HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

AN ADI GALERKIN METHOD WITH MOVING FINITE ELEMENT SPACES FOR A CLASS OF SECOND-ORDER HYPERBOLIC EQUATIONS

An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

SQUEEZE FLOW OF A SECOND-ORDER FLUID BETWEEN TWO PARALLEL DISKS OR TWO SPHERES

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

A Method for Calculation of Low-Frequency Slow Drift Motions Based on NURBS for Floating Bodies

Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.

Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems

The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.

A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations

A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for Second-Order Elliptic Problems

The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.

土壤学互融互补混合式智慧教学模式改革成效

土壤学是理论系统性高和应用实践性强的重要专业基础课。探索基于网络信息技术的土壤学线上线下混合式教学的新型模式,对于全面推进新时代一流专业建设及一流专业人才培养至关重要。综合应用文献查阅法、问卷调查法和经验总结法,以优化教学内容和变革教学策略为途径,构建土壤学“互融互补混合式智慧教学模式”。这一新型教学模式包含“思政元素、专业应用、学科前沿、行业发展”的四元融合知识体系、“课前-课中-课后”三环渐进混合式智慧教学方式、“一、二课堂互补,现实虚拟互补”的二维互补实践创新能力培养体系。模式实施以来有力地提升土壤学“一流课程”“思政示范课”建设质效,以及富有“三农”情怀、能“识土-辨土-用土-改土”的新农科复合型高级人才质量,为其他传统专业课改革提供借鉴。

地—井瞬变电磁三维各向异性响应特征研究

地—井瞬变电磁法由于抗干扰能力强、响应信号明显等优势而应用广泛。在深部矿产资源调查和地质构造勘查等任务中,多个油气储存在层理发育的沉积岩地区大多数情况下表现为电各向异性,但是目前地—井瞬变电磁反演算法均基于各向同性模型,传统反演成像技术不再适用。为了分析地层电导率各向异性对地—井瞬变电磁勘探结果的影响,对各向异性介质模型研究其电磁响应特性。基于各向异性介质的电导率张量,提出了一种基于有限元方法的三维分析模型,采用PARDISO求解器进行求解。针对多个各向异性角度的情况模拟了各向异性介质的瞬变电磁响应,分析介质各向异性对电磁波传播规律的影响,探讨了各向异性瞬变电磁响应特征。研究结果表明:在垂直各向异性介质中,电磁波传播方向垂直于电导率最大的方向时,电磁响应变化最明显;电磁波传播方向平行于电导率最大的方向时,电磁响应变化最弱。在水平各向异性介质中,电磁波垂直于电导率最小的方向时,电磁响应变化最明显;电磁波平行于电导率最小的方向时,响应变化较弱。最后,针对地—井瞬变电磁方位测井,分析了发射源沿不同方向条件下各向异性地层和异常体模型的电磁响应,结果表明其瞬变电磁响应特征与发射源的方向有关,且对于主轴各向异性异常体,发射源方向的选择直接影响对异常体各向异性方向的判断。该研究结论对油气开发地球物理勘探方法的研究具有一定的参考价值。

考虑间断速度场的光滑有限元极限分析上限法

基于应变光滑技术的有限元极限分析方法,为岩土工程稳定性分析提供了一种有效和高精度的数值分析途径。通过改进基于节点光滑域的方法,使其可以考虑间断的运动许可速度场,提出一种新型节点光滑有限元极限分析上限法。在土与结构接触面处引入间断速度场,以间断面处节点速度差表征间断速度场的大小,进而基于间断节点重新构造节点光滑域。在Mohr-Coulomb屈服准则和关联流动法则的基础上,分别计算间断面和光滑域内的内能耗散,并将屈服准则和流动法则的约束条件转化为一系列的二阶锥约束方程,最终将考虑间断速度场的节点光滑有限元上限法转化为标准的二阶锥规划模型。此模型可以采用高效的原对偶内点算法进行求解。通过岩土工程中经典问题的数值分析,验证了新方法的可靠性,并通过数值分析发现,结构与土体接触的强度性质对结构的失稳模式和极限承载力具有明显的影响。

发夹式换热器管板的应力分析与强度评定

应用ANSYS有限元分析软件,考虑压力载荷和温度载荷对管板整体应力分布的影响,采用顺序耦合法对发夹式循环冷却器的热端管板在7种工况下进行有限元应力分析。结果表明:在压力载荷与温度载荷共同作用下,管板最大等效应力为329.9 MPa,位于布管区内换热管与管板连接处。壳程先停工况下管板的最大等效应力值最大值为332.5 MPa,是发夹式循环冷却器管板的最危险工况。在对管板上最大等效应力处进行当量线性化处理,结合分析设计标准进行强度评定,评定结果均合格。

基于二阶抛物问题的虚拟元方法

应用虚拟元方法研究了求解二阶抛物问题.首先,将连续问题转化为相应的变分形式,并构造虚拟元空间;其次,通过引入投影算子,将空间变量从虚拟元空间投影到多项式空间,得到半离散问题;第三步,再对时间变量进行离散得到全离散问题,借助自由度得到问题的近似解;最后,对所得的离散格式进行误差分析.通过数值算例验证了该理论分析的正确性和有效性.

国际艺术教育中的中国元素:传统色彩教学的比较研究

随着全球化趋势日益加深,艺术教育也需要践行跨文化交流和多元化教学。中国元素作为东方文化的重要组成部分,将其融入国际艺术教育,不仅有助于丰富教学内容,还能促进不同文化之间的相互理解与尊重。本文探讨了中国元素在国际艺术教育中的应用及其带来的影响,提出了具体的融入路径,旨在为全球艺术教育的发展贡献力量,增强艺术教育在全球文化多样性和包容性方面的作用。研究揭示了中国元素如何丰富学生的艺术表达和创造力,同时促进不同文化间的交流与理解。中国色彩的独特视角提升了学生的国际视野,还激发了他们对传统与现代艺术实践的深入探索。

Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.

Thermal stress in SiC element used in heat exchanger

An especial snake SiC pipe was designed for collecting losing heat from furnaces. The three-dimensions thermal, fluid and thermal stress coupled field of heat exchanger was analyzed by using the commercial engineering computer package ANSYS. The structural and operational parameters of heat exchanger, the junction between standpipe and snake pipe, the diameter of snake pipe, ratio of thickness to diameter of pipe, velocity of inlet air were optimized for thermal stress. The computed results show that the large thermal stress exits in the SiC, and the stand pipe should be ellipse for the least thermal stress; the optimal ratio of thickness to diameter of pipe is 6, the velocity of inlet air is 25 m/s. The most thermal stress is in inverse proportion to diameter of pipe and velocity of inlet air.

Near-zone Direct and Indirect Topographic Effects Based on the Rectangular Prism and Surface Element

Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.

大型NEN型立式换热器计算要点分析

目前大型NEN型立式换热器广泛应用于各生产装置,文章结合此类换热器计算方面的发展情况,阐述了几个计算要点:首先计算载荷问题,应考虑重力、压降等换热器标准中易忽略的载荷;其次总结了几种处理此类设备的Ansys有限元模型,包括实体模型、多点约束(MPC)法模型、管板简化为当量实心板等简化模型;最后论述了各种模型的应用场合。基于目前JB/T 4732标准中针对壳体与管板连接处分析评定保守的问题,除了考虑ASME中简化弹塑性方法和一次结构法外,建议采用塑性极限载荷法,分析时还可结合子模型结构以提高效率。最后以1台NEN型反应器为例,对计算结果进行了总结。

基于二阶梁柱单元的精细塑性铰算法

采用精细塑性铰法考虑残余应力和逐步塑性,并引入弓形效应来提高计算精度,同时基于截面组合法建立的工字形或H形截面的屈服面方程进行严格推导,提出一种单元恢复力迭代算法,减少了半理论半经验公式的使用。此外,所采用的梁柱单元还可以考虑梁构件剪切变形和几何初始缺陷的影响。相比之前的方法,该方法能在进行塑性铰分析的同时,在单元的轴力表达式中考虑二阶效应,更全面地考虑非线性因素影响。最后,通过两个经典算例的对比,证明了该方法具有高效率和高精度的特点。