Modeling of piezoelectric semiconductor cylindrical nanoshells: A fully coupled analysis accounting for flexoelectric and strain gradient effects

Piezoelectric semiconductor (PS) cylindrical shells offer a promising platform for flexible electronics, owing to their curvature-induced superior strain distribution and high tunability of carrier transport. However, to enable their application at the nanoscale, it is necessary to take account of size effects stemming from large strain gradients. This paper proposes a comprehensive theoretical model for PS cylindrical nanoshells that concurrently incorporates flexoelectric and strain gradient effects, alongside the macroscopic PS characteristics. The structural model is derived from a general orthogonal curvilinear coordinate system and the principle of virtual work, with static and dynamic solutions obtained by solving the eigenvalue problem and validated against a mixed finite element model. Our analysis reveals two key and interesting findings: first, the strain gradient effect generally enhances global structural stiffness while triggering complex, nonuniform spatial redistributions of electromechanical fields; second, piezoelectricity and flexoelectricity demonstrate a complex synergistic–competitive interplay, manifesting primarily in their divergent effects on electric potential and charge redistribution. The developed PS shell model, combined with insights into the tuning mechanisms governing multifield interactions and vibrational characteristics, provides valuable guidance for the optimized design of self-sensing shell-type nanoelectronics.