本文選題：第二類超導材料　切入點：力學變形　出處：《蘭州大學》2015年碩士論文

【摘要】：超導材料在臨界磁場,臨界溫度與臨界電流密度確定的四面體參數(shù)空間內(nèi)表現(xiàn)出零電阻與邁斯納效應這一優(yōu)越特性,使其具有極其廣泛而重要的工程應用與前景。然而,超導材料往往工作于低溫與電磁場環(huán)境并伴隨體積的變化與不可避免的力學變形。已有研究結(jié)果表明超導材料的力學變形會對其超導特性產(chǎn)生顯著影響,諸如臨界電流、臨界溫度的改變等。本文采用time-dependent Ginzburg-Landau (TDGL)理論研究了外加均勻磁場中第二類超導材料力學變形下的超導磁學性能,考察了超導材料內(nèi)部的磁通與渦旋特性和行為�；诨旌献兎衷�,以序參量Ψ(或共軛Ψ*)、磁矢勢A與位移u為獨立變量,獲得了第二類超導材料考慮變形影響的基本控制方程與邊界條件；進一步運用有限元數(shù)值計算模型分析了第二類超導材料的磁通與渦旋特性與行為。首先,針對半無限大超導結(jié)構(gòu)運用有限元數(shù)值方法求解非線性耦合TDGL方程,討論了線彈性變形與外加均勻磁場對序參量Ψ、總能量的影響。研究結(jié)果表明：預應變與外加磁場對可變形超導材料的超導特性與能量均有較為顯著的影響。其次,針對磁場中受約束情形的可變形無限長超導材料開展了數(shù)值研究,考慮了TDGL方程與彈性變形場的耦合,詳細討論了不同磁場下超導能、磁能、彈性變形能、超導-磁場相互作用能、超導-彈性場相互作用能與總能量密度的變化規(guī)律,給出了耦合系數(shù)對序參量、磁矢勢、應變與能量影響結(jié)果。研究表明：在可變形超導材料中,超導冷凝態(tài)與晶格變形之間的相互作用不可忽略；序參量隨外加均勻磁場的增強而減小,應變隨磁場的增強而增大；耦合效應對序參量、磁矢勢和系統(tǒng)能量密度均有一定影響。最后,開展了帶孔超導二維薄板結(jié)構(gòu)磁通渦旋動力學研究,給出超導薄板變形與孔洞附近應力集中對超導特性與渦旋動力學行為影響。結(jié)果表明：預應力和超導材料內(nèi)部的應力集中對渦旋分布、渦旋動態(tài)與序參量有非常重要的影響；橢圓孔長短半軸比的變化不僅影響渦旋數(shù)目而且影響渦旋的穩(wěn)態(tài)構(gòu)型。
[Abstract]:In the tetrahedron parameter space determined by critical magnetic field, critical temperature and critical current density, superconducting materials exhibit the excellent characteristics of zero resistance and Meissner effect, which make them have extremely wide and important engineering applications and prospects.However, superconducting materials often work in low temperature and electromagnetic field environment, accompanied by volume changes and inevitable mechanical deformation.The results show that the mechanical deformation of superconducting materials has a significant effect on their superconducting properties, such as the critical current, the change of critical temperature, and so on.In this paper, the superconducting magnetic properties of the second kind of superconducting materials under mechanical deformation in an applied uniform magnetic field are studied by using time-dependent Ginzburg-Landau theory. The flux and vortex characteristics and behavior of the superconducting materials are investigated.Based on the mixed variational principle, the basic governing equations and boundary conditions of superconducting materials of the second kind considering deformation are obtained by taking order parameter 蠄 (or conjugate 蠄), magnetic vector potential A and displacement u as independent variables.The magnetic flux and vortex characteristics and behavior of the second type superconducting materials are analyzed by using the finite element numerical model.Firstly, the nonlinear coupled TDGL equation is solved by finite element method for semi-infinite superconducting structures. The effects of linear elastic deformation and applied uniform magnetic field on the order parameter 蠄 and total energy are discussed.The results show that both prestrain and applied magnetic field have significant effects on the superconducting properties and energy of deformable superconducting materials.Secondly, the deformable infinitely long superconducting materials in the magnetic field are studied numerically. The coupling between the TDGL equation and the elastic deformation field is considered, and the superconducting energy, magnetic energy and elastic deformation energy under different magnetic fields are discussed in detail.The interaction energy of superconducting magnetic field, the interaction energy of superconducting and elastic field and the total energy density are changed. The effects of coupling coefficient on order parameter, magnetic vector potential, strain and energy are given.The results show that the interaction between superconducting condensate state and lattice deformation can not be ignored in deformable superconducting materials, the order parameter decreases with the increase of the applied uniform magnetic field, the strain increases with the increase of the magnetic field, and the coupling effect is related to the order parameter.Both the magnetic vector potential and the energy density of the system have certain effects.Finally, the magnetic flux vortex dynamics of two-dimensional thin plate with holes is studied, and the effects of deformation and stress concentration near the hole on the superconducting characteristics and vortex dynamics are given.The results show that the stress concentration in prestressing and superconducting materials has a very important effect on the vortex distribution, vortex dynamics and order parameters, and the variation of the ratio of long and long axis of elliptical holes not only affects the number of vortices, but also affects the steady configuration of vortices.
【學位授予單位】：蘭州大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TM26

【共引文獻】

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