压电桁架结构系统可靠性分析
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摘要
由于日益迫切的振动控制和形状控制需要,智能结构特别引起了航空航天界的极大关注。目前,由传感器、致动器和处理中枢组成的智能结构已经应用到在许多领域中。智能结构是一种含有压电材料、电／磁致伸缩材料或形状记忆合金等主动材料的结构形式,因为压电材料与其它主动材料相比有很多优势,它已越来越多地应用到各种智能结构中。作为一种电介质材料和脆性材料,压电材料中不可避免的存在力失效和电失效的问题,而且由于结构系统本身及其所处环境的不确定因素,使得压电智能结构的可靠性分析变得复杂,随着其应用的广泛,智能结构的可靠性已成为一个热点问题,因此开展对压电智能结构的随机分析并评价其可靠性是非常必要的。
本文研究了同时考虑力／电失效的智能结构可靠性问题,主要有以下几个方面：
1、讨论和研究了压电晶体的力学、电学性能,从压电效应出发,对压电致动器的驱动技术进行了介绍。基于热力学原理推导了压电广义本构关系,阐述了压电材料各参数间的相互关系,给出了按IEEE标准记法的表达式,讨论了机械、电、热三种能量形态之间的相似性及耦合关系。
2、介绍了电介质材料的雪崩击穿机理,阐述了因电击穿机理的复杂性难以建立其解析表达式。本文基于诱发微短路的服从麦克斯韦—玻尔兹曼(Maxwell-Boltzmann)分布的假设,建立了压电材料电击穿统计公式,并与弱点击穿理论公式做了比较,指出了弱点击穿理论公式的局限性。
3、给出了考虑预压力的压电致动器的机电耦合方程,理论分析了致动器的最大输出位移／力。并算例分析了压电堆与预压弹簧的刚度比的可行最佳取值范围。
4、运用最小势能原理,给出了压电堆的有限元求解方程。并在此基础上,分析了主动杆的热力学控制方程,给出了主动杆(一般由压电段和普通段组成)的有限元机电耦合方程。
5、结合压电桁架结构的力学特点,给出了可靠性分析的安全余量表达形式,采用改进的一次二阶矩法(Advanced First Order Second Moment, AFOSM)和Taylor展开随机有限元法(Taylor Stochastic Finite Element Method, TSFEM)给出了安全余量可靠性指标的计算方法；运用可靠性的基本理论,进行压电桁架结构系统的可靠性分析,采用概率网络估算技术(Probabilistic Network Evaluation Technique, PNET)求出压电桁架结构系统的可靠性指标。最后用数值算例说明方法的详细步骤和有效性。
For a strong and increasing demand for vibration and shape control, intelligent structures receive a considerable interest in the field of aerospace, specially. Applications of intelligent structures consisting of large numbers of distributed sensors, actuators, and processors are found in a very broad range of industries. Intelligent structures are structural systems which include active materials, such as piezoelectrics, electrostrictives, magnetostrictives, or shape memory alloys etc. Because piezoelectric materials offer many advantages compared to other active materials, piezoelectric materials are increasingly used in various intelligent structures. As a storage dielectric or a brittle material for the applications, it is ineluctable that there are the problems of electrical failures and mechanical failures in it. Otherwise, because of the uncertainty factors of structure system or its work environment, the reliability analysis is becoming more difficult for piezoelectric intelligent structures. Along with the extension of their use, the reliability of intelligent structures has been an important issue. it is necessary to make stochastic analysis of piezoelectric structure and evaluate its reliability.
The thesis has made some progress in reliability analysis of intelligent structure with the electrical/mechanical failure have been taken into account. The main areas covered by the thesis are:
1. The performance of mechanics and electricity about piezoelectric crystal was discussed and studied. The drive techniques of piezoelectric actuators were introduced basing on the study of piezoelectric effect. Based on the thermodynamic principle, the generalized constitutive relations of piezoelectric materials were obtained. The interrelation of the each piezoelectric parameters were expatiated, also according to the IEEE Standard, the comparability and the bilateral coupling relationships between mechanical energy, electrical energy and thermal energy were discussed.
2. The avalanche mechanism of dielectric materials was introduced, and the complexities of the process of electrical breakdown were explained, so the statistics methods act as a more and more important role in this field. Assuming a Maxwell-Boltzmann distribution of defect energies that can produce micro-shorts, the statistical formula of electrical breakdown of piezoelectric materials was presented. Moreover, the comparative analysis with the weak point theory was given, and the limitation of the weak point theory was also pointed out.
3. The electro-mechanical coupling equations of spring-preloaded piezoelectric actuator were presented, the maximize displacement/force outputs were analyzed in theory. A numerical example was given to show the feasible range of stiffness ratio between the piezoelectric stack and the spring.
4. With the principle of minimum potential energy for piezoelectric stack applied, solving formulae of the finite element method was established. On the basis of analysis above, the electro-mechanical coupling finite element formulation of piezoelectric active bar, which are commonly composed of a piezoelectric stack and two metallic bars, was particularly deduced.
5. Combining the mechanical character of piezoelectric truss structure, the reliability analysis of piezoelectric truss structure was discussed, the safety margin functions for reliability analysis were established, adopting Advanced First Order Second Moment (AFOSM) and Taylor expansion Stochastic Finite Element Method (TSFEM), the method of reliability of piezoelectric truss structure was given, and using the theory of reliability, the reliability index of piezoelectric truss structure system was acquired by Probabilistic Network Evaluation Technique, (PNET). Finally, numerical example was presented to explain the detailed process and demonstrate the validity and effectiveness of the method.
本文研究了同时考虑力／电失效的智能结构可靠性问题,主要有以下几个方面：
1、讨论和研究了压电晶体的力学、电学性能,从压电效应出发,对压电致动器的驱动技术进行了介绍。基于热力学原理推导了压电广义本构关系,阐述了压电材料各参数间的相互关系,给出了按IEEE标准记法的表达式,讨论了机械、电、热三种能量形态之间的相似性及耦合关系。
2、介绍了电介质材料的雪崩击穿机理,阐述了因电击穿机理的复杂性难以建立其解析表达式。本文基于诱发微短路的服从麦克斯韦—玻尔兹曼(Maxwell-Boltzmann)分布的假设,建立了压电材料电击穿统计公式,并与弱点击穿理论公式做了比较,指出了弱点击穿理论公式的局限性。
3、给出了考虑预压力的压电致动器的机电耦合方程,理论分析了致动器的最大输出位移／力。并算例分析了压电堆与预压弹簧的刚度比的可行最佳取值范围。
4、运用最小势能原理,给出了压电堆的有限元求解方程。并在此基础上,分析了主动杆的热力学控制方程,给出了主动杆(一般由压电段和普通段组成)的有限元机电耦合方程。
5、结合压电桁架结构的力学特点,给出了可靠性分析的安全余量表达形式,采用改进的一次二阶矩法(Advanced First Order Second Moment, AFOSM)和Taylor展开随机有限元法(Taylor Stochastic Finite Element Method, TSFEM)给出了安全余量可靠性指标的计算方法；运用可靠性的基本理论,进行压电桁架结构系统的可靠性分析,采用概率网络估算技术(Probabilistic Network Evaluation Technique, PNET)求出压电桁架结构系统的可靠性指标。最后用数值算例说明方法的详细步骤和有效性。
For a strong and increasing demand for vibration and shape control, intelligent structures receive a considerable interest in the field of aerospace, specially. Applications of intelligent structures consisting of large numbers of distributed sensors, actuators, and processors are found in a very broad range of industries. Intelligent structures are structural systems which include active materials, such as piezoelectrics, electrostrictives, magnetostrictives, or shape memory alloys etc. Because piezoelectric materials offer many advantages compared to other active materials, piezoelectric materials are increasingly used in various intelligent structures. As a storage dielectric or a brittle material for the applications, it is ineluctable that there are the problems of electrical failures and mechanical failures in it. Otherwise, because of the uncertainty factors of structure system or its work environment, the reliability analysis is becoming more difficult for piezoelectric intelligent structures. Along with the extension of their use, the reliability of intelligent structures has been an important issue. it is necessary to make stochastic analysis of piezoelectric structure and evaluate its reliability.
The thesis has made some progress in reliability analysis of intelligent structure with the electrical/mechanical failure have been taken into account. The main areas covered by the thesis are:
1. The performance of mechanics and electricity about piezoelectric crystal was discussed and studied. The drive techniques of piezoelectric actuators were introduced basing on the study of piezoelectric effect. Based on the thermodynamic principle, the generalized constitutive relations of piezoelectric materials were obtained. The interrelation of the each piezoelectric parameters were expatiated, also according to the IEEE Standard, the comparability and the bilateral coupling relationships between mechanical energy, electrical energy and thermal energy were discussed.
2. The avalanche mechanism of dielectric materials was introduced, and the complexities of the process of electrical breakdown were explained, so the statistics methods act as a more and more important role in this field. Assuming a Maxwell-Boltzmann distribution of defect energies that can produce micro-shorts, the statistical formula of electrical breakdown of piezoelectric materials was presented. Moreover, the comparative analysis with the weak point theory was given, and the limitation of the weak point theory was also pointed out.
3. The electro-mechanical coupling equations of spring-preloaded piezoelectric actuator were presented, the maximize displacement/force outputs were analyzed in theory. A numerical example was given to show the feasible range of stiffness ratio between the piezoelectric stack and the spring.
4. With the principle of minimum potential energy for piezoelectric stack applied, solving formulae of the finite element method was established. On the basis of analysis above, the electro-mechanical coupling finite element formulation of piezoelectric active bar, which are commonly composed of a piezoelectric stack and two metallic bars, was particularly deduced.
5. Combining the mechanical character of piezoelectric truss structure, the reliability analysis of piezoelectric truss structure was discussed, the safety margin functions for reliability analysis were established, adopting Advanced First Order Second Moment (AFOSM) and Taylor expansion Stochastic Finite Element Method (TSFEM), the method of reliability of piezoelectric truss structure was given, and using the theory of reliability, the reliability index of piezoelectric truss structure system was acquired by Probabilistic Network Evaluation Technique, (PNET). Finally, numerical example was presented to explain the detailed process and demonstrate the validity and effectiveness of the method.
引文
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