This paper presents a novel multi-objective integrated optimization method for static shape control of piezoelectric functionally graded plates (FGPs). The new method combines isogeometric analysis (IGA) and an effective multi-objective non-gradient algorithm which has not been applied to the integrated design of piezoelectric FGPs. Mechanical behavior of the FGPs with surface bonded piezoelectric layers is derived using the IGA associated with a third-order shear deformation theory (TSDT). The high-order continuity of NURBS basis functions in IGA meets the demand of $C^1$-continuity of the TSDT. In optimal design problem, material layout of the FGPs and control voltages of piezoelectric layers are simultaneously optimized under the conditions of minimum static shape error and maximum first-order natural frequency. The B-spline control points for describing ceramic volume fraction distribution of the FGPs and the applied voltages are taken as design variables. In addition, an improved multi-objective particle swarm optimization algorithm is used as an optimization solver. The validity and applicability of this combination of innovative method are demonstrated through several numerical examples in integrated design.

本文提出了一种新的多目标集成优化方法，用于压电功能梯度板（FGP）的静态形状控制。该新方法结合了等几何分析（IGA）和有效的多目标非梯度算法，该算法尚未应用于压电FGP的集成设计中。使用与三阶剪切变形理论（TSDT）相关的IGA，可以得出具有表面粘结压电层的FGP的机械性能。IGA中NURBS基函数的高阶连续性可以满足$C^{\mathrm{1个}}$-TSDT的连续性。在最佳设计问题中，在最小静态形状误差和最大一阶固有频率的条件下，同时优化了FGP的材料布局和压电层的控制电压。描述FGP的陶瓷体积分数分布和施加电压的B样条控制点被用作设计变量。此外，改进的多目标粒子群算法被用作优化求解器。通过集成设计中的几个数值示例证明了这种创新方法组合的有效性和适用性。