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Background to Finite Element Analysis of Geometric Non-linearity

 Background to Finite Element Analysis of Geometric Non-linearity

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.



  • Scope Report Format
  • Classification of Non-Linearities
  • Geometric  Non-Linearity Finite Element Benchmarks

Theoretical Background To Geometric Non-Linearity

  • Some Features of GNL Strains and Stresses
  • Example of Limit Points And Snap-Through Behaviour
  • Example of Tangent Stiffness Matrix
  • Example of Bifurcation and Buckling Behaviour
  • Multi-axial GNL Strains and Stresses in a Continuum

Finite Element Treatment of Geometric Non-Linearity

  • Load and Displacement Control
  • Line Search Techniques
  • Arc Length Methods
  • Buckling and Instability Analysis

Fundamental Benchmarks  For Geometric Non-Linearity

  • Limit Load Fundamental GNL Benchmark (Test GNL-1)
  • Bifurcation Fundamental GNL Benchmark (Test GNL-2)
  • Snap-Back Fundamental GNL Benchmark (Test GNL-3)

2D Assembly Benchmarks For Geometric Non-Linearity

  • Rigid-Body Rotation GNL Benchmark (Test GNL - 4)
  • Straight Cantilever GNL Benchmark (Test GNL - 5)
  • Curved Cantilever GNL Benchmark (Test GNL - 6)

3D Assembly Benchmarks for Geometric Non-Linearity

  • Z-shaped 3D Cantilever GNL Benchmark (Test GNL - 7)
  • Torsional Buckling 3D GNL Benchmark


Purchasing Details

Members Price
£25 | $33 | €28

Non-Members Price
£75 | $98 | €84
Order Ref: R0065


A.A. Becker

First Published - January 1999

Softback, 67 Pages