The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method(NS-FEM)is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings.A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations.Numerical results obtained agree very well with those using the slip-line method,revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration.An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations.In addition,particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component.While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial,and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity.Both tables and charts are given for practical application to the seismic design of the foundations.

Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations

Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.

Stabilization for Equal-Order Polygonal Finite Element Method for High Fluid Velocity and Pressure Gradient

This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

Local and parallel finite element algorithms for time-dependent convection-diffusion equations

Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel proce- dures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analvsis.

3D Finite Element Numerical Simulation of Residual Stresses on Electron Beam Welded BT20 Plates

A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.

Stress-corrosion coupled damage localization induced by secondary phases in bio-degradable Mg alloys:phase-field modeling

In this study,a phase-field scheme that rigorously obeys conservation laws and irreversible thermodynamics is developed for modeling stress-corrosion coupled damage(SCCD).The coupling constitutive relationships of the deformation,phase-field damage,mass transfer,and electrostatic field are derived from the entropy inequality.The SCCD localization induced by secondary phases in Mg is numerically simulated using the implicit iterative algorithm of the self-defined finite elements.The quantitative evaluation of the SCCD of a C-ring is in good agreement with the experimental results.To capture the damage localization,a micro-galvanic corrosion domain is defined,and the buffering effect on charge migration is explored.Three cases are investigated to reveal the effect of localization on corrosion acceleration and provide guidance for the design for resistance to SCCD at the crystal scale.

3D Finite Element Analysis of the Stray Loss in Power Transformer Structure Parts

In order to analyze the leakage magnetic field and stray loss in power transformer, leakage magnetic field and stray loss in structure parts of a power transformer are calculated by three-dimensional (3-D) non-linear time harmonic finite element method (FEM). The results show that stray loss and loss density in structure parts are large and which may lead to local overheating and affect performance of the transformer. The magnetic shields are used to reduce the stray loss and loss density of power transformer. Effects of these shields on stray loss and loss density of structure parts are discussed. The results show that stray loss and local overheating can be reduced and eliminated effectively by adding magnetic shields. It provides some references for the analysis of stray loss and optimization design in transformer.

Finite Element Analysis of the Material’s Area Affected during a Micro Thermal Analysis Applied to Homogeneous Materials

Micro-thermal analysis (μ-TA), with a miniaturized thermo-resistive probe, allows topographic and thermal imaging of surfaces to be carried out and permits localized thermal analysis of materials. In order to estimate the effective volume of material thermally affected during this localized measurement, simulations, using finite element method were used. Several parameters and conditions were considered. So, thermal conductivity was found to be the driving physical parameter in thermal exchanges. Indeed, the evolution of the heat affected zone (HAZ) versus thermal conductivity can well be described by a linear interpolation. Therefore it is possible to estimate the HAZ before experimental measurements. This result is an important progress especially for accurate interphase characterization in heterogeneous materials.

CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.

锚杆倒肋式风机基础受力性能的数值模拟

为了解决风机基础施工成本高、施工难度大等问题,提出了一种新型锚杆倒肋式风机基础。利用有限元分析软件ABAQUS对该新型风机基础与传统梁板式风机基础在极端运行荷载工况下的混凝土应力、钢筋应力、基础位移以及基础倾斜率进行数值模拟分析,并进一步讨论二者的混凝土用量、钢筋用量、土方开挖量。结果表明,锚杆的添加以及倒肋的结构设计使锚杆倒肋式风机基础的受力性能、经济性等方面明显优于传统梁板式风机基础,具有较好的应用前景。

高温下焊接Q960钢H形截面柱局部稳定设计方法

为考察焊接Q960钢H形截面轴心受压柱局部稳定性能,采用ABAQUS软件建立有限元模型,经试验数据验证后,分析翼缘宽厚比、腹板高厚比、构件温度、构件长细比、初始几何缺陷和残余应力等参数对焊接Q960钢H形截面轴心受压柱局部屈曲强度的影响。研究表明,轴心受压柱的局部屈曲承载力主要与截面尺寸及构件温度有关。采用多国规范对试验试件的局部屈曲承载力进行计算,发现现有规范的设计方法不适用于高温下焊接Q960钢H形截面轴心受压柱局部屈曲承载力的计算。根据有限元分析结果提出焊接Q960钢H形截面轴心受压柱局部屈曲设计方法,与试验数据和有限元分析结果的对比表明所提方法能较准确地计算焊接Q960钢H形截面轴心受压柱不同温度下的局部屈曲承载力。

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.

OPTIMALITY OF LOCAL MULTILEVEL METHODS FOR ADAPTIVE NONCONFORMING P1 FINITE ELEMENT METHODS

In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.

潜蚀的局部守恒有限元和有限体积交替解法

潜蚀的模拟需要计算土中的渗流过程以及土中细粒随孔隙水流的运移过程。常规有限元法在求解纯运移方程时存在稳定性问题,为此提出了一个采用有限元法求解渗流方程、有限体积法求解细粒运移方程的交替方法。鉴于常规有限元法不能给出满足有限体积法输入要求的流速场,给出了一个基于单元不平衡流量总体再平衡修正单元边界流速的算法。利用该算法对有限元计算的单元边界流速进行局部守恒处理,即可实现在同一有限元网格上利用有限体积法求解细粒运移方程,因此可以方便地和现有的有限元计算程序结合。算例验证表明,所提出的局部守恒处理算法及交替解法计算效率高且具有可接受的精度,是模拟潜蚀问题的一条简单实用的途径。

A LOCAL MULTILEVEL PRECONDITIONER FOR THE ADAPTIVE MORTAR FINITE ELEMENT METHOD＊

In this paper, we propose a local multilevel preconditioner for the mortar finite element approximations of the elliptic problems. With some mesh assumptions on the interface, we prove that the condition number of the preconditioned systems is independent of the large jump of the coefficients but depends on the mesh levels around the cross points. Some numericM experiments are presented to confirm our theoreticM results.

A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media

A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2) for concentration c,in L2(0,T;L2)for cxand L∞(0,T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method,the nonlinearity,and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally,we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme.