Post-Critical Analysis

Technical Article

In the case of a post-critical failure, a substantial change in the geometry of a structure occurs. After reaching the instability of the equilibrium, a stable, strong position is reached again. The post-critical analysis requires an experimental approach. It is necessary to manually load the structure in increments step by step.

Example

This article shows the post-critical analysis. A structural component can be imagined as a flat roof subjected to compression from the outside. When slowly increasing the compression, it is visible that the load is absorbed by the compression stress and transferred to a support.

Figure 01 - Internal Forces According to Large Deformation Analysis

When a certain compressive load is reached, the structural system becomes unstable and the post-critical failure occurs.

Figure 02 - Unstable System: Post-Critical Failure

Figure 03 - Post-Critical Analysis

When increasing the load again, it is primarily absorbed by tensile stress in the structural component.

Figure 04 - Post-Critical Analysis: Increasing Load

Generally, the second-order analysis cannot detect the post-critical failure due to the linearisation of the deformation geometry description.

Further information and examples can be found in [1] and [2], among others.

Reference

[1] Werkle, H. (2008). Finite Elemente in der Baustatik: Statik und Dynamik der Stab- und Flächentragwerke (3rd ed.). Berlin: Springer.
[2] Lumpe, G. & Gensichen, V. (2014). Evaluierung der linearen und nichtlinearen Stabstatik in Theorie und Software - Prüfbeispiele, Fehlerursachen, genaue Theorie. Berlin: Ernst & Sohn.

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