Extended Multiscale Multi-Patch Isogeometric Analysis for Two-Dimensional Periodic Piezoelectric Structures Based on Penalty Function Method

High-fidelity analysis of periodic piezoelectric structures is computationally prohibitive due to the complex electromechanical coupling and periodic microstructural heterogeneity. Isogeometric analysis (IGA) using single-patch modeling cannot efficiently handle complex topologies such as honeycombs or lattice structures. To overcome these challenges, this paper proposes an extended multiscale multi-patch isogeometric analysis (EMs-MPIGA) based on the penalty method for two-dimensional periodic piezoelectric structures. The non-uniform rational B-spline (NURBS) basis functions are employed for geometrical description and mechanical simulation of unit cells to obtain the numerical heterogeneity basis functions of piezoelectric problems. The equivalent matrices, including the stiffness, piezoelectric coupling, and dielectric system matrices of unit cells, are constructed using the computed heterogeneity basis functions. Additionally, downscaling computation is applied to obtain the displacement, electric potential, and von Mises stress of the unit cells. The accuracy, reliability, and robustness of the proposed method are validated via several multiscale simulations.