Buckling Sensitivity Analysis and Optimal Design of Two-Layered Shells Under Circumferential Strain Load

Shell buckling under circumferential strain loading appears often in many biomedical problems, such as collapse of asthmatic airways, esophagus etc. Currently there is no analytic solution from which the critical buckling load can be calculated from the geometrical and material properties of the shell layers. The theoretical analysis leads to the numerical solution of a generalized eigenvalue problem. The purpose of the present paper is to present a method with which the sensitivity of the buckling load (minimum positive eigenvalue) to uncertainties of the geometrical and material parameters can be calculated. It is shown that the sensitivity can be evaluated with the aid of the left (adjoint) eigenvectors. The proposed method is validated against separate global computations using the finite difference method. Finally, we employ the information on sensitivity to optimize the thickness of the outer shell layer in order to maximize the buckling load.