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 引用本文: 王剑 赵国忠 张洪武. 压电曲壳结构形状控制和优化设计[J]. 力学学报, 2007, 23(5): 618-625.
Jian Wang, Guozhong Zhao, Hongwu Zhang. Shape control and design optimization of the piezoelectric curved shell structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 618-625.
 Citation: Jian Wang, Guozhong Zhao, Hongwu Zhang. Shape control and design optimization of the piezoelectric curved shell structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 618-625.

## Shape control and design optimization of the piezoelectric curved shell structures

• 摘要: 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.

Abstract: Some flexible structures, like airfoil and satelliteantenna, usually consist of shells and plates. Their working performancesare sensitive to their shape and deformation. However, there are lots ofunpredictable factors, such as temperature, impact, creep and moisture etc.,which could influence the performance of structure. It is impossible anduneconomical to consider all detrimental factors in the design stage. Thus, it isnecessary to control the structure shape by some technologies. This paperpresents a finite element formulation for the numerical simulation of thespatial curved shell structures with piezoelectric actuators, in which thehost shells and piezoelectric patches are related with constraint equationsdirectly. The use of the constraint equations reduces the number of the DOFand improves the computation efficiency. Based on the proposed model, theoptimum structure shape and a perfect voltage distribution can be obtainedby using the linear least squares method (LLSM). Furthermore, thicknessdistribution of the piezoelectric patches is obtained by nonlinearconstraint optimization method (NCOM). Numerical examples are given todemonstrate the validity of the model proposed.

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