STUDY ON BOUNDARY EFFECTS ON BI-STABLE THIN SHELL STRUCTURES

An improved model is proposed to derive the analytical expressions of strain energy taking into account boundary effects on the thin shell structures. Based on the principle of energy, the two stable configurations of the thin shell structures can be obtained, and the corresponding curvatures and rolled-up radii are derived. It is shown that the potential energy of the thin shell structure with initial stress is minimal when the shell is in the coiled state. The shell has the second stable configuration. Thusly, it is a bi-stable structure. Compared with the thin shell structure without a boundary effect, the computation shows that the rolled-up radius for the second stable state of the shell including a boundary effect becomes larger and the corresponding strain energy becomes smaller. In addition, the larger initial central angle for the cross-section of the thin shell structure, the smaller influence of the boundary effects will be. Compared with the rolled-up radii, the deformation caused by boundary effects is a higher order trace value. The theoretical results of this paper agree well with the exiting theoretical results and numerical results, which proves the validity of the models.