Isogeometric Reissner–Mindlin shell analysis for post-buckling of piezoelectric laminated shell panels

Isogeometric analysis (IGA) employs NURBS basis functions as shape functions, possessing geometric accuracy, high precision and high-order continuity, thereby making it very suitable for analyzing complex curved surface structures. By taking advantage of these benefits, this paper presents a geometrically nonlinear electro-mechanical coupled IGA model for accurately predicting the post-buckling behavior of piezoelectric laminated shell panels. The geometrically nonlinear governing equations for piezoelectric laminated shell panels are derived in accordance with the Reissner–Mindlin shell theory, Hamilton’s principle and Total Lagrangian (TL) incremental scheme. The geometrically nonlinear static bending, dynamic and post-buckling equations are solved using the Newton–Raphson iterative method, Newmark-$\beta$ direct integration method and Arc-length method. Several numerical examples involving geometrically nonlinear static bending, dynamic responses and post-buckling behaviors of piezoelectric laminated cylindrical and spherical shell panels subjected to electro-mechanical loads are performed, and then compared with the existing reference solutions and the results obtained by ABAQUS software to validate the accuracy and reliability of the proposed approach. The numerical results indicate that the present method exhibits high computational accuracy for piezoelectric laminated shell panels and can be applied to the analysis of arbitrary plate and shell structures.