Geometrically nonlinear electro-mechanical coupled multi-patch IGA for distributed piezoelectric structures based on Nitsche’s method

Numerical simulations play a crucial role in predicting electro-mechanical coupling nonlinear behavior of distributed piezoelectric smart structures, which have been greatly implemented in real-world engineering practices. This paper presents an original investigation into the application of non-conforming multi-patch methodology for analyzing the geometrically nonlinear behavior of distributed electroelastic coupled structures, effectively overcoming the limitations of conventional single-patch NURBS-based isogeometric analysis (IGA). In the framework of the first-order shear deformation theory (FSDT), von Kármán nonlinear theory, and Total Lagrangian (TL) formulations, the geometrically nonlinear multi-patch IGA formulations for piezoelectric smart structures are developed with regard to Nitsche’s method. Specifically, Nitsche’s method enforces field variable continuity across coupling interfaces between adjacent NURBS patches. Based on the verification of isotropic plates, the validated multi-patch geometrically nonlinear IGA is extended to investigate nonlinear static/dynamic behaviors and sensor output characteristics of fully-covered and distributed piezo-laminated plates. For broader applications, both conventional piezoceramics and advanced macro-fiber composites (MFC) are considered. The systematic comparative results demonstrate that the proposed methodology provides accuracy and efficiency in analyzing geometrically nonlinear behavior of distributed piezoelectric smart plates.