压电曲壳结构形状控制和优化设计

板壳结构作为航空、航天工程以及控制系统中的重要工作元件，在工作状态 中，要承受机械载荷、温度载荷、冲击载荷等各种负面影响， 而航空航天部件对结构形状变化非常敏感，如飞行器机翼、信息接收天线等结构, 微小的结构变形就会引起很大的性能改变，想要在设计初始阶段充分考虑所有不 利因素的影响显然是比较困难的. 利用压电材料控制结构变形往往是现代空间结 构开关控制中一个很好的选择. 基于一般壳体有限单元法, 推导了空间任意曲壳 压电单元, 利用约束方程连接主体壳元和压电壳元, 模型中约束方程的使用大大 减少了结构自由度, 使得计算速度有了明显的提升. 在此基础上, 重点研究了压 电曲壳结构的形状控制方法, 首先利用最小二乘法优化结构的电压分布, 控制结 构形状接近最优工作状态; 其次构建了以压电壳元厚度和电压联合作为设计变量 的优化控制模型, 采用非线性优化求解方法, 取得了更好的控制效果. 数值算例 表明了该文计算模型、 优化设计和控制方法的有效性.

SHAPE CONTROL AND DESIGN OPTIMIZATION OF THE PIEZOELECTRIC CURVED SHELL STRUCTURES

Some flexible structures, like airfoil and satellite antenna, usually consist of shells and plates. Their working performances are sensitive to their shape and deformation. However, there are lots of unpredictable factors, such as temperature, impact, creep and moisture etc., which could influence the performance of structure. It is impossible and uneconomical to consider all detrimental factors in the design stage. Thus, it is necessary to control the structure shape by some technologies. This paper presents a finite element formulation for the numerical simulation of the spatial curved shell structures with piezoelectric actuators, in which the host shells and piezoelectric patches are related with constraint equations directly. The use of the constraint equations reduces the number of the DOF and improves the computation efficiency. Based on the proposed model, the optimum structure shape and a perfect voltage distribution can be obtained by using the linear least squares method (LLSM). Furthermore, thickness distribution of the piezoelectric patches is obtained by nonlinear constraint optimization method (NCOM). Numerical examples are given to demonstrate the validity of the model proposed.