The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.

Characteristic-Based Time Domain Method for Cylindrically Conformal Microstrip Patch Antennas

The characteristics of a cylindrical conformal microstrip patch antenna are analyzed by using the characteristic-based time domain （CBTD） method. A governing equation in the cylindrical coordinate system is formulated directly to facilitate the analysis of cylindrically conformal microstrip patch antennas. The algorithm has second-order accuracy both in time and space domain and has the potential to eliminate the spurious wave reflection from the numerical boundaries of the computational domain, Numerical results demonstrate the important merits and accuracy of the proposed technique in computational electromagnetics,

Combined adaptive meshing technique and characteristic-based split algorithm for viscous incompressible flow analysis

A combined characteristic-based split algorithm and all adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. Tile method uses the three-node triangular element with equal-order interpolation functions for all variables of tile velocity components and pressure. The main advantage of the combined nlethod is that it inlproves the sohltion accuracy by coupling an error estinla- tion procedure to an adaptive meshing technique that generates small elements in regions with a large change ill sohmtion gradients, mid at the same time, larger elements in the other regions. The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder, for their transient and steady-state flow behaviors.

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

Numerical Simulation of the Solitary Wave Interacting with an Elastic Structure Using MPS-FEM Coupled Method

Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method(MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit(MPS) method is used to calculate the fluid domain, while the Finite Element Method(FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

基于DEM的沥青混合料劈裂强度尺寸效应

为了探究沥青混合料劈裂抗拉强度的尺寸效应,应用颗粒离散元数值模拟技术,对4种级配(AC-13、AC-16、AC-20、AC-25)不同尺寸的沥青混合料进行巴西劈裂数值试验,每组级配模型尺寸缩放系数分别为0.6、0.8、1.0、1.2、1.4,并建立尺寸缩放系数与沥青混合料抗拉强度尺寸效应的关系,得到4种级配下的沥青混合料抗拉强度的临界尺寸和临界强度。试验结果表明,4种级配的沥青混合料抗拉强度均具有明显的尺寸效应,级配越大,尺寸效应越不明显,级配AC-25的试样抗拉强度尺寸相关系数约为级配AC-13试样的94.37%。

Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations

In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.

Splitting positive definite mixed element method for viscoelasticity wave equation

A splitting positive definite mixed finite element method is proposed for second-order viscoelasticity wave equation. The proposed procedure can be split into three independent symmetric positive definite integro-differential sub-system and does not need to solve a coupled system of equations. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete scheme are proved. Finally, a numerical example is provided to illustrate the efficiency of the method.

The dimension splitting element-free Galerkin method for 3D transient heat conduction problems

By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem; the essential boundary conditions are imposed with the penalty method; and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems.

Approach to minish scattering of results for split Hopkinson pressure bar test

Split Hopkinson pressure bar(SHPB) apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement mechanism and energy consumption. However, the possible reasons of sampling disturbance, machining error and so on often lead to the scattering of test results, and bring ultimate difficulty for forming general test conclusion. Based on the stochastic finite element method, the uncertain parameters of specimen density ρs, specimen radius Rs, specimen elastic modulus Es and specimen length Ls in the data processing of SHPB test were considered, and the correlation between the parameters and the test results was analyzed. The results show that the specimen radius Rs has direct correlation with the test result, improving the accuracy in preparing and measuring of specimen is an effective way to improve the accuracy of test and minish the scattering of results for SHPB test.

FINITE ELEMENT ANALYSIS ON EVOLUTION PROCESS FOR DAMAGE MICROCRACK HEALING

Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid.

基于DEM的直升机沙盲加速计算方法

直升机沙盲数值模拟是研究沙盲演化特性的重要手段,而沙盲由众多动力学特性复杂的沙粒构成,这导致沙盲数值模拟复杂且计算量庞大。基于离散单元法(DEM)和沙粒动力学方程,将沙粒映射至背景网格实现加速计算,并将背景网格分裂为多子区再次加速计算,构建背景网格映射-分裂加速计算模型,且耦合沙粒接触碰撞模型、沙粒-流场耦合模型、旋翼/地面气动干扰模型,提出基于DEM的直升机沙盲加速计算方法。通过与美国陆军EH-60L着陆-起飞沙盲测试结果对比表明:所提方法能准确捕捉着陆-起飞状态的直升机沙盲,且相比于沙盲直接模拟方法,所提方法计算量显著减小。直接模拟方法的计算量随沙粒数量抛物线增加,而所提方法计算量随沙粒数量线性增加。当沙粒数量大于1×10^(7)时,相比于仅背景网格映射模型加速方法,所提方法计算量减小70.29%。

XFEM和修正剑桥模型模拟高聚物劈裂注浆方法研究

针对自膨胀高聚物材料在土体中劈裂扩散仿真手段尚不完备的现状,初步建立了一种模拟高聚物对土体劈裂压密作用的仿真方法。该方法采用扩展有限元离散求解区域土体介质,用修正剑桥模型描述土体力学特性,利用高聚物密度-围压关系迭代计算作用于裂缝面的浆液膨胀压力,实现了对土体劈裂缝扩展过程的数值模拟,通过与试验结果的对比验证了该方法的适用性。算例分析表明,应用该方法能够模拟膨胀力作用下土体裂缝启裂过程、扩展走向和浆脉厚度变化,获得裂缝周围土体变形模量、孔隙比、应力场和密度场分布特征,为深入研究膨胀性高聚物注浆材料对土体劈裂压密机制奠定了基础。

Fracturing damage process in dynamic split experiments of a brittle glass

In this study, the 3-dimensional discrete element method is firstly introduced to explain the fracturing damage process of the dynamic split experiment of a special brittle glass ZnS. The corresponding dynamic split experiment is also performed by using the split Hopkinson pressure bar. Then the numerical results correspond closely to those obtained by experiments, and the fracturing damage mode shows that the sample under high strain rate loading would crack along vertical diameter in the band region between two loading edges, which differs from the static damage mode. Furthermore, by comparing a group of contrast numerical tests, the numerical results prove that loading area upon the top side of samples would influence the fracture mode of dynamic split experiments, which indicates that the narrow loading plane is better.

基于非分裂CFS-PML边界条件的频散介质GPR时域有限元模拟

通过数值模拟研究探地雷达(GPR)高频电磁波在频散介质中的传播规律,对提高实测资料的解释精度具有重要意义.复频移完全匹配层边界条件(CFS-PML)以其优越的吸收特性被广泛用于一阶电磁波动方程的GPR时域有限差分数值模拟中,其实现过程大都涉及电磁场的卷积计算,辅助变量较多,降低计算效率.为此,本文从复拉伸坐标系下的Debye频散介质电磁波动方程出发,通过合理构造辅助微分方程,推导了二阶Debye频散介质电磁波动方程的非分裂CFS-PML边界条件实现公式,避免了电磁波场的分裂和卷积计算.在此基础上,利用Galerkin法和Newmark-β差分法推导了基于非分裂CFS-PML边界条件的GPR有限元方程及其时域差分离散格式.两个GPR模型的模拟结果表明:本文提出的基于辅助微分方程的非分裂CFS-PML边界条件实现方法可有效地吸收大角度入射的低频虚假反射波,提高模拟精度;相比于非频散介质,高频电磁波在频散介质中传播衰减更强、子波持续时间增大、分辨率和传播速度降低、直达波和反射波的主频更小,分析结果有助于提高实测GPR资料的解译精度.

狮子洋通道钢-混组合梁桥结构选型研究

狮子洋通道全长约35 km,为高速公路+城市道路双层复合过江通道,过江段采用双层桥梁方案(上层为高速公路,下层为市政道路),多处主线桥设计采用50~80 m跨径桥梁,主梁采用钢-混组合梁结构。通过对简支和连续体系进行比选,该项目采用结构简支、桥面连续的结构体系,并配合暗帽梁的设计方案;通过对工字形钢板组合梁、整体式钢箱组合梁、波形钢腹板组合梁、钢桁腹组合梁、分体式小钢箱组合梁进行比选,选择分体式小钢箱作为该项目钢-混组合梁的钢主梁形式;通过对结构受力性能、经济性、施工便利性、运输便利性和对变宽路段的适应性等综合分析比选,钢主梁采用4片主梁方案,该方案有利于设计、制造及施工标准化,结构受力更合理、造价更经济。从施工场地、设备、工期和安全性等方面分析,该项目施工采用标准化加工钢结构、工厂化预制混凝土桥面板,在桥位上通过湿接缝和集束式剪力钉形成组合结构的方案。

偏载作用下超宽幅分体钢箱梁扭转效应分析

为研究不同成桥偏载作用下宽幅分体钢箱梁的扭转效应及结构参数对扭转效应的影响规律,以西堠门公铁两用大桥主桥斜拉-悬索协作区段宽幅分体钢箱梁为背景进行有限元分析。该桥为主跨1488 m的斜拉-悬索协作体系桥,主梁为由3个流线型扁平钢箱通过箱形横梁连接组成的超宽幅分体钢箱梁。采用Abaqus软件建立该桥斜拉-悬索协作区段宽幅分体钢箱梁精细化有限元模型,计算3种偏载工况作用下钢箱梁3个典型截面(吊索作用截面、无横梁连接截面、斜拉索作用截面)顶、底板扭转翘曲正应力;分析腹板厚度、横梁宽度以及吊索横向间距对宽幅分体钢箱梁扭转效应的影响。结果表明:3种偏载工况作用下宽幅分体钢箱梁扭转效应明显,其中无横梁连接截面扭转效应最为突出,设计时应予以关注;增大腹板厚度可以降低钢箱梁顶、底板扭转效应,增大横梁宽度会增大顶板、腹板中间位置附近的扭转翘曲正应力,但会降低底板的扭转翘曲正应力最大值;吊索横向间距对扭转效应影响较小。

求解三维弹性力学问题的快速耦合方法

将多种数值方法耦合,充分利用各种方法的优点建立新的数值方法,是求解三维复杂问题的有效途径之一.本文将无单元Galerkin(Element-Free Galerkin,EFG)方法、有限元法和维数分裂法耦合,提出了求解三维弹性力学问题的快速耦合方法(Fast Hybrid Method,FHM).将三维弹性力学问题分裂为若干个二维平面问题,对于每个二维问题采用罚函数法施加边界条件,并推导其相应的积分弱形式,引入Shepard基函数的移动最小二乘法建立形函数,进而推导二维平面问题的离散方程.第三个方向上采用有限元法将这些二维离散方程进行耦合,可以得到原三维弹性力学问题的快速耦合方法数值解的求解公式.通过数值算例验证了本文快速耦合方法求解三维弹性力学问题的收敛性,将数值解与解析解对比,说明了本文方法求解三维弹性力学问题的有效性.