摘要
结构优化设计不仅可以降低结构重量和材料成本，而且能够改进结构的强度、刚度、振动特性、屈曲稳定性等性能，在工业和国防中的应用不断发展。利用压电材料的正、逆压电效应，可以分别制成作动器和传感器，在准确建立含有压电材料的结构力学模型的基础上，能方便的进行结构变形控制和振动控制。
本文研究工作由两部分组成：1．在建立了压电材料的智能结构有限元分析模型的基础上，将优化方法运用到压电结构的变形和振动控制，提出了结构与控制的联合优化设计模型和计算方法。这部分是本文的主要工作。2．研究了组合结构屈曲优化设计和灵敏度分析的计算方法及其工程应用。
为了叙述方便，各章节内容安排如下：
第一章在查阅大量文献的基础上，综述了压电材料的性质和在结构控制方面的应用，重点叙述了考虑压电耦合效应后的带有压电材料的结构力学行为分析方法，控制器的设计理论和作动器／传感器的优化配置方法。在了解相关研究领域的基础上，给出了本文的研究内容和作者的工作。
第二章建立了多种单元组合结构屈曲稳定性优化设计的通用性模型和求解方法，提出了考虑内力场与外荷载变化的屈曲临界荷载灵敏度分析算法及其对尺寸变量和形状变量的不同计算模式，将屈曲优化与静力和动力优化联合执行以解决复杂的结构优化设计问题，在新一代有限元分析和结构优化软件JIFEX中实现。第二章中还研究了复合材料层合板的分层优化设计，所谓分层就是把层合板分成几个分层，每个分层又是由铺层厚度和角度完全相同的单层组成。本文推导了结构强度和自振频率对分层厚度和角度作为设计变量时的灵敏度计算公式，推导过程中考虑了分层厚度变化时层合板中心也要发生改变的情况，保证了计算准确性。
第三章给出了作者完成的结构屈曲优化设计的工程应用实例，进一步验证了第二章提出的关于屈曲稳定性优化方法和程序的有效性，以及解决复杂结构优化设计问题的能力。同时，本章在典型结构优化设计中得到的结论也可做为工程实际问题的参考。
第四章建立了压电材料结构屈曲稳定性的有限元分析模型，主要研究了压电薄板和压电桁架的有限元模型及其计算方法。结合四边形薄板单元(DKQ)研究了压电薄板的整体屈曲稳定性分析的有限元方法，讨论了压电耦合效应以及电荷载对结构屈曲稳定性的影响；推导了以压电叠合体组成的压电桁架的有限元模型，同样研究了压电耦合效应对桁架整体屈曲稳定性的影响。
第五章在上一章压电桁架结构的有限元分析模型的基础上，进一步研究了考虑电荷载和机械荷载联合作用下的压电桁架结构的刚度，自由振动和屈曲稳定性的优化设计。不但给出了位移、自振频率和屈曲临界荷载系数对常规尺寸设计变量和形状设计变量的
大连理工大学博土学位论文
一
灵敏度计算公式，而且增加了电压这一类新的设计变量，给出了位移和屈曲荷载系数对
电压的灵敏度计算方法。在此基础上实现了通过优化压电主动析架的电压进行变形控制
和屈曲控制的新方法。
第六章首先采用位移和速度的同位状态反馈控制策略，建立了压电椅架进行振动控
制的控制方程，实现了压电析架的振动主动控制，并通过数值算例的分析得到了当消耗
同样的电能时，选用不同的压电主动杆件，控制效果有可能大不相同的结论。然后本文
章以杆件截面积和控制反馈增益系数同时作为设计变量，结构重量、动力响应和电压的
积分值作为优化约束或目标，在时域内结合Newmark微分方程的求解方法推导了约束
函数对设计变量的灵敏度分析公式，并采用序列线性／H次规划进行了优化求解，实现
了控制－结构一体化设计。最后，采用拓朴优化中的（0，l）方法将配置变量连续化处
理，进行结构自振频率、动力响应和电压对配置变量的灵敏度分析，优化求解后再进行
圆整，以解决压电智能扭架结构控制中作动器的优化配置问题。
第七章对全文工作进行了总结，并提出了还需进一步研究的内容和工作。
本文第二章第二部分是作者完成的军工预研课题“复合材料层合板分层优化设计技
术”的内容，第三章是作者完成的军工预研课题“超塑成形钛合金结构件优化设计，’和
“钛合金82Fo Bat纹板框粱优化设计软件”的研究内容。此外，作者在学位论文工作
阶段还完成了“机身结构综合优化设计”的军工预研课题。
本论文研究工作是国家杰出青年科学基金门9525206人国家重点基础研究专项经
费（GI 999032805）和高等学校骨干教师资助计划的一部分。
By means of the design optimization method, not only the weight of structures can be reduced, but also the strength, stiffness, vibration behavior, buckling stability, and other performances of structures can be improved efficiently. Now the application of structural design optimization has been promoted in the industries. The piezoelectric material, as an important type of intelligent structure materials, has the mechanical-electric coupling property to be able served as the actuators and the sensors. Therefor, based on the proper mechanical model of structures composed of piezoelectric elements, the control on structural deformation and vibration can be performed conveniently.
In this dissertation, firstly, the design optimization method of structural buckling and its engineering application are proposed. Then, the finite element formulation and vibration control model with piezoelectric material is developed. Finally, by applying the optimization method to the deformation and vibration control, the computing methods and design optimization of the structure control have been presented.
In Chapter 1, the property of the piezoelectric material and its application to the structure control are discussed. The structure mechanics analysis with piezoelectric material, the design theory of the controller and the optimum layout method of the actuator/sensor are reviewed. Based on the relative research, the main work and research contents in this paper are given.
In Chapter 2, a general-purpose model and solution algorithm for the design optimization of buckling behavior is developed for built-up structures and implemented within the JIFEX, a general purpose software for finite element analysis and design optimization. The sensitivity analysis methods accounting for the variations of pre-buckling stresses and external loads have been proposed. The computing formula of the shape optimization is different from that of the size optimizations, and the buckling optimization can also be combined with static, frequency and dynamic response optimizations in order to solve the complicated structure design optimization problem. The sub-layer design optimization of the composite laminated plate is also discussed. Sub-layer means the laminated plate can be divided into several sub-layers and each sub-layer is made of layer plate with the same thickness and fiber-stacking angle. The sensitivity analysis formulation of structural displacement and free-vibration frequency are deriv
ed. Particularly the case that the variations of the thickness of sub-layer will change the centerline of the laminated plate has been considered.
In Chapter 3, the engineering application examples of the buckling design optimization have been presented in order to demonstrate the effectiveness of the buckling optimization method presented in Chapter 2 and the ability to solve complex structure optimization problem. Additionally some conclusions about typical structure design are the reference of the engineering application.
In Chapter 4, the finite element analysis model for the piezoelectric structures has been developed. Based on the DKQ element, the finite element equations of the buckling analysis are derived for the piezoelectric thin plate structures and numerical examples show the mechanical-electric coupling effect can affect the buckling stability of thin plates and regulating external voltages can control buckling stability of piezoelectric thin plate. In the second part of chapter 4, the finite element model for piezoelectric bar composed of a number of piezoelectric thin pieces has been developed and the influence of mechanical-electric property on the buckling stability of piezoelectric trusses has also been discussed.
In Chapter 5, on the basis of former finite element method and in counting of the mechanical-electric coupling effect under electric load and mechanical load, the optimum design and sensitivity analysis methods of piezoelectric intelligent trusses on the structural stiffness, buckling stability and free-vibration freq
引文
1．高德川，王依民，邹黎明．智能材料及其应用．2000，(4)：17～19．
2. Rogers C A Intelligent Materials-The Dawn of a New Materials Age. J. Intelligent Materials System Structure, 1993,4(1):4～12.
3．陶宝祺，梁大开，王征等．智能复合材料结构在未来飞机上的应用．航空学报，1992，13(12)：642～650．
4. Utku S, Ramesh AV and Das S K. Control of a Slow-Moving Space Crane As an Adaptive Structure. AIAA J. 1991,29(6).
5．沈大荣等．埋入式光纤传感受器在重力坝的自诊断应用初探．94秋季中国材料研讨会论文摘要集，CMRS，北京：1994．
6．李长春，陶宝祺．光导纤维在钢筋混凝土土木工程中的应用．光纤与电缆及其应用技术，1994，(6)：41～45．
7. Saravanos AS and Heyliger PR. Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells. Appl. Mech. Rev., 1999,52(10):305～320.
8．陶宝祺．智能材料结构．国防工业出版社，1997，北京．
9．张涛，孙立宁，蔡鹤皋．压电陶瓷基本特性研究．光学精密工程，1998，6(5)：26～32．
10．姚守拙．压电生物传感．国防工业出版社，1997，北京．
11. Meixner H. Passive Infrared Detector Based on PVDF. Ferroelectrics, 1986,61:52～54.
12．李全禄．压电与压磁声电转换材料的研究及应用．压电与声光，1995，17(2)：43～51．
13. Warkentin, DJ and Tani J. Rainbow Actuators for Accoustic Control: The Active Wall Concept. Eight Intemational Conference on Adaptive Structures and technologies. 1997.
14. Fahy F. Sound and Structure Vibration. London: Academic Press, 1985.
15. Clark R L and Fuller C P. Experiments on Active Control of Structurally Radiated Sound Using Multiple Piezocramic Actuators, J. Acoust. Soc. Am., 1992,91(6):3313～3320.
16. Clark RL and Fuller CR. Modal Sensing of Efficient Acoustic Aadiators with Polyvinylidene Fluorick Distributed Sensors in Active Structural Acoustical Control Approaches. J. Acoust. Soc. Am., 1992,91(6):3321～3329.
17. Wang BT and Fuller CR. Near-field Pressure, Intensity and Wave-Number Distribution for Active Structural Acoustic Control of Plate Radiation: Theoretical Analysis. J. Acoust. Soc. Am., 1992,92(3):1489～1498.
18. Clark RL and Fuller CR. Optimal Placement of Piezoelectric Actuators and Polyvinlidene Fluoride Error Sensors in Active Structural Acoustic Control Approaches. J. Acoust. Soc. Am., 1992,92(3):1521～1533.
19. Guigou C and Fuller CR. Active Control of Sound Radiation from a Semi-infinite Elastic Beam with a Clamped Edge. Journal of Sound and Vibration, 1993,168(3):507～523.
20. Dimitriadis EK, Fuller CR and Rogers C A. Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates. Journal of Vibration and Acoustic, 1991,113:100～107.
21. Dimitriadis EK and Fuller CR. Active Control of Sound Transmission Through Elastic Plates Using Piezoelectric Actuators. AIAA J., 1991,29(11):1771～1777.
22. Braga AMB, Honein B, Barbone PE, Herrman G. Suppression of Sound Reflected from a Piezoelectric Plate. J. Intell. Mater Syst. and Struct., 1992,(3):209～223.
23．李山青，刘正兴，章建国．压电材料在反问题中应用的进展．上海交通大学学报，1999，33(10)：1317～1321．
24. Banks HT, Wang Y and Inman DJ. Bending and Shear Damping in Beams Frequency Domain Estimation Techniques. Transactions of ASME J of Vibration and Acoustics, 1994,116:188～197.
25. Banks H T, Smith R C and Wang Y. Smart Material Structures-Modeling Estimation and Control. New York: John Wiley and Sons Ltd, 1996.
26. Cole RG, Saunders WR and Robertshaw HH. Modal Parameter Estimation for Piezoelectric. Transactions of ASME J of Vibration and Acoustics, 1995,117:431～438.
27. Mitsum E and Norio S. Local Strain Sensing Using Piezoelectric Polymer. Journal of Intelligent Material Systems and Structures, 1993,4:558～560.
28. Galea SC, Chiu WK and Paul JJ. Use of Piezoelectric Films in Detecting and Monitoring Damage in Composites. J. Intell. Mater. Sys. and Struct., 1993,4:330～336.
29. Kudva JN, Munir N and Tan PW. Damage Detection in Smart Structures Using Neural Networks and Finite Element Analyses. Smart Material Structures, 1992,1:108～112.
30. Rees D, Chiu WK and Jones R. A Numerical Study of Crack Monitoring in Patched Structures Using a Piezoelectric Sensor. Smart Material Structures, 1992,1:202～205.
31. Yin L, Wang XM and Shen YP. Damage-Monitoring in Composite Laminates by Piezoelectric Films. Computers and Structures, 1995,59(4):623～630.
32. Yin L, Wang XM and Shen YP. Detection of Edge Delamination on Composite with Piezoelectric Sensors. Acta Mechanical Siniea, 1995,8(SI):521～524.
33．尹林，王晓明，沈亚鹏．压电传感器探测层合板分层的数值分析．力学学报，1995，27(增刊)：58～65．
34. Egashira M and Shinya N. Local Strain Sensing Using Piezoelectric Polymer. J. of Intell. Mater. Syst. and Struct., 1993,4:558～560.
35．石荣，陈伟民等．采用压电片陈列传感进行损伤监测的研究．压电与声光，2000，22(4)：277～280．
36．石立华，陶宝祺．埋入压电元件的自诊断智能结构的理论分析与实验研究．实验力学，1998，13(3)：370～376．
37. Choi K and Cheng FK. Identification of Impact Force and Location Using Distributed Sensors. AIAA J., 1996,34(1):136～142.
38. Ashida F, Choi JS and Noda N. Control of Elastic Displacement in Piezoelectric-based Intelligent Plate Subjected to Thermal Load. Int. J. of Engineering Science, 1997,35(9):851～868.
39. Ashida F, Choi JS and Noda N. Temperature Determination for a Contact Body Based on an Inverse Piezothermoelastic Problem. Int. J. of Solids Structures, 1997,34(20):2549～2561.
40. Yao, JTP. Concept of Structural Control. ASCE, J, Struct, 1972,98(7):1567～1574
41．丁文镜．振动主动控制当前的主要研究课题．力学进展，1994，24(2)：173～180．
42．李桂青，邹祖军．结构振动控制述评．地震工程与工程振动，1987，7(1)：83～93．
43．董聪，夏人伟．智能结构设计与控制中的若干核心技术问题，力学进展 1996，26(2)：166～176．
44. Rrinig KD. Disturbance Accommodating Controllers for Rotating Mechanical System, J of Dynamic System, Measurement and Control, Trans. ASME, 1986,108.
45. Leipholz HHE. Structural Control, North Holland Amsterdam, 1980.
46. Toshihisa Fujiwara et al. Optimization Analysis for Vehicle Vibration Mode Control, Trans. SAE, Section 3,1986.
47．刘文锋．现代结构控制的最新进展．力学与实践，1997，19(2)：18～19．
48．江冰，李兴丹，吴代华．Smart结构及其应用．力学进展，1994，24(3)：353～361．
49. Crawley EF. Intelligent Structures for Aerospace: A Technology Overview and Assessment. AIAA J., 1994,32(8):1689～1699.
50. Curie P and Curie J. Development by Pressure of Polar Electricity in Hemihedal Crystals with Inedined Faces. Bull Soc Min de France, 1880,3:90～93.
51. Cady WG. Piezoelectricty 1&2. Dover Publ., New York.
52. Tiersten HF. Linear Piezoelectric Plate Vibrations. Plenum Press, New York.
53．孙慷、张福学，压电学．国防工业出版社，1984，北京．
54. Ray MC, Rao KM and Samanta B. Exact Analysis of Coupled Electroelastic Behavior of a Piezoelectric Plate under Cylindrical Bending. Comput. Struct., 1992,45(4):667～677.
55. Ray MC, Bhattachanrya R and Samanta B. Exact-solutions for Static Analysis of Intelligent Structures. AIAA J., Comput. Struct., 1993,31(9):1684～1691.
56. Ray MC, Bhattachanrya R and Samanta B. Static Analysis of an Intelligent Structure by the Finite Element Method, Comput. Struct., 52(4):617～631.
57. Heylger P and Brooks S. Free-Vibration of Piezoelectric Laminates on Cylindrical Bending. Int. J. Solids Struct. 1995,32(20):2945～2960.
58. Dube GP, Kapuria S and Dumir PC. Exact Piezothermoelastic Solution of Simplysupported Orthotropic Circular Cylindrical Panel in Cylindrical Bending, Arch. Appl. Mech., 1996,66(8):537～554.
59. Tzou HS. A New Distributed Sensor and Actuator Theory for Intelligent Shells. J. Sound and Vibration, 1992,153(2):335～349.
60. Chen CQ, Shen YP and Wang XM. Exact Solution of Orthotropic Cylindrical Shell with Piezoelectric Layers under Cylindrical Bending. Int. J. Solids Structures, 1996,33(30):4481～4494.
61. Chen CQ and Shen YP. Three-dimensional Analysis for Free Vibration of Finitely Long Orthotropic Piezoelectric Circular Cylindrical Shells. ASME J. Vibration and Acoustics, 1998,120:54～58.
62. Sosa HA and Castro MA. Electroelastic Analysis of Piezoelectric Laminated Structures. Appl. Mech. Rev., 1993,46.
63．陈伟球，梁剑，丁皓江．压电复合材料矩形原板弯曲的三维分析．复合材料学报，1997，14(1)：108～115．
64．丁皓江，陈伟球，徐荣桥．横观各向同性层和矩形板弯曲、振动和稳定的三维精确分析．应用数学和力学，22(1)：16～21．
65．石志飞，黄彬彬，杜善义．功能材料力—电耦合问题的几个基本解—(Ⅰ)悬臂梁受力偶作用．复合材料学报，2001，18(1)：105～108．
66．石志飞，黄彬彬，杜善义．功能材料力—电耦合问题的几个基本解—(Ⅱ)悬臂梁梁端受轴向集中力作用．复合材料学报，2001，18(1)：109～111．
67．章木辛茂，石志飞，黄彬彬．功能材料力—电耦合问题的几个基本解—(Ⅲ)悬臂梁梁端受横向集中力．复合材料学报，2001，18(1)：112～114．
68．王子昆，尚福林．压电层合板柱形屈曲．固体力学学报，1997，18(2)：101～108．
69．王子昆，尚福林，李中华等．压电层合板热屈曲问题的精确分析．固体力学报，1997，18(1)：1～10．
70. Bailey TL and Hubbard JE. Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam. Journal of Guidance, Control, and Dynamics. 1985,8(5):605～611.
71. Crawley EF and Luis JD. Use of Piezoelectric Actuators as Elements of Intelligent Structures. AIAA J., 1987,25(10):1373～1385.
72. Crawley EF and Lazanis KB. Induced Strain Actuation of Isotropic and Anisotropic Plates. AIAA J., 1991,29(6):944～951.
73．马治国，闻邦椿，颜云辉．压电智能梁的拉伸—弯曲耦合模型．机械工程学报，1999，35(5)：24～26．
74．马治国，闻邦椿，颜云辉．智能梁结构中压电材料厚度的设计．机械设计，1999，1(1)：15～17．
75. Dimitriadis EK, Fuller CR and Rogers CA. Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates. J. Vibration and Acoustic, 1991,113(1):100～107.
76. Wang BT and Rogers CA. Modeling of Finite-Length Spatially-distributed Induced Strain Actuators for Laminate Beams and Plates. J. Intelligent. Mat. Syst. Street., 1991a,2(1):38～58.
77. Wang BT and Rogers CA. Laminate Plate Theory for Spatially Distributed Induced Strain Actuators. J. Composite Mat., 1991b, 25(4):433～452.
78. Im S and Atluri SN. Effects of a Piezo-Actuator on a Finitely Deformed Beam Subject to General Loading. AIAA J., 1989,27(12):1801～1807.
79. Chandra R and Inderjit C. Structural Modeling of Composite Beams with Induced-Strain Actuators. AIAA J., 1993,31(9):1692～1701.
80. Meressi T and Paden B. Buckling Control of a Flexible Beam Using Piezoelectric Actuators. J. Guidance, Control, and Dynamics, 1993,16(5):977～980.
81. Ding HJ, Liang J, Chen B. Fundamental Solutions of Transversely Isotropic Piezoelectric Media. Science in china (Series A), 1996,39(7):766～775.
82. Ding HJ, Chen B, Liang J. General Solutions for Coupled Equations for Piezoelectric Media. Int. J. Solids Struct., 1996,33(16):2283～2298.
83．丁皓江，王国庆，梁剑．压电介质平面问题的一般解和基本解．力学学报，1996，28(4)：441～448．
84. Ha SK, Keilers C and Chang FK. Finite Element Analysis of Composite Structures Containing Distributed Piezoceramic Sensors and Actuators. AIAA J., 1992,30(3):
772-780．
85． Wang ZD, Cheng SH and Han WZ. The Static Shape Control for Intelligent Structures. Finite Elements in Analysis and Design, 1997,26: 303-314．
86． Allik H and Hughes TJR. Finite Element Method for Piezoelectric Vibration. International Journal For Numerical Methods in Engineering, 1970,2: 151-157．
87． Tzou HS and Tseng CI. Distributed Piezoelectric Sensor/Actuator Design for Dynamic Measurement/Control of Distributed Parameter Systems: a Piezoelectric Finite Element Approach. J. Sound and Vibration, 1990,138(1) : 17-34．
88． Ha SK, Keilers C and Cheng FK. Finite Element Analysis of Composite Structures Containing Distributed Piezoceramic Sensors and Actuators. AIAA J., 1992 30(3) -772-780．
89． Chandrashekhara K and Agarwal AN. Active Vibration Control of Laminated Composite Plates Using Piezoelectric Devices: a Finite Element Approach. J. Intel. Mater. Sys &Struc., 1993,4(4) : 496-508．
90． Ray MC, Bhattacharrya R and Samanta B. Static Analysis of an Intelligent Structure by the Finite Element Method. Computers &Structures, 1994, 52(4) : 617-631．
91． Samanta B, Ray MC and Bhattacharyya R. Finite Element Model for Active Control of Intelligent Structures. AIAA J., 1996, 34(9) : 1885-1893．
92． Tzou HS and Ye R. Analysis of Piezoelastic Structures with Laminated Piezoelectric Triangle Shell Elements. AIAA J., 1996, 34(1) : 110-115．
93． Chen SH, Yao GF and Huang C. A New Intelligent Thiin-shell Element. Smart Mater Struct. 2000,99(6) : 10-18
94． Zhang XD and Sun CT. Analysis of a Sandwich Plate Containing a Piezoelectric Core Smart Mater. Struct. 1999, 8(1) : 31-40．
95． Dan DD, Aditi C and Gu HZ. Dynamics of Delaminated Composite Plates with Piezoelectric Actuators. A1AA-98-2043: 865-867．
96． Chattopadhyay A, Dan Dragomir-Daescu and Gu HZ. Dynamics of Delaminated Smart Composite Cross-ply Beams. Smart Mater. Struct. 1999, 8(4) : 92-99．
97． Benjeddou A, Trindade MA and Ohayon R. A New Shear Actuated Smart Structure Beam Element. AIAA-98-1922: 1831-1839．
98． Detwiler DT, Shen M H and Venkayya VB. Finite Element Analysis of Laminated Composite Structures Containing Distributed Piezoelectric Actuators and Sensors. Finite Elements in Analysis and Design. 1995, 20: 87-100．
99． Sze KY and Yao LQ. Modeling Smart Structures with Segmented Piezoelectric Sensors and Actuators. Journal of Sound and Vibration, 2000, 235(3) : 495-520．
100． Chen GS, Bruno RJ and Salama M. Optimal Placement of Active/Passive Members in Truss Structures Using Simulated Annealing. AIAA Journal, 1991,29(8) : 1327-1334．
101． Lu LY, Utku S and Wada BK. Vibration Suppression for Large Scale Adaptive Truss Structures Using Direct Output Feed Back Control. Journal of Intelligent Material Systems & Structures, 1993,4(3) : 385-397．
102． Sun CT and Wang T. Damping Augmentation by Delayed Actuation in Adaptive Structures. AIAA Paper 93-1692-CP.
103． Lammering R and Jia JH, Rogers CA. Optimal Placement of Piezoelectric Actuators in
Adaptive Truss Structures. Journal of Sound and Vibration, 1994,171(1):67～85.
104. Giurgiutin V, Rogers CA and Chaudhrg Z. Energy-based Comparison of Solid-state Induced-strain Actuators. J. of Intell. Mater. Syst. & Struct., 1996,7(1):4～17.
105．聂润兔，邵成功，邹家祝．自适应桁架结构机电耦合动力学方程．力学与实践，1997，19(5)：32～33．
106．聂润兔，邵成功，邹家祝．智能桁架机电耦合动力分析与振动控制．振动工程学报，1997，10(2)：119～124．
107．李俊宝，葛建明，杨庆佛．智能桁架结构机电耦合有限元分析与实验研究．太原理工大学学报，1998，29(6)：577～581．
108. Mindlin RD. On the Equations of Motion of Piezoelectric Crystals Problems of Continuum Mechanics. J. Radok(ed), SIAM, Philadelphia, 1961:282～290.
109. Mindlin RD. Equations of High Frequency Vibrations of Thermopiezoelectric Crystal Plates. Int. J. Solids Struct., 1974,10(6):625～637.
110. Rao SS and Sunar M. Analysis of Distributed Thermopiezoelectric Sensors and Actuators in Advanced Intelligent Structures. AIAA J., 1993,31(7):1280～1286.
111. Chattopadhyay Aditi, Li J and Gu HZ. Coupled Thermo-Piezoelectric-Mechanical Model for Smart Composite Laminates. AIAA J., 1999,37(12):1633～1638.
112. Chandrachekhara K and Koli M. Thermally Induced Vibration of Adaptive Doubly Curved Composite Shells Piezoelectric Devices. AIAA/ASME/ASCE/AHS/ASC 36th Structures, Structural Dyn., and Mat. Conf., New Orleans LA, 1995:1628～1629.
113. Tzou HS and Ye R. Piezothermoelasticity and Precision Control of Piezoelectric Systems: Theory and Finite Element Analysis, J. Vib. Acoust., 1994,116(4):489～495.
114. Lee HJ and Saravane DA. Coupled Layerwise Analysis of Themopiezoelectric Composite Beams. AIAA J. 1996,34(6):1231～1237.
115. Sessler GM. Piezoelectricity in Polyvinylidenefiouride. Journal of the Acoustical Society of America, 1981,70(6):1567～1576.
116. Cross LE. Polarization Controlled Ferroelectric High Strain Actuators. Journal of Intelligent Material Systems and Structures, 1991,2(3):241～260.
117. Damjanovic D and Newnham RE. Electrostrictive and Piezoelectric Materials for Actuators Application. Journal of Intelligent Material systems and Stuctures, 1992,3(2):190～208.
118. Pai PF, Nayfeh AH, Oh K and Mook DT. Refined Nonlinear Model of Composite Plates with Integrated Piezoelectric Actuators and Sensors. Int. J. Solids Struct., 1993,30(12):1603～1630.
119. Tzou HS and Bao Y. Nonlinear Piezothermoelasticity and Multi-field Actuations. Part 1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates, J Vib. Acoust., 1997,119(3):374～381.
120. Tzou HS and Bao Y. Nonlinear Piezothermoelasticity and Multi-field Actuations, Part 2: Control of nonlinear Deflection Bucking and Dynamics. J. Vib. Acoust., 1997,119(3):382～389.
121. Fripp MLR and Hagood NW. Distributed Structural Actuation with Electrostrictors. J. Sound Vib., 1997,203(1):11～40.
122. Debus J C, Pubus B and Coutte J. Finite-element Modeling of Lead Magnesium Niobate Electrostrictive Materials-static Analysis. J. Acoust. Soc. Am., 1998,103(6):3336～3343.
123. Parton VZ. Fracture Mechanics of Piezoelectric Materials. Acta Astro, 1976,3:671～683.
124. Dee WF. The Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids. Ph D Thesis, Sanford University, 1980.
125. Wang ZK. Penny Shaped Crack in Transversely Isotropic Piezoelectric Materials. Acta Mech. Sinica, 1994,10(1):43～49.
126. Gao H, Zhang TY and Tong P. Local and Global Energy Release Rates for an Electrically Yielded Crack in a Piezoelectric Ceramic. J. Mech Phys Solids, 1997,45(4):491～510.
127. Chen ZT and Yu SW. Crack Tip Fields of Piezoelctric Materials under Anti-plane Impact. Chin. Sci. Bull., 1997,42(19):1615～1619.
128. Chen ZT and Yu SW. A Semi-infinite Crack in a Piezoelectric materials under Anti-plane Impact. Int J. Fracture, 1999,91(2):197～213.
129. Huang SH, et al. Active Optimal Vibration Control for a Lumped System. Computers & Structures, 1994,51(6).
130．钟万勰．矩阵黎卡提方程的精细积分法．计算结构力学及其应用，1994，11(2)：113～119．
131. Sungkook Kang et al. Criterion Functions and Their Control Characteristics for Active Vibration Control. JSME International Journal, Series C, 1994,37(3).
132．刘华，黄田，曾子平．一类非线性振动的智能主动控制方法．非线性动力学报，1994，1(3)：288～292．
133．黄田，刘华，曾子平．基于神经网络的振动主动控制方法的研究．机械科技的未来—国家自然科学基金机械科技青年科学家论坛，北京：机械工业出版社，1993．
134．聂润兔，邵成勋，邹振祝．压电桁架结构动力学建模与振动控制．宇航学报，1998，19(4)：8～14．
135. Wang ZD, Chen SH and Han WZ. Integrated Structural and Control Optimization of Intelligent Structures. Engineering Structures, 1999,21:183～191.
136．顾仲权．振动主动控制中低阶控制器的优化设计．振动工程学报，1990，3(3)：1～8．
137. Hughes PC and Skelton RE. Controllability and Observability of Linear Matrix-second-order Systems. Journal of Applied Mechanics, 1980,47:415～420.
138. Hamdan AMA and Nayfeh AH. Measures of Modal Controllability and Observability for First and Second-order Linear Systems. Journal of Guidance, Control, and Dynamics, 1989,12(3):421～428.
139. Maghami PG and Joshi SM. Sensor-actuator Placement for Flexible Structures with Actuator Dynamics. Journal of Guidance, Control, and Dynamics, 1993,16(2):301～307.
140. Gawronski W and Lim KB. Balanced Actuator and Sensor Placement for Flexible Structures. In: Proceedings of SDM Conference. AIAA-95-3259-cp, 1995,1871～1880.
141. Viswanathan CN, Longman RW and Likins PW. A Degree of Controllability Definition Fundamental Concepts and Applications to Modal Systems. Journal of Guidance, Control, and Dynamics, 1984,7(4):222～230.
142．顾荣荣，童忠钫，程耀东．挠性结构主动减振中传感器和激振器的优化布置．振动与冲击，1995，14(3)：12～18．
143. Xu K, Warnitchai P and Igusa T. Optimal Placement and Gains of Sensors and Actuators for Feedback Control. J. Guidance, Control, and Dynamics, 1994,17(5):929～934.
144. Abdullah MM. Optimal Location and Gains of Feedback Controllers at Discrete Locations. AIAA J., 1998,36(11):2109～2116.
145. Schulz G and Heimbold G. Dislocated Actuator/Sensor Positioning and Feedback Design for Flexible Structures. J. Guidance, 1983,6(5):361～367.
146. Rao SS and Pan TS. Optimal Placement of Actuators in Actively Controlled Structures Using Genetic Algorithms. AIAA J., 1991,29(6):942～943.
147．严天宏，段登平，王建宇等．振动主动控制中传感器/作动器最优配置问题的模拟退火方法研究．振动与冲击，19(2)：1～4．
148. Kang YK, Park HC et al. Optimum Placement of Piezoelectric Sensor/Actuator for Vibration Control of Laminated Beams. AIAA J., 1996,34(9):1921～1926.
149．钱振东，黄卫等．振动控制中压电传感/驱动器的位置评估．东南大学学报，1999，29(3)：125～129．
150．李俊宝，刘华等．自适应桁架结构振动控制中主动构件的最优配置．航空学报，1996，17(6)：755～759．
151．李俊宝，刘华等．桁架结构振动阻尼控制中阻尼构件的优化配置．振动、测试与论断，1996，16(4)：26～30．
152．陈仁文，陶宝祺，陈勇．利用压电元件的空间挠性结构振动主动控制研究．数据采集与处理，1999，14(1)：128～132．
153．古渊，陈伟民等．压电减振机敏柔性板上的布片位置优化研究．压电与声光，1999，21(1)：32～40．
154．马扣根，顾仲权．振动主动控制中传感器与作动器参数的优化设计．振动工程学报，19914(1)：85～89．
155．马扣根，顾仲权．最优极点配置法在梁式结构振动主动控制中的应用．振动与冲击，1991，10(3)：63～66．
156．李宾，李玉刚等．智能结构压电执行器位置优化的模态力准则．中国空间科学技术，2000，10：1～5．
157．李宾，李玉刚等．压电智能杆梁结构总执行器的位置优选准则．压电与声光，1999，21(3)：185～190．
158．孙东昌，王大钧，Xu Zhongling．智能桁架振动控制的模态方法及主动杆优化配置．中国空间科学技术，1998，4：1～6．
159. Chen G S, Bruno R J and Salama M. Optimal Placement of Active/Passive Members in Truss Structures Using Simulated Annealing. AIAA J., 1991,29(8):1327～1334.
160. Ryou JK, Park KY and Kim SJ. Electrode Pattern Design of Piezoelectric Sensors and Actuators Using Genetic Algorithms. AIAA J., 1998,36(2):227～233.
161．张俊华，张方等．压电结构的控制-结构一体化设计．南京航空航天大学学报，1999，31(4)：410～414．
162．曹宗杰，孙长江，陈塑寰．奇异值摄动法及其在智能结构振动控制中的应用．吉林工业大学自然科学学报，2000，30(1)：44～47．
163. Delorenzo ML. Sensor and Actuator Selection for Large Space Structure Control. Journal of Guidance, Control, and Dynamics, 1990,13(2):249～257.
164. Hale AL, Lisouski RJ and Dohl WE. Optimal Simultaneous Structural and Control Design of Maneuvering Flexible Spacecraft. Journal of Guidance and Control, 1985,8(1):86～93.
165. Miler DF and Shim J. Gradient-based Combined Structural and Control Optimization. Journal of Guidance and Control, 1987,10(3):291～298.
166. Thomas HL. Control-Augmented Structural Synthesis with Dynamic Stability Constraints. AIAA J., 1991,29(4):619～626.
167. Rao SS, Venkayya VB and Khot NS. Game Theory Approach for the Integrated Design of Structures and Controls. AIAA J., 1998,26(4):463～469.
168. Rao SS. Combined Structural and Control Optimization of Flexible structures. Eng. Opt., 1988,13:1～16.
169. Rao SS, Venkayya VB and Khot NS. Optimization of Actively Controlled Structures Using Goal Programming Techniques. Int. J. for Numer. Methods Eng., 1988,26:183～197.
170. Grandhi RV. Structural and Control Optimization of Space Structures. Computers & Structures, 1989,31(2):139～150.
171. Wang ZD and Chen SH. Sensitivity Analysis of Eigenmodes and Dynamic Responses for Intelligent Structures. Finite Elements in Analysis and Design, 1999,33:71～81.
172. Wang ZD, Chen SH and Han WZ. Integrated Structural and Control Optimization of Intelligent Structures. Engineering Structures, 1999,21:183～191.
173．钟万勰．计算力学与最优控制．大连：大连理工大学出版社，1993．
174. Khot NS, Venkayya VB and Berke L. Optimal Structural Designs with Stability Constraints, Int. J. Numer. Methods Eng., 1976,10:1097-1114.
175. Gu YX and Cheng GD, Structural Modeling and Sensitivity Analysis of Shape Optimization, 1993, J. Struct. Opti., 6(1):29-37.
176．顾元宪，程耿东．结构形状优化设计数值方法的研究和应用，计算结构力学及其应用，1993，10(3)：321-335．
177. Gu YX, Kang Z and et al. Dynamic Sensitivity Analysis and Optimum Design of Aerospace Structures, Int. J Struct. Eng. Mech., 1998,6(1):31-40.
178. Gu YX, Zhang HW and et al. New Generation Software of Structural Analysis and Design Optimization--JIFEX, Int. J. Struct. Eng. Mech. 1999,7(6):589-599.
179. Nogis U. Design Sensitivity Analysis for Buckling Load of Elastic Structures, ZAMA, Z. Angew., Math. Mech., 1986,66:775-776.
180. Hirano. Y, Optimum Design of Laminated Plates under Axial Compression. AIAA, 1979,17(9):1017-1019.
181．蒋咏秋．纤维增强复合材料层合板的优化设计．计算结构力学及其应用，1984，1(1)：39-46．
182．唐俊．复合材料层合板的铺层优化分析及拉伸—弯曲耦合刚度的影响．计算结构力学及其应用，1984，1(2)：75-84．
183．蒋咏秋．纤维增强复合材料层合圆柱壳的优化设计．复合材料学报，1985，2(3)：13-21．
184. Riche RL, Haftka RT. Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm. AIAA J., 1993,31(5):951-956.
185. Mateus HC, Mota Soares CM and Mota Soares CA. Senstivity Analysis and Optimal Design of Thin Laminated Composite Structures. Computers & Structures, 1991,41(3):501～508.
186．陈塑寰，关鹏，梁平．复合材料对称层合板特征值问题的灵敏度分析．复合材料学报，1996，13(3)：87～92．
187．顾元宪，曾庆刚．一种新的四边形层合板与夹层板单元．大连理工大学学报，1997，37(4)：392-397．
188. Gu YX, Zhao GZ, Zhang HW, Kang Z and Grandhi HV. Buckling Design Optimization of Complex Built-up Structures with Shape and Size Variables. Struct Multidisc Optimi, 2000,19(3):183-191.
189．尹林，王小明，沈亚鹏．用压电元件实现复合材料层合板振动控制的数值分析．振动工程学报，1992，9(2)：107-115．
190．姚林泉，俞焕然．具有压电材料薄板稳定性的有限元法．兰州大学学报，1999，35(1)：44-48．
191．葛增杰、张京街．薄板稳定性分析中的一个精化不协调元．大连理工大学学报，1999，39(5)：616-620．
192．薛宏宇．关于十二参数任意四边形Kirchhoff薄板单元的研究．大连理工大学硕士学位论文，大连，1997．
193. Botoz JL and Tahar MB. Evaluation of a New Quadrilateral Thin Plate Bending Element. Int. J. Num. Meth. Eng, 1982,18:1655-1677.
194．史宝军，鹿晓阳，许焕然．一个简明有效的四边形杂交/混合薄板弯曲单元．工程力学，2000，17(2)：102-107．
195．唐家祥．结构稳定理论，北京：中国铁道出版社，1989
196．陈万吉．精化直接刚度法及九参数三角形薄板单元，大连理工大学学报，1993，33(3)：289-296．
197. Tseng CI. Electromechanical Dynamics of a Coupled Piezoelectric/mechanical System Applied to Vibration Control and Distributed Sensing, PH. D. Dissertation, univ. of kentucky, Lexington, Ky. July, 1989.
198. Tzou HS. Piezoelectric Shells: Distributed Sensing and Control of Continua. Kluwer Academic Publishers, 1993, Netherlands.
199．姚林泉．具有压电材料弹性环形板的屈曲．力学学报，1998，30(2)：233-236．
200．田晓耕，沈亚鹏，高坚新．压电板屈曲与后屈曲的有限元分析．固体力学学报，2000，21(2)：123～130．
201．邓可顺等．组合结构总体弹性屈曲分析，大连工学院学报，1984，23(1)：129～135．
202．朱小锦，陶宝祺等．压电机敏桁架结构振动自适应控制及实验研究．振动、测试与诊断，1998，18(2)：98～102．
203．李俊宝，刘华等．自适应桁架结构动态测试中主动构件配置研究．振动、测试与诊断，1998，18(3)：184～189．
