焦热电陶瓷材料流固两相界面效应的三维格林函数分析方法
发布时间：2018-07-24 20:48
【摘要】：格林函数法是求解数学物理方程的一种常用方法,在固体力学的理论和应用研究中起着重要作用。格林函数的描述对象是点源产生的场,它是许多理论和数值计算的基础,如边界元法等。采用叠加原理,格林函数可以用于对任意载荷作用下的复杂工程问题进行求解。此外它们还可以被用来对工程中常见的裂缝,损伤和杂质问题进行解析求解。 近几年来正在高速发展的功能材料,实际使用中一般需要与其他材料结合在一起,由此产生界面效应和多物理场耦合,无论从结构的安全性,还是从功能元件的可靠性考虑,都必须作多场耦合的分析和评价。流固耦合及其界面问题是这些工程实际问题的重要组成部分。横观各向同性焦热电陶瓷是工程中常见的材料,这种材料经常与匀质介电流体配合使用,本文以这两种材料作为流固耦合模型的对应两相,采用格林函数分析方法,研究点源作用下两相体的多物理场耦合关系。力电耦合是焦热电陶瓷材料的固有特性,此外该材料也对温度相当敏感,鉴于焦热电陶瓷材料制品实际工作环境的复杂性,在研究焦热电陶瓷材料的流固两相界面效应时,应主要着眼于两相体内部热-电-弹性场的变化。 本文首先介绍了横观各向同性焦热电材料在考虑力-热-电耦合效应下的三维本构方程、平衡方程和热传导方程。利用微分算子理论和Almansi理论,得到了用单调和函数表示的三维稳态简洁通解。对于匀质介电流体,给出了用调和函数表示的电位和温度增量的通解。这些调和函数形式表示的稳态通解为后续的两相体多场耦合研究奠定了基础。 后面章节分别对点热源作用在焦热电陶瓷材料流固两相体固体内部和流体内部,点电荷、点力作用于焦热电陶瓷材料流固两相体固体内部,点电荷作用于两相体中流体内部的情况,运用格林函数分析方法,引入多个含待定常数的调和函数,考虑相应的边界条件、连续性条件和平衡条件来确定待定常数,求解扩展的Mindlin和扩展的Lorentz解。各章最后通过数值算例分析,给出了各点源作用形式下,耦合场无量纲温度增量、应力分量和电位移分量的等值线图,获得了一些有工程应用价值的结论,比如指导俘能器和传感器的设计。格林函数的分析方法,为考虑力-热-电耦合效应的流固耦合问题进行理论分析和数值计算提供了一种可以选择的平台,所构造的基本解用初等函数表示,形式简洁,便于在理论和工程中推广应用。
[Abstract]:The Green's function method is a common method for solving mathematical and physical equations, which plays an important role in the theoretical and applied research of solid mechanics. The description object of Green's function is the field produced by point source, which is the basis of many theories and numerical calculations, such as boundary element method. Using the superposition principle, Green's function can be used to solve complex engineering problems under arbitrary loads. In addition, they can be used to solve the problems of cracks, damage and impurity in engineering. In recent years, functional materials, which are developing at a high speed in practice, usually need to be combined with other materials in practical use, resulting in interface effects and multi-physical field coupling, both in terms of structural safety and reliability of functional components. The analysis and evaluation of multi-field coupling must be made. The fluid-solid coupling and its interface problems are important components of these engineering practical problems. Transversely isotropic pyroelectric ceramics are common materials in engineering. These materials are often used in conjunction with homogeneous dielectric fluids. In this paper, the two materials are used as the corresponding two phases of the fluid-solid coupling model, and the Green's function analysis method is used. The multi-physical field coupling relation of two-phase body under the action of point source is studied. Electromechanical coupling is an inherent characteristic of pyroelectric ceramic materials. In addition, the material is also sensitive to temperature. In view of the complexity of the actual working environment of pyroelectric ceramic materials, the fluid-solid two-phase interface effect of pyroelectric ceramic materials is studied. The change of thermoelectric-elastic field in the two-phase body should be focused on. In this paper, the three dimensional constitutive equations, equilibrium equations and heat conduction equations of transversely isotropic pyroelectric materials are first introduced. By using the theory of differential operator and Almansi theory, a simple and simple solution of three-dimensional steady state is obtained, which is expressed by monotone sum function. For homogeneous dielectric fluid, the general solution of potential and temperature increment expressed by harmonic function is given. The steady-state general solutions of these harmonic function forms lay a foundation for the further study of two-phase multifield coupling. In the following chapters, the point heat source acting on the solid of the fluid-solid two-phase body and the fluid, the point charge and the point force acting on the solid of the fluid-solid two-phase body of the pyroelectric ceramic material, The point charge acts on the fluid in a two-phase body. By using Green's function analysis method, several harmonic functions with undetermined constants are introduced, and the corresponding boundary conditions, continuity conditions and equilibrium conditions are considered to determine the undetermined constants. The extended Mindlin and the extended Lorentz solution are solved. At the end of each chapter, through numerical example analysis, the isoline diagrams of dimensionless temperature increment, stress component and electric displacement component of coupling field under the action of point source are given, and some valuable conclusions of engineering application are obtained. Such as guiding the design of energy capture and sensors. The analysis method of Green's function provides an alternative platform for the theoretical analysis and numerical calculation of fluid-solid coupling problem considering the force thermoelectric coupling effect. The basic solution is expressed by elementary function and the form is simple. It is easy to be popularized and applied in theory and engineering.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O302;TQ174.1
本文编号：2142611
[Abstract]:The Green's function method is a common method for solving mathematical and physical equations, which plays an important role in the theoretical and applied research of solid mechanics. The description object of Green's function is the field produced by point source, which is the basis of many theories and numerical calculations, such as boundary element method. Using the superposition principle, Green's function can be used to solve complex engineering problems under arbitrary loads. In addition, they can be used to solve the problems of cracks, damage and impurity in engineering. In recent years, functional materials, which are developing at a high speed in practice, usually need to be combined with other materials in practical use, resulting in interface effects and multi-physical field coupling, both in terms of structural safety and reliability of functional components. The analysis and evaluation of multi-field coupling must be made. The fluid-solid coupling and its interface problems are important components of these engineering practical problems. Transversely isotropic pyroelectric ceramics are common materials in engineering. These materials are often used in conjunction with homogeneous dielectric fluids. In this paper, the two materials are used as the corresponding two phases of the fluid-solid coupling model, and the Green's function analysis method is used. The multi-physical field coupling relation of two-phase body under the action of point source is studied. Electromechanical coupling is an inherent characteristic of pyroelectric ceramic materials. In addition, the material is also sensitive to temperature. In view of the complexity of the actual working environment of pyroelectric ceramic materials, the fluid-solid two-phase interface effect of pyroelectric ceramic materials is studied. The change of thermoelectric-elastic field in the two-phase body should be focused on. In this paper, the three dimensional constitutive equations, equilibrium equations and heat conduction equations of transversely isotropic pyroelectric materials are first introduced. By using the theory of differential operator and Almansi theory, a simple and simple solution of three-dimensional steady state is obtained, which is expressed by monotone sum function. For homogeneous dielectric fluid, the general solution of potential and temperature increment expressed by harmonic function is given. The steady-state general solutions of these harmonic function forms lay a foundation for the further study of two-phase multifield coupling. In the following chapters, the point heat source acting on the solid of the fluid-solid two-phase body and the fluid, the point charge and the point force acting on the solid of the fluid-solid two-phase body of the pyroelectric ceramic material, The point charge acts on the fluid in a two-phase body. By using Green's function analysis method, several harmonic functions with undetermined constants are introduced, and the corresponding boundary conditions, continuity conditions and equilibrium conditions are considered to determine the undetermined constants. The extended Mindlin and the extended Lorentz solution are solved. At the end of each chapter, through numerical example analysis, the isoline diagrams of dimensionless temperature increment, stress component and electric displacement component of coupling field under the action of point source are given, and some valuable conclusions of engineering application are obtained. Such as guiding the design of energy capture and sensors. The analysis method of Green's function provides an alternative platform for the theoretical analysis and numerical calculation of fluid-solid coupling problem considering the force thermoelectric coupling effect. The basic solution is expressed by elementary function and the form is simple. It is easy to be popularized and applied in theory and engineering.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O302;TQ174.1
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