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

Abstract

The purpose of this paper is to examine computationally the stability of shells consisting of two layers when subjected to external circumferential strain. This loading appears often in biomedicine when the smooth muscle surrounding various organs such as esophagus, lung airways, or gastrointestinal tract contracts. The differential stability equations are discretized using the finite volume method and the resulting generalized eigenvalue problem is solved using the QZ decomposition technique. The predicted number of folds agrees well with available experimental measurements. The present results show that the buckling behavior under circumferential strain loading is entirely different compared with external hydrostatic pressure loading. More specifically, in the latter case, the number of folds with the smallest critical load is always equal to 2. In the former case, however, it depends on the thickness and modulus of elasticity of each layer. The thickness of the inner layer significantly affects the number of folds and the critical buckling load. The influence of the thickness of the outer layer and the ratio of the two moduli of elasticity was also examined, but their effect was not as strong as that of the thickness of the inner layer.