Abstract This paper presents a computationally efficient multifield finite element (FE) model for accurate analysis of smart composite and sandwich shells equipped with piezoelectric patch actuators and sensors, featuring multiple delaminations and transducer debonding. It employs a facet shell element with four physical nodes and one electric node, based on the third order zigzag theory approximations for displacements and a piecewise quadratic through-thickness variation for the electric potential. A hybrid point-least squares method recently proposed by the authors is extended to impose the condition of continuity of the nonlinear displacement field at the delamination, debonding, and patch fronts. The methodology is generic for multiple patch transducers, delaminations, and debonding, occurring at any arbitrary interface and in-plane locations. The model shows excellent accuracy in comparison with the coupled full-field 3D FE solutions, for the natural frequencies and complex global, local and hybrid mode shapes of delaminated smart composite shells and soft-core sandwich plates, with partially debonded actuators and sensors. The developed model will be of immense use for the design of active vibration control and structural health monitoring strategies for smart laminated shell-type structures featuring such damages.

中文翻译：

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一种耦合高效分层有限元模型，用于对具有分层和换能器脱粘特征的智能压电粘合层压壳进行自由振动分析

摘要 本文提出了一种计算效率高的多场有限元 (FE) 模型，用于准确分析配备压电贴片致动器和传感器的智能复合材料和夹心壳，具有多重分层和换能器脱粘。它采用具有四个物理节点和一个电节点的小平面壳单元，基于位移的三阶之字形理论近似值和电势的分段二次厚度变化。作者最近提出的混合点最小二乘法被扩展到在分层、剥离和贴片前沿施加非线性位移场的连续性条件。该方法适用于发生在任何任意界面和平面内位置的多个贴片换能器、分层和脱粘。与耦合全场 3D FE 解决方案相比，该模型在分层智能复合材料壳和软芯夹层板的固有频率和复杂的全局、局部和混合模式形状方面显示出出色的精度，部分脱粘的执行器和传感器。开发的模型将对具有此类损伤的智能层压壳型结构的主动振动控制和结构健康监测策略的设计具有巨大的用途。