流体和焦热电陶瓷两相材料的二维格林函数

发布时间：2018-06-11 09:41

本文选题：格林函数 + 横观各向同性　；参考：《湖南大学》2015年硕士论文

【摘要】：格林函数又称为源函数或影响函数,它是固体力学中数值计算和理论分析的基础。格林函数不但是边界元计算方法的必要条件,还是理论分析断裂、损伤、夹杂和接触分析的基础。随着时代的进步,焦热电材料在机械、航空航天、电子设备等工程领域中的应用越来越广泛,随之而来的焦热电材料问题也越来越多。在实际工作中,焦热电材料器件(如传感器、激励器和俘能器等)经常需要工作在流体中。由于两者之间存在力电热耦合效应,使得对于焦热电材料器件耦合场分析和设计具有相当的难度。本文即是在这种背景下,针对流体和焦热电陶瓷材料的二维耦合场进行了系统研究,得到力电热集中载荷作用下耦合场的通解和二维格林函数。首先介绍了流体和横观各向同性焦热电材料的本构方程,在不计体力的情况下,将其代入平衡方程、热传导方程,并且结合Almansi定理,微分算子理论和参数代换,导出在不同载荷条件下的二维稳态通解。其次,对于力、电载荷分别作用在流体和横观各向同性焦热电材料中,文中分为两个章节予以阐述。基于流固平面的通解,构造载荷作用在两种不同材料中的调和函数,然后将其带入通解中,得到各个分量的基本解,并且使其满足力电平衡方程、连续条件、边界条件,以确定函数中的待定常数。再对相应力、电载荷作用下的基本解分量进行无量纲化,通过数值计算绘制出各分量的等值线图,通过对等值线图的分析,得到界面效应的结论。最后,对于线热源分别作用在横观各向同性焦热电陶瓷材料和流体中的流固平面,构造六个新的调和函数,再将得到的基本解代入到边界条件、连续条件和力热平衡方程中,从而确定通解中的待定系数,最后得出各个分量的表达式,结合数值计算并绘制出温度增量、应力分量和电位移分量的等值线图,经过分析得到有实际工程应用价值的结论。
[Abstract]:Green function, also known as source function or influence function, is the basis of numerical calculation and theoretical analysis in solid mechanics. Green's function is not only a necessary condition for boundary element calculation, but also the basis for theoretical analysis of fracture, damage, inclusion and contact analysis. With the progress of the times, pyroelectric materials are widely used in engineering fields such as machinery, aerospace, electronic equipment and so on, followed by more and more problems of pyroelectric materials. In practice, pyroelectric materials such as sensors, actuators and energy capture devices are often required to work in fluids. It is difficult to analyze and design the coupling field of pyroelectric materials due to the electromechanical and thermal coupling effect between the two. In this paper, the two dimensional coupling fields of fluid and pyroelectric ceramic materials are studied systematically in this paper. The general solution of the coupled field and the two-dimensional Green's function are obtained. Firstly, the constitutive equations of fluid and transversely isotropic pyroelectric materials are introduced. Combined with Almansi theorem, differential operator theory and parameter substitution, the two-dimensional steady-state general solution is derived under different loading conditions. Secondly, for the force, the electric load acts on the fluid and transversely isotropic pyroelectric materials, respectively. This paper is divided into two chapters. Based on the general solution of the fluid-solid plane, the harmonic function of the load acting on two different materials is constructed, and then the fundamental solution of each component is obtained by introducing it into the general solution, which satisfies the equation of force and electric balance, the continuity condition, and the boundary condition. To determine the undetermined constant in the function. Then the basic solution components under the corresponding force and electric load are dimensionless, the isoline diagram of each component is drawn by numerical calculation, and the conclusion of interface effect is obtained by analyzing the isoline diagram. For the fluid-solid plane acting on transversely isotropic pyroelectric ceramic materials and fluids respectively, six new harmonic functions are constructed, and the obtained fundamental solutions are added to the boundary condition, continuity condition and force and heat balance equation. Thus the undetermined coefficients in the general solution are determined, the expressions of each component are obtained, and the isoline diagrams of temperature increment, stress component and electric displacement component are drawn in combination with numerical calculation, and the conclusions of practical engineering application are obtained through analysis.
【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;TQ174.7

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