Post-Critical Analysis

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Figure 01 - Internal Forces According to Large Deformation Analysis

Figure 02 - Unstable System: Post-Critical Failure

Figure 03 - Post-Critical Analysis

Figure 04 - Post-Critical Analysis: Increasing Load

Technical Article

001464 07/25/2017 Technical Article Stability Analysis RFEM Sandy Matula Modeling | Loading

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 linearization 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.