This study presents an isogeometric layerwise element, L-IGA based on the principle of virtual displacement theory to model the bending behavior of laminated smart composite plates integrated with piezoelectric layers. Instead of using Lagrangian or Hermitian type polynomials encountered in standard finite element technology, L-IGA utilizes high-order Non-Uniform Rational B-Splines (NURBS) functions for both in-plane and through-the-thickness discretization of the geometry and the kinematic variables. Additionally, it allows different numbers of NURBS degrees and elements to be used for each patch through the thickness of the plate. In this way, exact geometry, and highly accurate solutions with rapid convergence for the benchmark electromechanical problems in the literature have been guaranteed by using L-IGA analysis. The precision of the results is meticulously verified by 3-D Ansys SOLID226 finite elements and analytical solutions. Thus, the L-IGA element can be adopted for computationally efficient and accurate static analysis of laminated plates having straight/curvilinear fibers for piezoelectric actuator and sensor configurations.

本研究提出了一种基于虚拟位移理论原理的等几何分层单元 L-IGA，用于模拟集成压电层的层压智能复合板的弯曲行为。而不是使用拉格朗日或在标准有限元技术中遇到的 Hermitian 类型多项式，L-IGA 利用高阶非均匀有理 B 样条 (NURBS) 函数对几何和运动学变量进行平面内和全厚度离散化。此外，它允许通过板的厚度为每个补丁使用不同数量的 NURBS 度数和元素。这样，通过使用 L-IGA 分析，可以保证文献中基准机电问题的精确几何和快速收敛的高精度解。结果的精度通过 3-D Ansys SOLID226 有限元和解析解进行了细致验证。因此，