A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.

ANALYSIS OF THE THERMOPHYSICAL PARAMETERS OF MOIST WOOD PARTICLE MATERIAL IN A COUPLED HEAT AND MASS TRANSFER PROCESS OF FREEZING BY USING FINITE ELEMENT METHOD

The coupled heat and moisture transfer in a freezing process of wood particle material was mathematically modeled in the paper. The models were interactively solved by using the numerical method(the finite element method and the finite difference method). By matching the theoretical calculation to an experiment, the nonlinear problem was analyzed and the variable thermophysical parameters concerned was evaluated. The analysis procedure and the evaluation of the parameters were presented in detail. The result of the study showed that by using the method as described in the paper, it was possible to determine the variable (with respect to temperature, moisture content and freezing state) thermophysical parameters which were unknown or difficult to measure as long as the governing equations for a considered process were available. The method can significantly reduces the experiment efforts for determining thermophysical parameters which arc very complicated to measure. The determined variable of the effective heat conductivity of wood particle material was given in the paper. The error of the numerical calculation was also estimated by the comparison with a matched experiment.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using Triangular Elements

This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.

Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model

A polymeric gel is an aggregate of polymers and solvent molecules, which can retain its shape after a large deformation. The deformation behavior of polymeric gels was often described based on the Flory-Rehner free energy function without considering the influence of chain entanglements on the mechanical behavior of gels. In this paper,a new hybrid free energy function for gels is formulated by combining the EdwardsVilgis slip-link model and the Flory-Huggins mixing model to quantify the time-dependent concurrent process of large deformation and mass transport. The finite element method is developed to analyze examples of swelling-induced deformation. Simulation results are compared with available experimental data and show good agreement. The influence of entanglements on the time-dependent deformation behavior of gels is also demonstrated.The study of large deformation kinetics of polymeric gel is useful for diverse applications.

Finite Element Methods for Coupled Stokes and Darcy Problems

We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H（div） finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems

This paper is an introduction to mesh based generated reluctance network modeling.An overview of scientific works which led to the development of this approach is first presented.Basic concepts of the approach are then presented in the case of electromagnetic devices.A step-by-step procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB and Scilab environments are also included.

Soret and Dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation

The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.

Reinforcing a Dangerous Rock Mass Using the Flexible Network Method

Because the main failure type of a dangerous rock mass is collapse, the treatment of such a mass should focus on controlling collapse failure. When treating dangerous rock masses, disturbing the mass （e. g. by blasting） needs to be avoided, as this new damage could cause collapse. So the self-bearing capacity of the mountain mass must be used to treat the dangerous rock mass. This article is based on a practical example of the control of a dangerous rock mass at Banyan Mountain, Huangshi, Hubei Province. On the basis of an analysis of damage mechanism and the stability of the dangerous rock mass, a flexible network reinforcement method was designed to prevent the collapse of the rock mass. The deformations of section Ⅱ w of the dangerous rock mass before and after the flexible network reinforcement were calculated using the two-dimensional finite element method. The results show that the maximum deformation reduced by 55 % after the application of the flexible network reinforcement, from 45.99 to 20.75 ram, which demonstrates that the flexible network method is effective, and can provide some scientific basis for the treatment of dangerous rock masses.

A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrodinger Equation

Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.

考虑激励幅值慢变的卷绕头转子系统动力学建模

卷绕头转子系统结构之间的耦合振动和时频变激励使振动问题十分复杂,为了更准确地研究其动力学特性,根据转子动力学理论,使用有限元方法建立了考虑多盘质量慢变的卷绕头非线性转子系统整机动力学模型,运用Newmark-β数值积分方法对其动力学特性求解,得到仅存在初始不平衡量以及卷装不良带来的激励频率、幅值慢变下的非线性动力学行为。通过分析轴心轨迹、时域波形和幅频特性曲线等结果,发现卷绕头转子系统对因卷装不良引起的激励幅值慢变较为敏感,出现新的频率成分。进一步对比分析了不同节点处的振动频谱,其结果可为卷绕头转子系统动力学设计和故障识别提供一定理论支持。

Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method

Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.

High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids

A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity.The stress field is approximated by symmetric H(div)−Pk(k≥3)polynomial tensors enriched with higher order bubbles so as to allow mass lumping,and the displacement field is approximated by C−1−Pk−1 polynomial vectors enriched with higher order terms.For both the proposed mixed elements and their mass lumping schemes,optimal error estimates are derived for the stress and displacement in H(div)norm and L 2 norm,respectively.Numerical results confirm the theoretical analysis.

液态金属堆内小长径比同轴双层薄壁结构的流固耦合试验研究

池式液态金属堆的主容器与热屏之间具有狭窄的流体间隙,该结构属于含窄缝间隙的小长径比同轴双层柔性壳体。窄缝间隙中流体与结构之间相互作用产生的流固耦合效应在抗震分析时必须加以考虑。现有研究主要针对长径比较大和流体间隙相对较大的圆柱壳体,对于小长径比和极小流体间隙的同轴柔性壳体研究较为缺乏。本文参考液态金属反应堆的结构设计了三种不同尺寸的窄缝间隙,开展窄缝间隙条件小长径比同轴双层壳体模型的振动试验,测量结构在不同间隙尺寸下的加速度,得到模态频率和主要振型。然后,使用有限元法进行模态分析,通过与试验结果的对比,验证了有限元法的准确性。最后,计算出不同间隙尺寸下模型的附加质量;且随着间隙尺寸的减小,模型附加质量随之增大。本研究可为类似的含窄缝小长径比同轴双层柔性壳体结构的抗震设计提供数据支持,对于液态金属堆的抗震分析具有重要意义。

地下水位对核电结构地震反应的影响分析

核电结构大多沿海或沿江、河而建,在地下水位以下,土体孔隙中的流体对土层的地震响应有较大影响,进而影响核电结构的响应。本文采用饱和多孔介质模型,考虑土-结相互作用效应,分析地下水位对核电结构地震反应的影响。通过传递矩阵方法,得到干土-饱和土水平成层场地的自由场,并结合透射人工边界,实现土-结相互作用分析的波动输入;采用土-结相互作用的分区并行计算方法,实现饱和土和结构相互作用分析。其中,含地下水位的场地土体采用广义饱和多孔介质模型描述,通过自编FORTRAN程序用集中质量显式有限元结合透射人工边界进行模拟,结构通过ANSYS中的隐式有限元进行分析。以某一核电结构为例,分析了0,−10,−20,−30,−40 m不同地下水位的五种场地上,土-基础-核电结构体系的动力响应。结果表明,地下水位对基础和结构的位移影响不大,对加速度的影响较大。

基于Workbench的导管架吊装分析

为对导管架整体吊装安全性进行数值模拟分析,采用有限元法。利用ANSYS Workbench对导管架进行整体建模。模型中全部采用壳单元进行模拟。有限元网格划分过程中对不同的板厚和位置设置不同的偏移方向。利用力质量单元向导管架模型赋值,利用重力加速度施加场力。导管架起吊的吊点采用远程点的方式进行模拟,远程点与吊点之间的控制方程简化钢丝绳的建模。对吊点等关键部位进行细化网格处理。在导管架吊装受力后处理时,检查结构的整体应力情况,并重点检查吊点的应力情况。检查远程点反力并与导管架重量进行比对。检查导管架整体位移避免发生翻转。

露天矿高陡边坡岩体参数获取与稳定性评价方法研究

针对露天矿高陡边坡岩体参数难获取和稳定性易变化的问题,以攀枝花露天矿高陡边坡为研究对象,采用非接触式无人机摄影测量技术获取研究区域的三维模型,统计结构面的分布情况,结合室内岩石力学试验数据,采用《工程岩体分级标准》(GB/T 50218—2014)进行岩体质量分级,并给出边坡岩体强度力学参数建议值。在此基础上,通过有限单元法分析了矿区在开采条件下边坡的稳定性动态演化特征,并对开挖过程边坡的稳定性做出了评价。结果表明:随着矿区的开采,边坡在开挖面附近由于卸荷作用发生位移回弹,最大位移增量为33.2 mm;塑性区主要集中在断层和矿岩界面附近,以剪切屈服为主;边坡稳定性随着矿区的开采逐渐降低,直至达到临界稳定状态。采用锚索对边坡进行加固,并采用塑性区面积占比对加固前后的稳定性进行评价,评价系数α由加固前的0.4降低至加固后的0.05,证明了加固措施的有效性。研究成果可为露天矿高陡边坡岩体参数取值和稳定性评价提供参考。

基于关键块体的井巷围岩稳定性分析及支护研究

为了进一步研究关键块体对巷道围岩稳定性的影响及通过关键块体分析进行支护措施的设计。以蒙库铁矿地下开采某一巷道为研究对象,通过工程地质调查与现场测试工作,对围岩节理裂隙统计与分段,并进行岩块强度试验和岩体的波速测试,获得了岩体完整性参数,依据此进行了详细的岩体工程分级,给出不同岩体的分级力学参数,再通过Unwedge进行关键块体分析,对不稳定岩块进行划定,确定了锚喷支护的参数及重点支护位置,然后采用有限元软件模拟开挖过程并分析了开挖过程中围岩及支护的应力应变变化情况,最后进行现场采动应力的监测与分析。研究结果表明:经过关键块体分析,更准确地辨别出可能导致巷道失稳的不稳定岩块,针对关键块体分析结果提出稳定性支护措施,并应用于现场,进行采动应力监测与分析,取得了良好的效果。研究结果在一定程度上为围岩稳定性分析及支护设计提供了可靠依据。

基于HSS技术的深基坑土体形变规律分析研究

针对深基坑土体形变的问题,提出了一种结合有限元软件和小应变土体硬化模型的数值模型,解决了深基坑工程中土体变形问题,结果实现了深基坑土体形变规律的分析。数值模型研究结果表明:深基坑开挖深度越大,土体水平位移和地表沉降便越大。

某高速公路高陡危岩体失稳对拟建桥梁的影响分析

以西南山区某高速公路高陡崖边坡对坡脚拟建桥梁影响分析为例,采用工程地质调查分析结合有限元强度折减法分析可知,该陡崖边坡整体处于欠稳定状态,变形模式为错落式滑坡变形。采取有限元-离散元耦合分析技术动态模拟研究边坡失稳对桥梁安全的影响。由模拟分析结果可知,陡崖边坡产生错落变形后,错落岩体最终与桥梁墩台底部发生撞击,桥墩从根部断裂,桥梁整体倒塌。基于分析结果,提出预应力锚索加固陡崖边坡、坡脚设置拦截挡墙、边坡失稳范围内避免设置桥墩3种方案应对高陡边坡对拟建桥梁的破坏性影响。