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 | $32.18 | €29.63 |
| Non-member Price | £75.00 | $96.53 | €88.89 |
| Order Ref | R0065 Download |
|---|---|
| Member Price | £25.00 | $32.18 | €29.63 |
| Non-member Price | £75.00 | $96.53 | €88.89 |
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