Tunable multi-stability of conical Kresling origami structures utilizing local imperfections

The classic Kresling origami structure has been widely studied in the past two decades because of its interesting mechanical properties, including compressive-twist coupling deformation and bistability. It is also known that the conical derivative of Kresling origami can achieve a wider range of structural configurations while preserving the bistability of the original design. Moreover, different origami structures exhibit different responses to local geometric or material imperfections which are often inevitable in practical applications. In this study, we utilize the bar-and-hinge model to convert local imperfections to corresponding variations in nodal coordinates and equivalent stiffness values. Subsequently, we examine the response of conical Kresling origami structures to certain local imperfections. It is demonstrated that the effect of geometric imperfections on the folding properties of such structures is more substantial than that of material imperfections. We show that the multistability of conical Kresling origami structures may undergo a radical transformation when the value of the imperfection exceeds a certain threshold. Furthermore, based on responses to local imperfections, a derivative of the conical Kresling origami structure is designed which manifests tristability. This work develops a strategy for the form-finding of origami structures with tunable multistability, and can be generalized to analyze combined results from multiple local imperfections.