Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

This study presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. This experiment is implemented through a two-dimensional spectral stochastic finite element formulation of an elliptic partial differential equation having stochastic coefficients. Deriving this spectral stochastic finite element formulation couples a two-dimensional deterministic finite element formulation of an elliptic partial differential equation with generalized polynomial chaos expansions of stochastic coefficients. Further inspection of the performance of resulting spectral stochastic finite element formulation with adopting linear and quadratic (9-node or 8-node) quadrilateral elements finds that more accurate standard deviations of unknowns are surprisingly predicted using quadratic quadrilateral elements, especially under high autocorrelation function values of stochastic coefficients. In addition, creating spectral stochastic finite element results using quadratic quadrilateral elements is not unacceptably time-consuming. Therefore, this study concludes that adopting high-order elements can be a lower-cost method to improve the performance of spectral stochastic finite element method.

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

深层超深层油气藏高应力下数字岩心构建方法

深层超深层油气藏由于埋藏深,其地应力达200 MPa,会显著改变储层岩石孔隙的微观结构。数字岩心是孔隙尺度数值模拟的重要载体,但是现有数字岩心重构方法是基于常温常压下岩心的扫描图像重构,不能反映高应力下的孔隙结构。为此,提出了一种基于离散元法考虑高应力影响的数字岩心重构方法。首先,采用分水岭算法分割CT图像,利用球面谐波分析方法建立轮廓数据库,并在PFC^(3D)中建立Clump(团簇)模板库;然后,根据孔隙度和粒径分布使用模板库中的Clump建立离散元模型,并用两点相关和线性路径相关函数曲线评价模型的准确性;随后,标定颗粒间微观力学参数,并加载应力模拟得到不同应力下的数字岩心;最后,分析了不同应力下数字岩心的孔隙几何拓扑结构,计算孔隙度和渗透率。以Bentheim砂岩为例,构建了其不同应力下的数字岩心,研究结果表明,应力增大,导致孔隙和喉道半径缩小、喉道伸长、连通性变差、孔隙度和渗透率减小。研究结果为深层超深层油气藏孔隙尺度模拟提供了技术途径。

高等几何中无穷远元素在虚拟仿真实验课程中的应用

高等几何是数学与应用数学专业本科教育的基础课程,无穷远元素是其中一个重要概念.结合摄像机的投影模型,把无穷远元素与计算机视觉相结合,体现了在工程实际中的应用价值.并把无穷远元素在虚拟仿真实验课程中给予体现,充分体现抽象的数学概念在实际中的应用,启发了学生的学习兴趣.

外包钢壳混凝土拱形桥塔节段拼装几何姿态预测研究

赣州市集结大桥主桥为外包钢壳混凝土拱形桥塔斜拉桥,为确保钢混组合拱形桥塔节段拼装精准合龙,采用MIDAS Civil软件建立拱形桥塔空间几何模型,分析外包钢壳和混凝土湿重对桥塔变形的影响,采用切线初始位移法对桥塔施工阶段位移进行预测,通过求解制造线形对桥塔待拼装节段进行预偏修正,并与实测数据进行对比。结果表明:外包钢壳能显著减小桥塔变形;施工阶段桥塔变形主要由混凝土湿重引起,临时支撑能有效减小混凝土浇筑产生的横向变形。基于切线初始位移法的几何姿态预测方法能有效预测桥塔拼装全过程几何姿态,实测成桥阶段桥塔各节段最大偏位为6 mm,小于施工控制要求,具有较高的实施精度,可保证成桥状态下桥塔几何姿态的准确性。

几何教育改革视域下的约翰·基尔《几何原本》

18世纪初,以欧几里得《几何原本》为核心的几何教育改革正在英国上演.牛津大学教授约翰·基尔以恢复欧几里得《几何原本》为主旨编成基尔《几何原本》,与大胆追求改革的数学教育者间产生“矛盾”.“矛盾”维持了传统的欧氏《原本》在几何教育中的地位,同时启发着人们对几何教育改革的思考.基尔《几何原本》的内容具有3个特征:摆脱了《几何原本》长久以来由大量注释所表现出的冗长和复杂;对公理和证明适做补充以使证明更加严谨、内容体系更加系统;针对命题制作立体几何模型以及单页设置平面图形.因此,无论是将基尔《几何原本》作为历史文化还是教科书,都会给予当今数学教育发展新启发.

Finite element simulation of elastoplastic fieldnear crack tips and results for a central crackedplate of le-lhp material under tension

The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.

Theoretical and experimental investigation of gas metal arc weld pool in commercially pure aluminum:Effect of welding current on geometry

Effects of welding current on temperature and velocity fields during gas metal arc welding(GMAW) of commercially pure aluminum were simulated. Equations of conservation of mass, energy and momentum were solved in a three-dimensional transient model using FLOW-3 D software. The mathematical model considered buoyancy and surface tension driving forces. Further, effects of droplet heat content and impact force on weld pool surface deformation were added to the model. The results of simulation showed that an increase in the welding current could increase peak temperature and the maximum velocity in the weld pool. The weld pool dimensions and width of the heat-affected zone(HAZ) were enlarged by increasing the welding current. In addition, dimensionless Peclet, Grashof and surface tension Reynolds numbers were calculated to understand the importance of heat transfer by convection and the roles of various driving forces in the weld pool. In order to validate the model, welding experiments were conducted under several welding currents. The predicted weld pool dimensions were compared with the corresponding experimental results, and good agreement between simulation and preliminary test results was achieved.

A Three-Dimensional Numerical Model for Predicting the Weld Bead Geometry Characteristics in Laser Overlap Welding of Low Carbon Galvanized Steel

Laser welding (LW) becomes one of the most economical high quality joining processes. LW offers the advantage of very controlled heat input resulting in low distortion and the ability to weld heat sensitive components. To exploit efficiently the benefits presented by LW, it is necessary to develop an integrated approach to identify and control the welding process variables in order to produce the desired weld characteristics without being forced to use the traditional and fastidious trial and error procedures. The paper presents a study of weld bead geometry characteristics prediction for laser overlap welding of low carbon galvanized steel using 3D numerical modelling and experimental validation. The temperature dependent material properties, metallurgical transformations and enthalpy method constitute the foundation of the proposed modelling approach. An adaptive 3D heat source is adopted to simulate both keyhole and conduction mode of the LW process. The simulations are performed using 3D finite element model on commercial software. The model is used to estimate the weld bead geometry characteristics for various LW parameters, such as laser power, welding speed and laser beam diameter. The calibration and validation of the 3D numerical model are based on experimental data achieved using a 3 kW Nd:Yag laser system, a structured experimental design and confirmed statistical analysis tools. The results reveal that the modelling approach can provide not only a consistent and accurate prediction of the weld characteristics under variable welding parameters and conditions but also a comprehensive and quantitative analysis of process parameters effects on the weld quality. The results show great concordance between predicted and measured values for weld bead geometry characteristics, such as depth of penetration, bead width at the top surface and bead width at the interface between sheets, with an average accuracy greater than 95%.

Computational Modeling of Dual-Phase Ceramics with Finsler-Geometric Phase Field Mechanics

A theory invoking concepts from differential geometry of generalized Finsler space in conjunction with diffuse interface modeling is described and implemented in finite element(FE)simulations of dual-phase polycrystalline ceramic microstructures.Order parameters accounting for fracture and other structural transformations,notably partial dislocation slip,twinning,or phase changes,are dimensionless entries of an internal state vector of generalized pseudo-Finsler space.Ceramics investigated in computations are a boron carbide-titanium diboride(B4C-TiB2)composite and a diamond-silicon carbide(C-SiC)composite.Deformation mechanisms-in addition to elasticity and cleavage fracture in grains of any phase-include restricted dislocation glide(TiB2 phase),deformation twinning(B4C and-SiC phases),and stress-induced amorphization(B4C phase).The metric tensor of generalized Finsler space is scaled conformally according to dilatation induced by cavitation or other fracture modes and densification induced by phase changes.Simulations of pure shear consider various morphologies and lattice orientations.Effects of microstructure on overall strength of each composite are reported.In B4C-TiB2,minor improvements in shear strength and ductility are observed with an increase in the second phase from 10 to 18%by volume,suggesting that residual stresses or larger-scale crack inhibition may be responsible for toughness gains reported experimentally.In diamond-SiC,a composite consisting of diamond crystals encapsulated in a nano-crystalline SiC matrix shows improved strength and ductility relative to a two-phase composite with isolated bulk SiC grains.

Approximation of H(div)with High-Order Optimal Finite Elements for Pyramids,Prisms and Hexahedra

Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div)-norm for general unstructured meshes containing hexahedra and prisms.We propose two new families of high-order elements for hexahedra,triangular prisms and pyramids that recover the optimal convergence.These elements have compatible restrictions with each other,such that they can be used directly on general hybrid meshes.Moreover the H(div)proposed spaces are completing the De Rham diagram with optimal elements previously constructed for H1 and H(curl)approximation.The obtained pyramidal elements are compared theoretically and numerically with other elements of the literature.Eventually,numerical results demonstrate the efficiency of the finite elements constructed.

The Mathematics of Harmony, Hilbert’s Fourth Problem and Lobachevski’s New Geometries for Physical World

We suggest an original approach to Lobachevski’s geometry and Hilbert’s Fourth Problem, based on the use of the “mathematics of harmony” and special class of hyperbolic functions, the so-called hyperbolic Fibonacci l-functions, which are based on the ancient “golden proportion” and its generalization, Spinadel’s “metallic proportions.” The uniqueness of these functions consists in the fact that they are inseparably connected with the Fibonacci numbers and their generalization― Fibonacci l-numbers (l > 0 is a given real number) and have recursive properties. Each of these new classes of hyperbolic functions, the number of which is theoretically infinite, generates Lobachevski’s new geometries, which are close to Lobachevski’s classical geometry and have new geometric and recursive properties. The “golden” hyperbolic geometry with the base (“Bodnar’s geometry) underlies the botanic phenomenon of phyllotaxis. The “silver” hyperbolic geometry with the base ?has the least distance to Lobachevski’s classical geometry. Lobachevski’s new geometries, which are an original solution of Hilbert’s Fourth Problem, are new hyperbolic geometries for physical world.

钢轨焊接接头不平顺演变条件下的轮轨接触分析

钢轨焊接接头处容易出现短波几何不平顺,严重制约着钢轨的服役寿命并影响行车安全。为研究钢轨焊接接头几何不平顺演变对轮轨接触行为的影响,首先,基于有限元方法建立三维轮轨滚动接触模型,分析我国某线路实测钢轨焊接接头几何不平顺处的轮轨动态响应;随后,建立局部钢轨有限元模型,通过引入钢轨材料的循环本构模型,研究循环荷载作用下钢轨接头处的应力-应变响应。研究表明:(1)随着钢轨焊接接头几何不平顺的演变,轮轨接触力和接触应力逐渐增大,其变化率也随之提高;(2)考虑列车牵引工况时,在轮轨切向力的作用下,钢轨焊接接头处的材料响应在其几何不平顺演变过程中均处于棘轮效应状态,尤其是几何不平顺演变中后期,循环积累的应变显著增加,累积应变变化率由之前的22.4%增长到53.2%,即加快了钢轨的劣化;(3)若不考虑列车牵引或制动操作时的作用力,材料响应则为塑性安定。

3D Radiative Transfer Equation Coupled with Heat Conduction Equation with Realistic Boundary Conditions Applied on Complex Geometries

This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.

面向大型复杂焊接结构仿真的组合式自适应四面体网格生成算法

目的研究高质量、高效率的网格生成技术以实现大型复杂结构的焊接工艺仿真优化。方法提出一种组合式的自适应四面体网格划分算法,即在高效生成各个零部件四面体网格的基础上,根据焊缝中心面的几何信息自动对焊缝附近网格进行细分,再缝合成高质量的大型复杂焊接结构的整体四面体网格,并集成到自主可控的商用网格划分软件Vision Mesh中。提出了摄动几何边界的方法,解决了大型复杂结构STL几何体在存在几何错误时网格难以生成的问题。提出了基于BVH树结构表达的背景网格表达方法,解决了多条焊缝同时高效、自动细分的难题,并通过“四面体分割–四面体合并–四面体翻转–点平滑优化”方法,实现了四面体网格的高质量优化。结果算法网格效率可以达到200万个/h,生成的四面体99%以上均接近正四面体。可以由多个零部件一步组合生成大型结构的整体网格,并可对焊缝区域进行自动细分,大幅度简化了划分流程。将生成的网格导入国产焊接仿真软件InteWeld中进行测试,验证算法可用于大型复杂焊接结构整体应力变形的计算中。结论实现了大型复杂焊接结构的高质量自适应四面体网格划分,使用简便操作得到了高质量网格,为焊接结构件工艺仿真优化提供了前提。

2 000 m级超大跨度悬索桥主缆架设影响参数研究

为研究地球曲率、温度、主缆弹性模量以及加劲梁恒载误差对2000 m级超大跨度悬索桥主缆成桥线形的影响,以主跨2180 m的广州狮子洋大桥为背景,采用BNLAS软件建立主桥有限元模型,基于单一变量法对上述参数的影响性进行分析。结果表明:地球曲率对超大跨度悬索桥的主缆成桥线形影响较大,可通过在索股制造时对分跨标记点进行修正以避免该因素的影响;主缆成桥线形对温度变化极其敏感,建议增加温度测试断面数量以得到更为精确的温度场分布,据此对主缆成桥线形进行修正;主缆弹性模量影响索股的无应力长度,进而影响主缆成桥线形,需增加钢丝弹性模量的测试精度及抽样比例,得到符合实际主缆弹性模量的检测值,据此修正主缆成桥线形;加劲梁恒载误差对主缆成桥线形的影响很大,主缆架设前需要对钢梁进行称重并测试铺装材料的容重,根据实际重量重新计算主缆成桥线形,并且在铺装层施工时精确控制铺装层厚度。

结构尺寸对316L矩形波纹管液压胀形的影响

目的掌握结构尺寸对矩形波纹管液压胀形的影响规律。方法利用有限元平台Abaqus/Explicit建立316L矩形波纹管的三维有限元模型,对其液压胀形过程进行数值模拟分析,并利用实验验证有限元模型的正确性,基于单因素法研究长宽比、过渡圆角半径及波距对矩形波纹管成形质量的影响。结果综合考虑成形波高、壁厚减薄率及周向轮廓3个指标,获得了长宽比、过渡圆角半径和波距对波纹管成形的影响规律,并给出了各参数对不同指标影响的显著性。结论随着长宽比的增大,长边壁厚减薄率明显减小,圆角与短边的壁厚变化不大,并且不同长宽比波纹管的成形轮廓均在圆角段上低于设计值,在直线段上高于设计值;增大过渡圆角半径更有利于圆角段的贴合,且有利于降低周向壁厚减薄率;波距对波纹管的壁厚减薄率影响显著,波距较小时,波峰上有明显的增厚现象,随着波距的增大,波峰上的增厚现象逐渐消失并开始减薄,波纹管周向波高增大,直边波高容易超出公差范围,可以通过降低成形内压或减小模片间距将波高修正到公差范围内,获得合格的波纹管产品。

三维正交织物织造过程模拟及其微观几何结构预测

为获得更为精确的织物模型,以满足织物及其纺织复合材料力学性能和破坏机制分析的需要,针对多尺度材料几何结构建模中存在宏观和介观尺度理想化假设,从而导致织物微结构特征缺失的问题,基于数字单元法理论,在纤维尺度提出一种织物织造过程动态仿真方法。该方法建立了织机关键部件的几何模型,由织造矩阵控制开口运动,通过计算纤维间的相互作用力,模拟织机五大运动,得到4个处于不同织造时期的单胞组成的三维正交织物数值模型。研究结果表明:织物单胞的微观几何结构受相邻单胞的影响,在织造过程中发生变化;最上层和最下层纬纱的应力高于中间层纬纱;模型较为准确地描述了纱线的卷曲、路径和横截面形状等织物的主要特征。