HT—7U超导托克马克纵场线圈等效模量的数值分析

HT－7U托克马克装置的纵场线圈是由多种材料组成的具有周期性分布的大型复杂结构，线圈可视为由超导线、支撑结构和绝缘材料组成的复合材料，结构极其复杂。整个线圈工作在液氦温区。在设计阶段对其宏观等效力学性能进行数值分析计算是十分必要的，但要对整个线圈直接进行有限元分析或实验是极其困难的，主要利用均匀化方法对其进行等效处理，从而分析计算其宏观等效模量，为线圈的设计和评估提供参考依据。另外本文对均匀化方法的边界条件进行了一些改进，提出了更加合理的三维边界条件。     

能量法研究矩形填充多孔材料夹芯层面内等效模量

多孔材料作为一种新材料体系被大量运用于航空航天等领域,其夹层结构是大型风力发电机叶片的重要组成元件.为了节省生产成本、提高产品质量和结构安全性,以及对叶片的设计、改造和优化,其夹层结构夹芯层的等效力学参数研究是十分必要的.目前对于夹芯中填充其他材料的分析大多是忽略了填充材料带来结构性能的影响.本文针对矩形填充多孔材料夹芯层的特点,提出了十字填充模型,接着从能量的角度出发,推导出矩形填充材料夹芯层面内等效模量,并将能量法推导出的结果和从变形分析角度得出的结果进行对比,得到两种方法的计算结果完全一致的结论,从而验证了能量法的合理性,为将来深入研究矩形填充材料夹层结构的其他等效参数提供理论依据,也为叶片结构的改造和优化提供技术支持.     

层级褶皱结构夹层板的等效弹性常数

针对二级层级褶皱结构夹层板,通过变形协调研究了其等效弹性常数。首先对一级层级褶皱结构进行正交各向异性等效,得到一级等效弹性常数;将二级层级褶皱结构看成是由正交各向异性材料组成的三角形桁架夹心,将二级层级褶皱结构等效为均匀连续正交各向异性板,依据夹层板面板与夹心变形协调特点得到夹层板整体等效弹性常数。结合结构几何参数对等效公式的误差进行了讨论,并对等效公式做出修正。通过与数值分析结果对比,表明本文提出的等效公式具有较高精度。     

脉冲载荷下加筋圆板的各向同性快速等效方法

加筋板在爆炸与冲击防护中应用广泛,而其动力响应的快速求解一直是工程中关注的重点。对于径向均匀加筋的圆板,基于刚度叠加思想,提出了一种将其等效为各向同性平板的方法,用于分析其在脉冲载荷下弹性阶段的动力响应。结合理论推导与数值方法,显式地给出了简洁的等效平板厚度公式。经验证,提出的等效方法建立了加筋圆板与均质圆板间的内在联系,适用于多种加筋尺寸、材料及载荷形式。等效圆板与加筋圆板的最大挠度偏差不超过6%,低阶振动频率偏差不超过10%。相比于直接对加筋圆板进行计算,等效分析方法大大提高了求解效率,且保证了很高的计算精度,在冲击响应预测和结构优化等工程应用中具有重要意义。     

一类混凝土力学参数的迭代多尺度有限元预测方法

根据多级配骨料混凝土特点,给出了一种迭代多尺度有限元方法预测其等效力学参数。本文首先介绍了多级配骨料混凝土的材料特点并给出了计算混凝土多尺度模型,然后基于多尺度方法介绍了计算混凝土力学参数的计算程序,最后针对小湾大坝中混凝土给出了算例说明了此种方法在预测混凝土等效力学参数的有效性。     

复合材料应力分析的均匀化方法

建立了基于均匀化理论的确定复合材料结构应力场的方法．其实质是用均质的宏观结构和非均质的具有周期性分布的细观结构描述原结构；将力学量表示成关于宏观坐标和细观坐标的函数，并用细观和宏观两种尺度之比为小参数展开，用摄动技术将原问题化为一细观均匀化问题和一宏观均匀化问题．这两个问题的解确定了包含等效位移和一阶近似位移的位移场，由此获得应力场．利用该方法给出了圆柱形孔隙材料和单向纤维复合材料在单向拉伸时的应力场以及空隙材料简支梁的局部应力场，说明了该方法的有效性     

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

正交各向异性韧性材料应力-应变关系

采用大变形弹塑性有限元方法分析了各向同性和正交各向异性韧性材料光滑圆棒拉伸试件的颈缩问题．首先给出了采用计算机模拟确定各向同性韧性材料真实应力-应变曲线的具体方法；对正交各向异性韧性材料的分析表明，颈缩截面呈椭圆形，其长短轴方向的等效塑性应变基本上均匀分布，与Bridgman假设一致；轴向拉伸载荷-位移曲线与其它两方向的各向异性参数关系不大．在此基础上，建议了一种确定正交各向异性韧性材料真实应力-应变曲线的方法．     

纳米级石墨晶体层片力学性能的等效模型及分析

石墨晶体是由碳原子以sp2杂化轨道和邻近的三个碳原子形成共价键,在其平面内再构成网状层片结构。文中对基于原子键合力能关系的CCBE等效模型和经典的BEAM单元等效模型作了比较分析。其中CCBE包括两个节点,每个节点包含三个平移自由度。与经典BEAM单元相比,其两个节点均没有转动自由度。CCBE和BEAM单元的各个参数可以通过石墨晶体的相关实验获得。通过对石墨晶体层片的拉伸、剪切等效模型的柔度(刚度)系数计算分析,并与实验数据相对比,验证了CCBE等效建模方法的正确性和合理性。该等效建模方法为研究石墨的微观结构、性能等提供了一种有效的数值模拟方法。     

HT-7U超导托卡马克装置极向场线圈的等效弹性常数及其残余刚度

HT－7装置的超导极向场线圈由导管，超导材料和绝缘体组合而成，具有复杂的正交各向异性的性质。本文从微观力学的观点出发，将极向场线圈整体作为一种复合材料来考虑，采用微观力学的复合律和损伤力学的细观损伤模型，求出了极向场线圈的等效弹性常数和残余刚度；并且，残余刚度的计算结果已得到了实验验证。这些材料特性已被用于有限元分析的输入数据。     

Bending and buckling of superconducting partial toroidal field coils

Based on the theory of curved beams and the Biot–Savart law, a new theoretical model for magnetoelastic bending and buckling of superconducting toroidal field coils is developed and corroborated numerically. In contrast to the existing models, this model incorporates in-plane deformation of the coil. A semi-analytical approach is used to obtain the solution to the coupled problem. In order to validate the model and associated solution method, the experiment of Miya et al., 1982 is modeled. The theoretical predictions of the critical current of coils with none or one pin support are shown to be in excellent agreement with the published experimental data. It is also shown that the in-plane deformation has a significant influence on the critical current.     

Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils

Quench and mechanical behaviors are critical issues in high temperature superconducting(HTS)coils.In this paper,the quench characteristics in the rare earth barium copper oxide(REBCO)pancake coil at 4.2K are analyzed,and a two-dimensional(2D)axisymmetric electro-magneto-thermal model is presented.The effects of the constituent materials,background field,and coil size are analyzed.An elastoplastic mechanical model is used to study the corresponding mechanical responses during the quench propagation.The variations of the temperature and strain in superconducting layers are compared.The results indicate that the radial strain evolutions can reflect the transverse quench propagation and the tensile hoop and radial stresses in superconducting layers increase with the quench propagation.The possible damages are discussed with the consideration of the effects of the background field and coil size.It is concluded that the high background field significantly increases the maximum tensile hoop and radial stresses in quenching coils and local damage may be caused.     

Nb3Sn超导线圈力学性能精确分析的双向均质化方法

Nb₃Sn超导磁体运行时产生很高磁场, Nb₃Sn超导线圈会受到很强电磁体力的作用, 从而会产生很大的力学应变. 由于Nb₃Sn超导材料的应变敏感性, 会使得Nb₃Sn磁体线圈的临界性能退化, 这对磁体的安全稳定运行造成极大影响, 所以精确计算超导磁体在电磁体力下的力学行为具有重要的科学意义. Nb₃Sn超导磁体主要是由超导线绕制成线圈结构再经过环氧树脂固化而成, Nb₃Sn超导线是主要由多根微米级的超导芯丝、铜形成的复合结构, 所以从超导芯丝到超导磁体其尺寸跨越了几个数量级, 从而给精确分析超导线圈力学变形带来挑战. 本文首先采用代表性单元均质化方法分析了整体线圈的等效力学参数, 通过对比等效均质化模型与线圈真实结构的计算结果, 发现等效均质化模型存在很大的误差. 因此, 提出一种高精度而且计算代价低的双向均质化分析方法, 研究超导线圈内各组分材料(Nb₃Sn芯丝、铜和环氧树脂)应力-应变分布. 该方法不需要进行大规模的数值建模, 并且与真实复合线圈下的结果对比吻合很好, 由此验证了该方法的有效性和准确性. 最后基于提出的双向均质化分析方法, 详细讨论了Nb₃Sn超导线圈各层材料在电磁力作用下应力-应变随匝数和层数的变化规律.      

Electric-magnetic-force characteristics of rare earth barium copper oxide superconductor high-field coils based on screening effect and strain sensitivity

Rare earth barium copper oxide (REBCO) is the most researched and commercialized second-generation high-temperature superconducting material. Due to the anisotropic structure, strong deformation sensitivity, and central field errors caused by screening current effects, it is still a challenge for commercialization applications. In this study, the transversely isotropic constitutive relationship is selected as the mechanical model based on the structural characteristics of REBCO tapes, and suitable microelements are selected to equate the elastic constants using their average stress-strain relationships. Then, a two-dimensional axisymmetric model for coils wound by single-layer tapes is constructed to analyze the dependence of the electric-magnetic-force distribution in the tape on the strain. Finally, the anisotropic approximation of the homogenized bulk method is used to equate large-turn high-field coils, and the electric-magnetic-force distribution characteristics of the coils with/without screening effects and mechanical strain conditions are investigated, respectively. The results reveal that the mechanical strain has a weakening effect on the electromagnetic field distribution of superconducting tapes, but causes a significant enhancement in the force field distribution. In the presence of 0.5% mechanical strain, the maximum weakening of the peak value of the current density and the critical current density inside the high-field coil can reach about 8% and 13%, respectively, with a nearly 5 times increase in the peak stress. The screening current makes the current field distribution inside the coil improve by about 10 times. The screening current induced magnetic field can reach up to 0.8 T, making the relative error of the high-field coil center up to 7.8%.     

Buckling behavior of a superconducting magnet coil

The buckling behavior of a superconducting magnet coil has been investigated for out of plane perturbations. It has been shown that such a coil becomes unstable due to its own magnetic field for out of plane bending at the operating values of electric currents. A technique devised by the author that computes the inductance change due to deformation, has been incorporated in this study. The evaluation shows that although the magnetic fields external to the coil are important and that there is additional structural stiffness provided by the surrounding structure, the effects of the self magnetic field should be evaluated and incorporated in the design of such coils. However, based on previous studies, both analytical and experimental, it has been established that the out-of-plane deformation is the most critical mode from a stability standpoint. Therefore, this mode has been exclusively addressed in this study.     

Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER Nb_3Sn cable-in-conduit conductors

The central solenoid(CS)is one of the key components of the International Thermonuclear Experimental Reactor(ITER)tokamak and which is often considered as the heart of this fusion reactor.This solenoid will be built by using Nb3Sn cablein-conduit conductors(CICC),capable of generating a 13 T magnetic field.In order to assess the performance of the Nb3Sn CICC in nearly the ITER condition,many short samples have been evaluated at the SULTAN test facility(the background magnetic field is of 10.85 T with the uniform length of 400 mm at 1%homogeneity)in Centre de Recherches en Physique des Plasma(CRPP).It is found that the samples with pseudo-long twist pitch(including baseline specimens)show a significant degradation in the current-sharing temperature(Tcs),while the qualification tests of all short twist pitch(STP)samples,which show no degradation versus electromagnetic cycling,even exhibits an increase of Tcs.This behavior was perfectly reproduced in the coil experiments at the central solenoid model coil(CSMC)facility last year.In this paper,the complex structure of the Nb3Sn CICC would be simplified into a wire rope consisting of six petals and a cooling spiral.An analytical formula for the Tcs behavior as a function of the axial strain of the cable is presented.Based on this,the effects of twist pitch,axial and transverse stiffness,thermal mismatch,cycling number,magnetic distribution,etc.,on the axial strain are discussed systematically.The calculated Tcs behavior with cycle number show consistency with the previous experimental results qualitatively and quantitatively.Lastly,we focus on the relationship between Tcs and axial strain of the cable,and we conclude that the Tcs behavior caused by electromagnetic cycles is determined by the cable axial strain.Once the cable is in a compression situation,this compression strain and its accumulation would lead to the Tcs degradation.The experimental observation of the Tcs enhancement in the CS STP samples should be considered as a contribution of the shorter length of the high field zone in SULTAN and CSMC devices,as well as the tight cable structure.     

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake (SP) insert no-insulation (NI) coil in a hybrid magnet during the charging and discharging processes. The coupled problem is resolved by means of the finite element method (FEM) for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system. The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet. Moreover, a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process, while a forward azimuthal current and a tensile hoop stress are observed during the discharging process. The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists. Therefore, it brings forth significant Joule heat, causing a temperature rise and a uniform distribution of this heat in the coil turns. Accordingly, a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil. It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil, while a discharging will not. The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.     

基于拓扑优化的均匀磁场励磁结构设计方法

在一定限度的空间内设计励磁结构以使在所需要的区域内产生足够强度和均匀度的磁场,是实现重要的医学诊断设备设计的关键。本文基于拓扑优化方法,建立了能够产生均匀磁场的核磁共振成像仪器中超导励磁线圈空间排布形式的优化设计方法。以励磁线圈在给定区域内的分布参数为设计变量,以在所需区域内磁场的均方差为均匀性描述指标,建立了包含线圈体积和磁场强度要求的均匀磁场设计优化问题的数学模型。基于所建立的优化模型,给出了具体的均匀磁场的励磁结构设计方案。该设计方案的仿真分析,验证了磁场的均匀性以及所建立的方法的有效性。