压电曲壳曲梁组合结构的有限元分析和形状控制
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摘要
压电智能结构的研究在近几年来备受关注,压电材料以其灵敏度高、反应迅速、应用方便而广泛应用于航空航天、精密仪器、电子、水声等各个领域。尤其是在需要高精度控制的方面,压电材料有着无可比拟的优势。本文以有限元方法为基础,讨论了热压电耦合场下桁架结构的力学行为,重点构建了空间压电曲壳、压电曲梁单元,进而实现了空间曲面结构的静态形状控制,并且在形状控制的同时实现了作动器的优化配置,得到了良好的控制效果。本课题是国家自然科学基金(10772038,10421202,10302006)和澳大利亚ARC基金(Austrian Research Council:LX0348548 and DP0666683)资助项目,全文内容分为以下几章:
第一章:绪论部分从智能结构的概念出发,简述了压电材料的力学特性和工程应用。总结了前人在相关领域的部分工作,提出了本文的研究内容、课题背景、研究意义以及研究工作的基本框架。
第二章:从平衡方程出发,综合考虑了温度场、机械场、电场的耦合作用,推导了热压电桁架结构的有限元静力分析方程、屈曲稳定性方程。根据算例指出了温度场对桁架结构的屈曲稳定性的影响。得到了热压电桁架结构的灵敏度公式,在此基础上对结构进行了优化。结论指出在把压电杆用作主动控制元件的时候,充分考虑多场耦合的影响,更能充分发挥材料的性能,得到更经济合理的结构设计。
第三章:推导了一个基于空间任意形状的压电曲壳单元,以此构造了有限元模型。特别是利用约束方程连接主壳结构和压电作动器,简化了模型,削减了计算规模。在此基础上,首先利用最小二乘法实现了对结构的静态形状控制,然后又提出了形状控制和优化一体化设计模型,实现了更为实用的同时考虑电压和厚度作为设计变量的结构形状控制,数值算例显示可以得到更好的控制效果。
第四章:基于连续体的弹性理论构造了空间曲梁单元,在曲梁的基础上推导了空间压电曲梁单元。为了削减计算量,在梁壳组合结构的有限元模型中利用约束方程连接梁壳单元。利用最小二乘法构建了形状控制的优化模型,以控制形状和目标形状之间的误差平方和做为优化目标,得到了形状控制的最优电压分布,实现了利用压电曲梁作动器对结构进行静态形状控制。
第五章:研究了形状控制中作动器的优化配置问题,在优化配置的过程中寻找控制电压在当前配置上的最优分布。优化方法采用带约束的遗传算法,利用二进制和实型数混合编码,构建了在形状控制的同时对作动器进行优化配置、寻找最优电压分布的优化模型。利用该模型,分别得到了不同优化目标、不同约束条件下的压电作动器的最优配置。
最后总结全文,并展望了可以进一步开展的工作。
The research on piezoelectric smart structure remains a major concern in recent years. Piezoelectric material plays an important role in smart materials group for its excellent characteristic. It has been widely used in the fields of aerospace system engineering, precise instrument, electronic engineering, and hydraulics etc. In this thesis, piezoelectric smart structure is discussed by finite element method to realize the structural self- adaptive control. Firstly, a finite element formulation of piezoelectric truss structures including static analysis and buckling analysis is presented here considering the thermal-piezoelectric effects. And then, shape control of the spatial shell structure strengthened by piezoelectric curve shell or piezoelectric curve beam is proposed. At the end, an optimal placement model of piezoelectric actuators is built according to genetic arithmetic. Concretely, the contents of the thesis are arranged as follows:
Chapter 1: Based on the concept of the smart structures, some characteriters and applications of the piezoelectric materials are outlined in this part. Moreover, some works in recent years on this field are summarized and the background and framework of the thesis are introduced in this section.
Chapter 2: Considering the Thermal-Mechanical-Electrical coupling effects, the thermal piezoelectric finite element formula of the static and buckling analysis is derived for truss structures from the basic equilibrium equation. Numerical result shows that the multi-field coupling effect has a significant influence on the buckling stability of the thermal piezoelectric truss structure. A sensitivity equation is formed in this section, and design optimization of truss structure is carried out based on the sensitivity equation.
Chapter 3: This section presents a finite element formulation for the numerical simulation of the spatial curve shell structures with piezoelectric actuators, in which the host shells and piezoelectric patches are combined with constraint equations directly. The use of the constraint equations reduces the number of the DOF and improves the computation efficiency. Based on the finite element model, the optimum structure shape and a perfect voltage distribution can be obtained by using the linear least square method (LLSM). Furthermore, for the better control results, both the thickness distribution and voltages distribution of the piezoelectric patches can be obtained by an integrative model of shape control and optimization builded in this thesis.
Chapter 4: A spatical piezoelectric curve beam is derived in this section according to the elastic theory of continuum. For decreasing the scale of the computation, nodal displacement constraint equations are adopted here to link the curve beam actuators to the host structures. LLSM is employed to build a shape contrl model and to find an optimal voltages distribution. The objective function of the model is set to an error function between the desired shape and the controlled shape by voltages.
Chapter 5: Optimal placement of the piezoelectric actuators including piezoelectric shell and piezoelectric curve beam is discussed in this section. Considering both the discreted variables and continued variables existed in the optimal placement model synchronously, mixed coding genetic arithmetic (GA) is used to solve the moel. An optimal placement of the actuators and voltages distribution can be obtained in this section.
The main contributions of this dissertation are summarized and further work is suggested at the end.
The research of this dissertation is part of National Science Foundation of China (10772038, 10421202, 10302006), and supported by Australian Research Council (LX0348548, DP0666683).
第一章:绪论部分从智能结构的概念出发,简述了压电材料的力学特性和工程应用。总结了前人在相关领域的部分工作,提出了本文的研究内容、课题背景、研究意义以及研究工作的基本框架。
第二章:从平衡方程出发,综合考虑了温度场、机械场、电场的耦合作用,推导了热压电桁架结构的有限元静力分析方程、屈曲稳定性方程。根据算例指出了温度场对桁架结构的屈曲稳定性的影响。得到了热压电桁架结构的灵敏度公式,在此基础上对结构进行了优化。结论指出在把压电杆用作主动控制元件的时候,充分考虑多场耦合的影响,更能充分发挥材料的性能,得到更经济合理的结构设计。
第三章:推导了一个基于空间任意形状的压电曲壳单元,以此构造了有限元模型。特别是利用约束方程连接主壳结构和压电作动器,简化了模型,削减了计算规模。在此基础上,首先利用最小二乘法实现了对结构的静态形状控制,然后又提出了形状控制和优化一体化设计模型,实现了更为实用的同时考虑电压和厚度作为设计变量的结构形状控制,数值算例显示可以得到更好的控制效果。
第四章:基于连续体的弹性理论构造了空间曲梁单元,在曲梁的基础上推导了空间压电曲梁单元。为了削减计算量,在梁壳组合结构的有限元模型中利用约束方程连接梁壳单元。利用最小二乘法构建了形状控制的优化模型,以控制形状和目标形状之间的误差平方和做为优化目标,得到了形状控制的最优电压分布,实现了利用压电曲梁作动器对结构进行静态形状控制。
第五章:研究了形状控制中作动器的优化配置问题,在优化配置的过程中寻找控制电压在当前配置上的最优分布。优化方法采用带约束的遗传算法,利用二进制和实型数混合编码,构建了在形状控制的同时对作动器进行优化配置、寻找最优电压分布的优化模型。利用该模型,分别得到了不同优化目标、不同约束条件下的压电作动器的最优配置。
最后总结全文,并展望了可以进一步开展的工作。
The research on piezoelectric smart structure remains a major concern in recent years. Piezoelectric material plays an important role in smart materials group for its excellent characteristic. It has been widely used in the fields of aerospace system engineering, precise instrument, electronic engineering, and hydraulics etc. In this thesis, piezoelectric smart structure is discussed by finite element method to realize the structural self- adaptive control. Firstly, a finite element formulation of piezoelectric truss structures including static analysis and buckling analysis is presented here considering the thermal-piezoelectric effects. And then, shape control of the spatial shell structure strengthened by piezoelectric curve shell or piezoelectric curve beam is proposed. At the end, an optimal placement model of piezoelectric actuators is built according to genetic arithmetic. Concretely, the contents of the thesis are arranged as follows:
Chapter 1: Based on the concept of the smart structures, some characteriters and applications of the piezoelectric materials are outlined in this part. Moreover, some works in recent years on this field are summarized and the background and framework of the thesis are introduced in this section.
Chapter 2: Considering the Thermal-Mechanical-Electrical coupling effects, the thermal piezoelectric finite element formula of the static and buckling analysis is derived for truss structures from the basic equilibrium equation. Numerical result shows that the multi-field coupling effect has a significant influence on the buckling stability of the thermal piezoelectric truss structure. A sensitivity equation is formed in this section, and design optimization of truss structure is carried out based on the sensitivity equation.
Chapter 3: This section presents a finite element formulation for the numerical simulation of the spatial curve shell structures with piezoelectric actuators, in which the host shells and piezoelectric patches are combined with constraint equations directly. The use of the constraint equations reduces the number of the DOF and improves the computation efficiency. Based on the finite element model, the optimum structure shape and a perfect voltage distribution can be obtained by using the linear least square method (LLSM). Furthermore, for the better control results, both the thickness distribution and voltages distribution of the piezoelectric patches can be obtained by an integrative model of shape control and optimization builded in this thesis.
Chapter 4: A spatical piezoelectric curve beam is derived in this section according to the elastic theory of continuum. For decreasing the scale of the computation, nodal displacement constraint equations are adopted here to link the curve beam actuators to the host structures. LLSM is employed to build a shape contrl model and to find an optimal voltages distribution. The objective function of the model is set to an error function between the desired shape and the controlled shape by voltages.
Chapter 5: Optimal placement of the piezoelectric actuators including piezoelectric shell and piezoelectric curve beam is discussed in this section. Considering both the discreted variables and continued variables existed in the optimal placement model synchronously, mixed coding genetic arithmetic (GA) is used to solve the moel. An optimal placement of the actuators and voltages distribution can be obtained in this section.
The main contributions of this dissertation are summarized and further work is suggested at the end.
The research of this dissertation is part of National Science Foundation of China (10772038, 10421202, 10302006), and supported by Australian Research Council (LX0348548, DP0666683).
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