Three-dimensional analysis of elastic stress distribution of indented ceramic surface by finite element method

The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials, Al2O3, Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens, surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress, shear stress, and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions, the crack length and its density of probability are in good agreement with the experimental results.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils

Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

Numerical Investigation of Thermal Behavior of CNC Machine Tool and Its Effects on Dimensional Accuracy of Machined Parts

The dimensional accuracy of machined parts is strongly influenced by the thermal behavior of machine tools (MT). Minimizing this influence represents a key objective for any modern manufacturing industry. Thermally induced positioning error compensation remains the most effective and practical method in this context. However, the efficiency of the compensation process depends on the quality of the model used to predict the thermal errors. The model should consistently reflect the relationships between temperature distribution in the MT structure and thermally induced positioning errors. A judicious choice of the number and location of temperature sensitive points to represent heat distribution is a key factor for robust thermal error modeling. Therefore, in this paper, the temperature sensitive points are selected following a structured thermomechanical analysis carried out to evaluate the effects of various temperature gradients on MT structure deformation intensity. The MT thermal behavior is first modeled using finite element method and validated by various experimentally measured temperature fields using temperature sensors and thermal imaging. MT Thermal behavior validation shows a maximum error of less than 10% when comparing the numerical estimations with the experimental results even under changing operation conditions. The numerical model is used through several series of simulations carried out using varied working condition to explore possible relationships between temperature distribution and thermal deformation characteristics to select the most appropriate temperature sensitive points that will be considered for building an empirical prediction model for thermal errors as function of MT thermal state. Validation tests achieved using an artificial neural network based simplified model confirmed the efficiency of the proposed temperature sensitive points allowing the prediction of the thermally induced errors with an accuracy greater than 90%.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

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.

Finite Element Simulation of the Polymeric Liquid Flow in Coat-hanger Die

A three - dimenslonal finite element model is developed to deal with the polymeric liquid flow in coat - hanger die. This model is used to predict the flow behavior of the 2％ CMC/watsr solution in the coat - hanger die with linearly taper manifolds and its validity is experimentally verified quantitatively and qualitatively by using Laser Doppler Velocimetry and Particle Image Velocimetry respectively.

变摩擦条件下高速钢轨焊缝处轮轨滚动接触-冲击行为研究

采用变摩擦系数能够较为准确地刻画轮轨滚动接触行为。为研究变摩擦系数对钢轨焊缝处轮轨滚动接触行为的影响,建立三种不同钢轨焊缝工况的三维轮轨瞬态滚动接触有限元模型,通过对比库伦型摩擦系数的结果,计算分析变摩擦系数对轮轨力、接触斑内的微滑以及黏滑分布等接触行为的影响。结果表明:变摩擦系数接触斑内的滑动区域占比会更大且在滑动区域会引起黏滑振荡现象,当轮轨界面滑动现象越明显时,黏滑振荡越剧烈;变摩擦系数对法向接触解的影响不大,切向接触解会因接触状态的改变显著受到影响,造成凸形1焊缝的不均匀磨耗;变摩擦系数会影响von Mises应力分布,其最大von Mises应力发生的位置会向轨底移动,对伤损出现的位置产生影响。

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.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

基于FEM-MEI和正余弦算法的二维电磁成像方法

针对二维介质目标的电磁成像问题,将正余弦算法(Sine Cosine Algorithm,SCA)与有限元方法(Finite Element Method,FEM)和不变性测试方程(Measured Equation of Invariance,MEI)进行结合提出一种新的成像方法。将FEM与MEI进行结合求解二维介质目标的电磁散射正问题,即求解Helmholtz方程。其中,MEI保证边界截断的精度,FEM适用于复杂介质目标的准确模拟。对于电磁散射逆问题,引入SCA并加以改进提出一种新的重构方法。该方法采用等效原理与格林函数的渐近式求得远区散射场,以测量的散射场和计算的散射场最大偏差为目标函数,采用改进的SCA优化介质参数,使目标函数达到最小值,以此重构散射体。为提高计算效率,采用MPI算法进行并行计算。文中采用基准函数展示了改进的SCA算法的快速收敛性,并采用非规则的均匀介质柱目标验证了成像方法的正确性。

Influence of Residual Stress on the Dimensional Instability of 7075 Aluminum Cone-Shaped Shells

This paper dealt with the influence of residual stress on the dimensional instability of 7075 aluminum cone-shaped shells. Finite element method was introduced to calculate residual stress distributions in 7075 aluminum cone-shaped shells during conventional heat treatment (CHT) and deep cryogenic treatment (DCT). An example was given to demonstrate effects of deep cryogenic treatment (DCT) and conventional heat treatment (CHT) on dimensional instability. It is concluded that initial residual stresses have detrimental influence on the dimensional instability of 7075 aluminum cone-shaped shells.

SV和SH波垂直入射下二维盆地-子盆地共振对比研究

盆地-子盆地中的子盆地除了底部直达的入射体波外,还存在大盆地产生的横向传播的面波入射,导致子盆地共振特性的变化。基于显式有限元法,对比分析了SH波和SV波垂直入射下,子盆地基底阻抗比、大盆地倾角和半宽对二维梯形盆地-子盆地的二维共振频率及其对应放大系数的影响。研究表明:受大盆地产生的横向传播面波的影响,子盆地的速度峰值PGV和累积能量Ex最大值均有明显放大,且SV波入射下的放大系数大于SH波;子盆地基底阻抗比对盆地-子盆地的PGV最大值、Ex最大值、二维共振频率及其对应放大系数影响较大,大盆地倾角和半宽的影响不大。SV波和SH波入射下子盆地二维共振频率较单一小盆地均有所增加,且同阻抗比下SV波入射的增幅大于SH波。SH波入射下二维共振频率下的放大系数基本大于单一小盆地,而SV波在低阻抗比下低于单一小盆地,高阻抗比下高于单一小盆地和SH波入射下的结果。SV波入射下盆地-子盆地的二维共振频率及其对应放大系数受大盆地的影响较SH波更大。

Three-dimensional stochastic seepage field for embankment engineering

Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.

Three dimensional tectonic stress field in North China

According to the latest data of geological structure, geophysics, in-situ stress measurement and focal mechanism,3-D tectonic stress field model in North China is built and 3-D tectonic stress field pattern of North China aresimulated by finite element method. Then the overall characteristics and regional specific feature of North Chinaare studied. Finally, the influences of the valid dynamic boundary conditions of North China Block, active faultsand the inhomogeneity of crustal medium on tectonic stress field of North China are investigated.