $32.76 | €29.68 |
Non-member Price | £75.00 | $98.27 | €89.02 |
Stay up to date with our technology updates, events, special offers, news, publications and training
If you want to find out more about NAFEMS and how membership can benefit your organisation, please click below.
Joining NAFEMS© NAFEMS Ltd 2024
Developed By Duo Web Design