Geometric non-linear elastic method

The geometric non-linear elastic method is split into two approaches:

•small displacements geometric non-linear behaviour, where cos (rotation) is neglected (up to .3 rad)

•large displacements geometric non-linear behaviour, where the rotation is fully taken into account.

Basic difference between the geometric linear and geometric non-linear methods is that in the first case equilibrium between external loadings and internal forces is based on the undeformed structure, whereas in the second case the equilibrium is based on the deformed structure.

In order to illustrate the influence of geometric non-linearity the results of a geometric linear analysis are compared to the results of a geometric non-linear analysis.

The model is kept simple to make understanding easy. A both sides hinge supported pipe, diameter 100 mm and wall thickness 5 mm. Span 10 m. Deadweight loading 1 kN/m. Temperature decrease 50° C. The displacements as well as the maximum axial stresses are shown.

In the non-linear analysis the elongation due to the deadweight is taken into account (cos (rotation) becomes unequal to 1) and an additional axial force due to the temperature decrease counteracts the bending of the pipeline.

Displacements example lin-non-lin

Max. axial stress example lin-non-lin

The difference between the two analysis methods is evident. In general one can say that as soon displacements become larger than the pipe diameter, a geometric non-linear analysis is needed to obtain reliable results. The same applies if temperature differences from the construction temperature become larger than 35° K.

GeometricNonLinear, last changed: 1/31/2020

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