INTEGRATED LAYOUT AND TOPOLOGY OPTIMIZATION DESIGN OF PIEZOELECTRIC SMART STRUCTURE IN ACCURATE SHAPE CONTROL
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摘要: 智能结构集智能材料与传统材料于一体，能够实现结构的主动控制，在航空航天等领域具有巨大的应用潜力.由于其系统复杂且具有多场耦合效应，智能结构的整体式优化设计方法成为结构控制技术研究的关键之一.为了提高压电智能结构的整体性能和变形精度，提出了同时考虑压电驱动器布局（分布位置及角度）和基体结构拓扑构型的协同优化设计新方法.采用多点约束方法（multi-point constraints，MPC）建立压电驱动器和基体结构的连接，定义一种与测量点目标位移相关的权重函数，以实现结构的精确变形控制.通过协同优化设计，压电驱动器可以获得最优的分布位置及角度，同时基体结构获得最优的拓扑构型，从而提升了压电智能结构系统的整体驱动性能和变形精度.通过进一步分析，研究了精确变形、体分比约束与结构优化构型和整体刚度的关系，以及优化结果中可能存在的传力路径畸变现象.数值算例的设计结果表明，采用协同优化设计方法，能够扩大结构的寻优空间，有效减小变形误差，实现压电智能结构的精确变形控制.Abstract: Smart structures are those equipped with sensors/actuators made of smart materials, which have the capability to control structure movement in such a way that makes the design more efficient. However, due to systematic complexity and multidisciplinary objectives, the optimization design of such structures in accurate shape control becomes very challenging. This paper proposes an integrated layout and topology optimization design method for accurate shape control of smart structures with surface bonded piezoelectric actuators. The multi-point constraints (MPC) method is used to simulate the bonding connections between movable piezoelectric actuators and host supporting structures. A new weighted shape error function based on desired deflections of observation points is defined to fulfill accurate shape control of piezoelectric smart structure. Through the proposed method, the optimal position and orientation of each piezoelectric actuator as well as the topology configuration of host supporting structure are founded, which significantly improves the systematic actuating and morphing performance of piezoelectric smart structures. Further studies on the relationships of structural stiffness with shape morphing constraint and volume fraction constraint are carried out, and distortions of load carrying path in optimized designs are illustrated. With several numerical results, the proposed integrated optimization method is proved to be an efficient way to decrease the error between computed and desired surface and achieve the accurate shape control of piezoelectric smart structures.
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图 1 压电智能结构协同优化示意图
Figure 1. Illustration of integrated layout and topology optimization design of piezoelectric smart structure
图 3 MPC模拟压电片与基体结构连接示意图
Figure 3. MPC connections to simulate bonding between piezoelectric actuators and host structure
图 5 压电智能悬臂板结构示意图 ( $\bigcirc $ ：测量点)
Figure 5. Schematic of a piezoelectric integrated cantilever plate ( $\bigcirc $ :observation points)
图 6 弯曲变形结构构型优化历史
Figure 6. Iterative history of optimization design of structure configuration in bending deformation
图 7 实际变形与目标变形曲面误差绝对值分布优化历史
Figure 7. Iterative history of absolute value of error distribution between computed shape and desired shape
图 9 协同优化收敛曲线
Figure 9. Convergence history of objective function and $E_{\rm r}$ constraint of iterative optimization design
图 10 形状误差约束上限对结构应变能和结构构型的影响
Figure 10. Compliance energy and structure optimized design under different $E_{\rm r}$ constraint upper bounds
图 11 体分比对结构应变能和结构构型的影响
Figure 11. Compliance energy and structure optimized design under different volume fractions
表 1 两种形状误差函数的对比
Table 1. Comparison of two shape error functions
表 2 测量点位移
Table 2. Deflections of each observation point in bending deformation
表 3 不同初始布局下的优化构型
Table 3. Different optimized design due to different original layouts
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