| 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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