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Background to Finite Element Analysis of Geometric Non-linearity Benchmarks

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.

1INTRODUCTION3
1.1Scope3
1.2Report Format3
1.3Classification of Non-Linearities4
1.4Geometric Non-Linearity FE Benchmarks5
2THEORETICAL BACKGROUND TO GEOMETRIC NON-LINEARITY6
2.1Some Features of GNL Problems6
2.2Uniaxial GNL Strains and Stresses12
2.3Example of Limit Points and Snap-Through Behaviour14
2.4Example of Tangent Stiffness Matrix18
2.5Example of Bifurcation and Buckling Behaviour20
2.6Multi-Axial GNL Strains and Stresses in a Continuum29
3FINITE ELEMENT TREATMENT OF GEOMETRIC NON-LINEARITY31
3.1Load and displacement control32
3.2Line Search Techniques32
3.3Arc Length Methods33
3.4Buckling and Instability Analysis35
4FUNDAMENTAL BENCHMARKS FOR GEOMETRIC NON-LINEARITY37
4.1Limit Load Fundamental GNL Benchmark (Test GNL-1)37
4.2Bifurcation Fundamental GNL Benchmark (Test GNL-2)40
4.3Snap-Back Fundamental GNL Benchmark (Test GNL-3)46
52D ASSEMBLY BENCHMARKS FOR GEOMETRIC NON-LINEARITY50
5.1Rigid-Body Rotation GNL Benchmark (Test GNL-4)50
5.2Straight Cantilever GNL Benchmark (Test GNL-5)52
5.3Curved Cantilever GNL Benchmark (Test GNL-6)57
63D ASSEMBLY BENCHMARKS FOR GEOMETRIC NON-LINEARITY60
6.1Z-Shaped 3D Cantilever GNL Benchmark (Test GNL-7)60
6.2Torsional Buckling 3D GNL Benchmark (Test GNL-8)63
REFERENCES66

Document Details

ReferenceR0065
AuthorBecker. A
LanguageEnglish
AudiencesAnalyst Developer
TypePublication
Date 1st January 1999
RegionGlobal

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