ProMultAx - Experimental investigation and probabilistic analysis of the buckling load of cylindrical shells subjected to multiaxial loadcases


Cylindrical shells are often used as structural elements, for example in the aerospace industry. Due to advances in manufacturing and machining, fibre-reinforced plastic composites have in recent times increasingly been given preference over conventional metallic materials. Thin-walled shell elements of this type exhibit failure by buckling under critical load cases, such as bending, torsion and axial compression, which can result in the sudden, total failure of the entire structure. In practice, the mentioned load cases usually do not occur isolated, but in varying combinations. Currently existing design guidelines consider the interaction of the load types in different ways, but always from a purely deterministic point of view. Furthermore, all design approaches dealing with this problem have only been established for metallic cylinders.


The core objective of this project is to determine and analyse the load distribution of orthotropic cylindrical shells under multiaxial loading as a function of the load combination. The main focus lies on the development of a probabilistic design method for multiaxially loaded cylindrical shells. In addition, the measured geometric imperfection patterns of the shells will be published in the form of Fourier coefficients after completion of the project, which contributes to expanding the existing statistical database.

Research Method

In cooperation with the Institute for Structural Mechanics in Lightweight Design (ISML), a series of cylindrical shells made of carbon fibre reinforced plastic (CFRP) as well as orthotropically stiffened 3D-printed cylinders are being tested and the resulting buckling loads are analysed. The PKT is focussing on the investigation of the CFRP shells. First, the geometric imperfections of the undamaged shells are measured before the buckling loads of the cylinders are experimentally determined on the hexapod test rig under various combined load cases. The load combinations investigated are axial compression and torsion, axial compression and bending, as well as the combination of all three load types. For these experiments, 12 cylindrical shells are available that have already been investigated within the RADIUS project. In addition, six new shells with nominally identical properties to the smaller, already existing cylinders will be manufactured. The nominal specifications of the CFRP cylindrical shells can be taken from the following table.

  Cylinder Type 1 (RADIUS) Cylinder Type 2 (RADIUS) Cylinder Type 3 (ProMultAx)
Specimens 6 6 6
Fibre/Matrix AS7/8552 AS7/8552 AS7/8552
Laminate [90,-30,30,-30,30,90] [90,-30,30,-30,30,90] [90,-30,30,-30,30,90]
Radius 115 mm 300 mm 115 mm
Length 255 mm 800 mm 255 mm
Wall Thickness 0,75 mm 0,75 mm 0,75 mm

Using FE-simulations, the buckling loads are also numerically determined for the tested load combinations and compared with the experimental data. With the help of probabilistic analyses based on the measured and available imperfection data, the buckling load distribution is  determined for each load case investigated. The distributions found by simulation are compared with the results of the test series in regards to agreement of data and plausibility. Finally, a design process is to be derived from the results of all analyses, which allows the determination of a probabilistically motivated design load for any load combination.

Project Organisation

Principal Investigator (PKT): Prof. Dr.-Ing. Dieter Krause

Co-Investigator: Stefan Panek, M.Sc.


This project is funded by the German Research Foundation (DFG) with the project-number 463883313 (GEPRIS). The duration of the project is 36 months and ranges from March 2022 to February 2025.