Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement

We propose a high-order enriched partition of unity finite element method for linear and nonlinear time-dependent diffusion problems.The solution of this class of problems often exhibits non-smooth features such as steep gradients and boundary layers which can be very challenging to recover using the conventional low-order finite element methods.A class of steady-state exponential functions has been widely used for enrichment and its performance to numerically solve these challenges has been demonstrated.However,these enrichment functions have been used only in context of the standard h-version refinement or the so-called q-version refinement.In this paper we demonstrate that the p-version refinement can also be a very attractive option in terms of the efficiency and the accuracy in the enriched partition of unity finite element method.First,the transient diffusion problem is integrated in time using a semi-implicit scheme and the semi-discrete problem is then integrated in space using the p-version enriched finite elements.Numerical results are presented for three test examples of timedependent diffusion problems in both homogeneous and heterogeneous media.The computed results show the significant improvement when using the p-version refined enriched approximations in the finite element analysis.In addition,these results support our expectations for a robust and high-order accurate enriched partition of unity finite element method.

Positive definiteness of fourth-order partially symmetric tensors

In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dimensional partially symmetric tensors.Then,we obtain several sufficient conditions for rank-one positive definiteness of fourth-order three dimensional partially symmetric tensors.

Local pointwise convergence of the 3D finite element

For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.

利用CiteSpace分析有限元技术在法医学中的应用现状

本文利用CiteSpace可视化软件对CNKI和ISI Web of Science数据库所收录的有限元技术在法医学中应用的研究文献进行统计和可视化对比分析,得出国内外法医领域有限元应用研究文献的关键词、机构合作、作者合作的可视化知识图谱。在此基础上,作者对文献内容进行深入研究,发现有限元技术在法医学中的研究及应用主要集中在损伤机制分析方面,以车祸损伤、高坠损伤、钝器损伤、锐器损伤、枪弹损伤等为重点,研究方法主要是通过对人体、致伤物等建立高仿真模型,利用有限元技术,以数字化、可视化、可量化的方式研究各类损伤的生物力学机制。目前,国内外法医学者主要借助Mimics等软件将人体影像数据转换为分割化的三维模型,依托较为成熟的THUMS、ANSYS等有限元系统构建多种损伤模型,有效揭示了各类损伤的发生机制,在一定程度上推动了法医病理损伤专业的发展,为法医学者开展相关研究提供了参考和借鉴。同时,有限元技术在法医学中的应用属于学科交叉,但目前的研究人员多以法医为主,缺少相关学科专业技术人员的深度介入,在某种程度上限制了该技术在法医学中的应用发展,有必要加强与从事有限元等相关研究的专业技术人员之间的交流合作。

基于NITE平台的卓越工程师培养模式探索

NITE定位于国家重点领域信息技术紧缺人才培养,担负为国家培育人才,为产业储备人才,为企业提供人才的职责。从行业工程师认证、建立联合培养学院、多渠道师资来源等方面探索了基于NITE平台的卓越工程师培养模式。

NiTe/TiO2复合材料的制备与多模式光催化降解染料

以硝酸镍、碲粉和异丙氧基钛(TTIP)为原料,采用程序升温水热法结合高温煅烧,通过控制Ni∶Ti摩尔比制备一系列NiTe/TiO2复合材料.结果表明,所制备的NiTe/TiO2复合材料为六方相NiTe和锐钛矿相TiO2的混合晶相,且在可见光区具有较强的光吸收能力.通过紫外光、可见光和模拟日光等多模式光催化降解孔雀石绿(MG)考察NiTe/TiO2复合材料的光催化性能.结果表明,当摩尔比为1∶7时,复合材料的光催化活性最佳.该复合材料对不同结构的有机污染物降解具有一定的广泛性.

循环模及有限生成模的McCoy性

本文研究了McCoy环上的循环模和有限生成模的McCoy性,得到一定条件下,McCoy环上的左循环模是McCoy模,并分别给出了一个McCoy环上的单模均为McCoy模,以及一个非McCoy环上的单模是McCoy模的例子.最后证明在一定条件下,环R上的有限生成自由模是McCoy模的充要条件是环R为McCoy环.

明挖卸荷施工对下卧既有地铁盾构隧道的影响研究

为研究明挖卸荷施工对下卧既有地铁盾构隧道的影响,文章以济南某明挖基坑近接既有地铁隧道为背景,基于midas GTS NX有限元软件,考虑3个方面因素并假设28种对比工况,开展数值模拟对比分析。得到不同因素影响下明挖卸荷施工对下卧既有地铁盾构隧道影响规律,并提出相应的建议措施。研究结果表明,明挖基坑与既有隧道夹角保持在45°及以上,可降低明挖卸荷施工对既有隧道的影响;明挖基坑与既有隧道竖向距离在0.5D(D为隧道直径)以上时,竖向距离对于控制隆起变形效果较为明显;在0.5D以下时,竖向距离对于控制隆起变形并不明显;明挖基坑横向卸荷面积对既有地铁隧道竖向变形影响随基坑加宽或加深而呈线性增加,基坑深度因素影响尤为显著。

NiTe电极材料的制备及其在超级电容器中的应用

采用二氧化碲(TeO_2)为碲源,泡沫镍作为镍源及基底,水合肼(N_2H_4·H_2O)为还原剂,利用一步水热法原位生长片状Ni Te材料。将制得的Ni Te作为超级电容器的电极材料,研究了水热温度对产物的微观形貌及电化学性能的影响规律,结果表明:当水热温度为180℃时,所制得的Ni Te为均匀的片状结构,在三电极体系下获得的Ni Te电极最大的质量比电容为603.6 F·g^(-1)。利用Ni Te和AC分别作为正极和负极,制备了非对称超级电容器(ASC)。NiTe//AC ASC可以将电位窗口扩展到1.6 V,最大的能量密度和功率密度分别为25.8 Wh·kg^(-1)和3994W·kg^(-1)。ASC显示出良好的循环稳定性,5000次循环之后保持了初始电容的83.3%。

NITE工艺制备SiC_f/SiC复合材料的研究进展

NITE(nano-infiltration and transient eutectic)工艺作为一种制备碳化硅纤维增强碳化硅基(SiCf/SiC)复合材料的新方法,具备周期短、工艺简单、生产成本低等优点,制备出的复合材料基体致密、孔隙率低、不含残余硅,适用于1400℃及以上高温长时服役环境应用。目前,日本、美国等国家基于其成熟的第三代碳化硅纤维,对该技术开展了较为深入的研究,并在核能工业热交换器、航空发动机燃烧室衬套等领域进行了应用验证。本文针对NITE工艺从基本概念、工艺流程、制备的SiCf/SiC复合材料和构件考核验证及前景展望四方面进行综合阐述,以期为国内该工艺的发展及应用提供一定程度的参考。

A p-version embedded model for simulation of concrete temperature fields with cooling pipes

Pipe cooling is an effective method of mass concrete temperature control, but its accurate and convenient numerical simulation is still a cumbersome problem. An improved embedded model, considering the water temperature variation along the pipe, was proposed for simulating the temperature field of early-age concrete structures containing cooling pipes. The improved model was verified with an engineering example. Then, the p-version self-adaption algorithm for the improved embedded model was deduced, and the initial values and boundary conditions were examined. Comparison of some numerical samples shows that the proposed model can provide satisfying precision and a higher efficiency. The analysis efficiency can be doubled at the same precision, even for a large-scale element. The p-version algorithm can fit grids of different sizes for the temperature field simulation. The convenience of the proposed algorithm lies in the possibility of locating more pipe segments in one element without the need of so regular a shape as in the explicit model.

P-version间断有限元方法求解奇异摄动问题

主要讨论用p-version间断有限元方法(DG)求解一维奇异摄动反应扩散问题。证明了数值解的存在唯一性,并给出了相应的数值算例.数值结果表明,与h-version DG方法相比较,为了达到同样数量级的误差,p-version DG方法的自由度大大下降,并且具有指数收敛性。

Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation

寻求新无限的顺序象 soliton 一样非线性的进化方程的准确答案(旧姓) 由在辅助方程方法上开发建设和机械化的二个特征，秒种椭圆形的方程高度被学习并且新类型答案和 B ? cklund 转变被获得。( 2+1 )然后，维的碎 soliton 方程作为一个例子和它的无限的顺序被选象soliton一样准确解决方案在符号的计算系统 Mathematica 的帮助下被构造，它包括无限的顺序 Jacobi 椭圆形的类型的光滑的象soliton一样解决方案， Jacobi 椭圆形的类型的无限的顺序协议 soliton 解决方案和指数的函数类型和三角形的功能的无限的顺序山峰 soliton 解决方案打字。

The closed finite-to-one mappings and their applications

In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gfcountability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.

Quantile inference for nonstationary processes with in nite variance innovations

Based on the quantile regression,we extend Koenker and Xiao(2004)and Ling and McAleer(2004)'s works from nite-variance innovations to in nite-variance innovations.A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper.It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge.The nite sample studies show that the proposed t-ratio test always performs signi cantly better than the conventional unit-root tests based on least squares procedure,such as the Augmented Dick Fuller(ADF)and Philliphs-Perron(PP)test,in the sense of power and size when in nitevariance disturbances exist.Also,quantile Kolmogorov-Smirnov(QKS)statistic and quantile Cramer-von Mises(QCM)statistic are considered,but the nite sample studies show that they perform poor in power and size,respectively.An application to the Consumer Price Index for nine countries is also presented.

The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras

As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.

Lumped Mass Finite Element Method of the Nonlinear BBM Equation

In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.

CAD技术、RP技术联合三维有限元分析对骨科临床教学成绩、实践技能的影响研究

目的研究计算机辅助设计(computer aided design,CAD)技术和快速成型(rapid prototyping,RP)技术联合三维有限元分析对骨科临床教学成绩、实践技能的影响。方法选取2021年12月—2022年12月苏州大学附属第一医院骨科临床医学实习生60名作为研究对象,以随机数表法分为两组,对照组(共30名)采取以问题为基础的教学(problem-based learning,PBL)模式,观察组(共30名)以对照组为基础,并采取CAD技术、RP技术联合三维有限元分析进行教学,对两组学生考试成绩、实践技能、满意度、自我能力、问卷评分和教学质量进行对比观察。结果观察组考试成绩、实践技能均显著优于对照组,差异有统计学意义(P<0.05)。观察组满意度为96.67%,较对照组的76.67%明显更高,差异有统计学意义(P<0.05)。与对照组相比,观察组学生自我能力明显更优,差异有统计学意义(P<0.05)。与对照组相比,观察组学生问卷评分明显更优,差异有统计学意义(P<0.05)。与对照组相比,观察组教学质量明显更优,差异有统计学意义(P<0.05)。结论在骨科临床教学中运用CAD技术、RP技术联合三维有限元分析,可对教学质量提升、满意度提升起到促进作用,并有效增强学生教学成绩、实践技能以及自我能力。

散货船双层底纵桁板缝布置和尺寸优化设计

[目的]为提高有限元结构强度校核效率,减少尺寸优化迭代成本,提出散货船双层底纵桁的板缝布置和尺寸优化方法。[方法]首先,基于理论公式论证子模型技术的可靠性,提出双层底纵桁优化设计的多工况筛选方法。然后,以某散货船双层底纵桁为例,对纵桁进行板格划分,以板格厚度为变量、《散货船和油船共同结构规范》(HCSR)的许用应力为约束条件进行尺寸优化,用穷举法列举所有板缝布置方案对优化后的板格厚度进行合并,选出重量最轻的板缝布置优化方案。最后,基于HCSR舱段有限元计算的屈服强度要求,对上述散货船双层底纵桁需加强的区域进行板缝布置优化,在此基础上,采用尺寸优化方法实现满足屈服强度要求的结构尺寸优化。[结果]结果显示,采用提出的基于尺寸优化的板缝布置优化和结构加强方法能减轻优化区域重量4.9%。[结论]所提方法能有效减少人为有限元加强时的随机性,优化有限元结构加强方案,减轻结构加强重量。

1100 kV GIS断路器合闸电阻紧固螺栓断裂分析

某型1 100 kV断路器合闸电阻触头发生故障,其中两颗短螺栓呈脱落状态,两颗长螺栓断裂分离。通过宏观检查、尺寸测量、金相分析等技术手段,从材料、连接和运行工况等方面进行分析。建立高精度有限元分析模型,考虑长、短螺栓的螺孔高度差异和运行荷载作用,分析其故障成因。结果表明:长、短螺栓材质均完好,但长螺栓呈现明显疲劳断裂形貌。进一步分析发现,当合闸电阻和主动弧触头压气缸完全紧固后,长、短螺栓的螺孔高度差异形成张力,使得长螺栓发生松动,连接板部位产生缝隙,长螺栓在长期分、合闸作用下发生疲劳断裂。螺孔高度差可认定为合闸电阻紧固螺栓断裂的主因。