Multi-patch isogeometric analysis for smart plates with distributed piezoelectric patches

The previous isogeometric analysis (IGA) on piezoelectric smart structures mainly focused on plates and shells that were fully covered with piezoelectric materials. However, the piezoelectric materials in smart structures commonly exist in the form of patches that are locally attached to the substrate structures, in practical engineering applications. Thus, this paper aims to apply IGA to analyze the electro-mechanical coupled behaviors of distributed piezoelectric smart plates. The Nitsche-based non-conforming multi-patch technology is adopted to deal with the precision limitations associated with single-patch IGA for distributed piezoelectric smart plates. In accordance with first-order shear deformation theory (FSDT) and NURBS-based IGA, the non-conforming multi-patch governing equations for piezoelectric smart plates are then derived. In particular, the Nitsche’s method is adopted for addressing the non-conforming meshes and ensuring the continuity of the field variables on the coupling boundary between two adjacent patches. The developed methodology is further extended to analyze the fully-covered and distributed piezoelectric smart plates. Meanwhile, to enhance the general applicability of the method, the piezoelectric smart plates integrated with traditional piezoelectric ceramics and macro-fiber composite (MFC) materials are designed in numerical examples. Finally, comprehensive assessments for natural frequency and static response of piezoelectric smart plates are carried out and then compared with the existing reference solutions or the results calculated by ABAQUS software to demonstrate the effectiveness and accuracy of the developed method. These numerical examples validate that the proposed method is capable of addressing the limited accuracy of single-patch IGA in distributed piezoelectric smart structures.