Linear Stability Analysis and Buckling of Two-Layered Shells Under External Circumferential Loading: A Numerical Investigation

The aim of the paper is the numerical investigation of the stability of two-layered shells under the action of imposed azimuthal strain on the external surface. Although this type of loading is not common in engineering practice, it appears often in biomedicine (for example buckling of esophagus, asthmatic airways, gastrointestinal tract etc). The differential stability equations are discretised using the finite volume method and the resulting generalised eigenvalue problem is solved using the QZ decomposition technique. The results show that the buckling behaviour under circumferential loading is entirely different compared to hydrostatic pressure loading. More specifically, it is well known that in the latter case the number of folds with the smallest critical load is equal to 2. In the former case however it depends on the thickness of each layer and their moduli of elasticity. Comparison with experimental measurements shows good agreement. The thickness of the inner layer significantly affects the number of folds and the critical load (it was found that the number of folds is reduced with increasing layer thickness). Comparison of the eigenfunctions of radial and azimuthal displacements also shows more complex behavior compared to pressure loading.