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  本文選題：格林函數(shù) + 橫觀各向同性��； 參考：《湖南大學》2015年碩士論文

【摘要】：格林函數(shù)又稱為源函數(shù)或影響函數(shù),它是固體力學中數(shù)值計算和理論分析的基礎。格林函數(shù)不但是邊界元計算方法的必要條件,還是理論分析斷裂、損傷、夾雜和接觸分析的基礎。隨著時代的進步,焦熱電材料在機械、航空航天、電子設備等工程領域中的應用越來越廣泛,隨之而來的焦熱電材料問題也越來越多。在實際工作中,焦熱電材料器件(如傳感器、激勵器和俘能器等)經(jīng)常需要工作在流體中。由于兩者之間存在力電熱耦合效應,使得對于焦熱電材料器件耦合場分析和設計具有相當?shù)碾y度。本文即是在這種背景下,針對流體和焦熱電陶瓷材料的二維耦合場進行了系統(tǒng)研究,得到力電熱集中載荷作用下耦合場的通解和二維格林函數(shù)。 首先介紹了流體和橫觀各向同性焦熱電材料的本構方程,在不計體力的情況下,將其代入平衡方程、熱傳導方程,并且結合Almansi定理,微分算子理論和參數(shù)代換,導出在不同載荷條件下的二維穩(wěn)態(tài)通解。 其次,對于力、電載荷分別作用在流體和橫觀各向同性焦熱電材料中,文中分為兩個章節(jié)予以闡述�；诹鞴唐矫娴耐ń�,構造載荷作用在兩種不同材料中的調和函數(shù),然后將其帶入通解中,得到各個分量的基本解,并且使其滿足力電平衡方程、連續(xù)條件、邊界條件,以確定函數(shù)中的待定常數(shù)。再對相應力、電載荷作用下的基本解分量進行無量綱化,通過數(shù)值計算繪制出各分量的等值線圖,通過對等值線圖的分析,得到界面效應的結論。 最后,對于線熱源分別作用在橫觀各向同性焦熱電陶瓷材料和流體中的流固平面,構造六個新的調和函數(shù),再將得到的基本解代入到邊界條件、連續(xù)條件和力熱平衡方程中,從而確定通解中的待定系數(shù),最后得出各個分量的表達式,結合數(shù)值計算并繪制出溫度增量、應力分量和電位移分量的等值線圖,經(jīng)過分析得到有實際工程應用價值的結論。
[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.
【學位授予單位】：湖南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O302;TQ174.7

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8 錢夢

本文編號：2004803