Example of linear, geometrical non-linear, local non-linear and material non-linear behaviour

A steel pipeline component with 90 degree bend R = 3*D with legs and Do = 100 mm and wall thickness t = 1 mm is loaded by horizontal prescribed displacements as shown in the picture below.

model layout

The differences in calculated bending moments at the middle of the bend are shown below for the various analysis options on the model.

Click to expand

The differences in calculated bending moment distributions over the pipeline component are shown below for the various analysis options on the model.

Click to expand

The differences in calculated max. stress distributions at the middle of the bend are shown below for the various analysis options on the model. The yield stress taken into account is 300 N/mm2 and the applied sig-eps diagram applied is the DSH option. (see table ISTROP)

model max stress

The maximum equivalent stress distribution over the circumference is shown for the various analysis options in the diagram below.

Click to expand

For the material non-linearity the stress distribution is highly influenced by the local yielding of the pipe material as shown already above in the comparison of analysis options. Below the stress components together forming the equivalent stress are shown.

Click to expand

In case of material non-linearity the strains deviate from the stresses in case of local yielding and the results are shown below.

Click to expand


ExamplesAnalysisMethods, last changed: 14/09/2016

See also:

Main analysis methods

Linear elastic method

Geometric non-linear elastic method

Local non-linear ovalisation

Local material yielding