Cracking analysis of fracture mechanics by the finite element method of lines(FEMOL)

The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

Static and Dynamic Analysis of Mooring Lines by Nonlinear Finite Element Method

This study has focused on developing numerical procedures for the static and dynamic nonlinear analysis of mooring lines. A geometrically nonlinear finite element method using isoparametric cable element with two nodes is briefly presented on the basis of the total Lagrangian formulation. The static and dynamic equilibrium equations of mooring lines are established. An incremental-iterative method is used to determine the initial static equilibrium state of cable systems under the action of self weights, buoyancy and current. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method, and examine the effect of various parameters.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variationM principle, a sub-region mixed version of the newly-developed semi-analytical ＇finite element method of lines＇ （FEMOL） is proposed in this paper for accurate and efficient computation of stress intensity factors （SIFs） of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations （ODEs） and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

Finite Element Analysis of the Dynamic Behaviour of Transmission Line Conductors Using MATLAB

The dynamic behaviour of power line cables have been a source of interest to researchers ever since the phenomenon was first noticed in the 1920s. Conductor oscillation is mostly caused by the dynamic forces of nature such as wind loading. This imposes a periodic force on the conductors which is highly undesirable. It is therefore important for engineers to account for the possible effect of the wind loading when designing the power line. Investigations have shown that modeling the exact dynamic behaviour of a conductor is very difficult. Based on this fact, getting the exact analytical solution to conductor vibration is difficult, which is almost impossible, hence the numerical approximation becomes an option. This paper presents the developed finite element method used to analyse the dynamic behaviour of transmission line conductors. The developed FEM （finite element method） is implemented on MATLAB. The numerical analysis using MATLAB that is presented in this paper is used to simulate the response of the conductor when subjected to external loading in the time domain. The simulation is used to analyse the transverse vibration of the conductor. The formulation of the stiffness matrix and load vector is done and the results obtained are used to evaluate the conductor＇s internal energy dissipation. This finite element solution is compared with the results documented in literature. This numerical simulation is also used to investigate the effects of varying the axial tension on energy dissipation within the strands. Hence, this evolved in physically appropriate energy characterization process that can be used to evaluate the conductor self-damping with respect to line contact.

Nonlinear dynamical response of high-voltage transmission lines based on cable dropping

In order to study the dynamic response of high-voltage transmission lines under mechanical failure, a finite element model of a domestic 500-kV high-voltage transmission line system is established. The initial equilibrium condition of the coupling system model is verified by nonlinear static analysis. The transient dynamic analysis method is proposed to analyze the variation law of dynamic response under cable or insulator rupture, and the dynamic response of structural elements next to the broken span is calculated. The results show that upper crossarm cable rupture has no effect on cable tension at adjacent suspension points, but it has a significant influence on tension in the insulator and the tower component of the upper crossarm next to the broken span. The peak tension in the conductor of the upper crossarm at the suspension point exceeds the design value under insulator rupture. Insulator rupture has no effect on the tower component of the upper crossarm, but it has a significant influence on insulator tension of the upper crossarm. Insulator rupture should be taken into account in the design of overhead transmission lines. The research results can provide a theoretical basis for the design of transmission lines.

Reduction of electric field strength by two species of trees under power transmission lines

Electrical pollution is a worldwide concern,because it is potentially harmful to human health.Trees not only play a significant role in moderating the climate,but also can be used as shields against electrical pollution.Shielding effects on the electric field strength under transmission lines by two tree species,Populus alba and Larix gmelinii,were examined in this study.The electrical resistivity at different heights of trees was measured using a PiCUS sonic tomograph,which can image the electrical impedance for trees.The electric field strength around the trees was measured with an elf field strength measurement system,HI-3604,and combined with tree resistivity to develop a model for calculating the electric field intensity around trees using the finite element method.In addition,the feasibility of the finite element method was confirmed by comparing the calculated results and experimental data.The results showed that the trees did reduce the electric field strength.The electric field intensity was reduced by 95.6%,and P.alba was better than L.gmelinii at shielding.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

This article extends the finite element method of lines to a parabolic initial boundary value problem whose diffusion coefficient is discontinuous across an interface that changes with respect to time.The method presented here uses immersed finite element(IFE)functions for the discretization in spatial variables that can be carried out over a fixedmesh(such as a Cartesianmesh if desired),and this featuremakes it possible to reduce the parabolic equation to a system of ordinary differential equations(ODE)through the usual semi-discretization procedure.Therefore,with a suitable choice of the ODE solver,this method can reliably and efficiently solve a parabolic moving interface problem over a fixed structured(Cartesian)mesh.Numerical examples are presented to demonstrate features of this new method.

Dynamic Analysis of Overhead Transmission Lines under Turbulent Wind Loading

Transmission tower-line systems are designed using static loads specified in various codes. This paper compares the dynamic response of a test transmission line with the response due to static loads given by Eurocode. Finite element design software SAP2000 was used to model the towers and lines. Non-linear dynamic analysis including the large displacement effects was carried out. Macroscopic aspects of wind coherence along element length and integration time step were investigated. An approach is presented to compare the probabilistic dynamic response due to 7 different stochastically simulated wind fields with the response according to EN-50341. The developed model will be used to study the response recorded on a test line due to the actual wind speed time history recorded. It was found that static load from EN overestimated the strength of conductor cables. The response of coupled system considering towers and cables was found to be different from response of only cables with fixed supports.

AN ENERGY-STABLE PARAMETRICFINITE ELEMENT METHOD FOR SIMULATING SOLID-STATE DEWETTING PROBLEMS INTHREE DIMENSIONS

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space.The model describes the motion of the film/vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line.We present a weak formulation for the problem,in which the contact angle condition is weakly enforced.By using piecewise linear elements in space and backward Euler method in time,we then discretize the formulation to obtain a parametric finite element approximation,where the interface and its contact line are evolved simultaneously.The resulting numerical method is shown to be well-posed and unconditionally energystable.Furthermore,the numerical method is generalized to the case of anisotropic surface energies in the Riemannian metric form.Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.

基于BIM技术的浅埋隧道无限元法数值研究

近年来,BIM技术在交通运输基础工程领域的应用日益广泛,如地铁、高铁、公路、隧道等项目全生命周期的管理都有BIM技术的参与。本研究通过BIM软件–Revit建立浅埋隧道的信息模型,基于BIM信息模型,导入ABAQUS有限元分析软件,对越秀公园站浅埋暗挖多孔隧道进行有限元与无限元耦合模拟,验证了无限元在隧道数值模拟中的可行性。其次通过设置不同的工况,验证了无限元与有限元耦合模拟的准确性,并且研究了隧道的开挖对不同工况下,地表沉降和衬砌内力的影响,得出最优的开挖工序,为后续浅埋隧道的力学行为的研究提供借鉴。

柔性版超弹性现象对线条微观变形影响研究

为了探究柔性版和贴版胶带在印刷过程中的超弹性现象对线条变形影响,本研究运用超弹性理论与压缩实验相结合的方法,构建柔性版和贴版胶带的超弹性模型。通过有限元法分析压印滚筒挤压印版滚筒时柔性版上的线条宽度变化。对多种柔性版材和贴版胶带进行压缩实验,发现压力与变形量呈非线性增长,存在明显的超弹性现象。在柔性版线条压缩的有限元分析中,通过对比柔性版和贴版胶带超弹性模型与线性模型对线宽变形量的影响,发现超弹性模型的线宽变形量大于线性模型。在柔性版印刷过程中,在考虑材料超弹性现象的条件下,选用较大弹性模量的柔性版和较小弹性模量的贴版胶带,能有效地减小柔性版上线条的变形。

盾构法联络通道施工对始发端隧道的影响分析

在盾构法联络通道施工中,隧道的结构形式、盾构机顶推力、内支撑支撑力是影响隧道受力及变形的关键因素,为了探究联络通道施工对始发端隧道衬砌结构的影响,本文依托天津地区某盾构法联络通道项目进行了盾构法联络通道施工过程的有限元分析,将施工过程分为初始、预支撑、切削、破洞以及拆撑五个阶段,总结了始发过程中各阶段的结构应力及内力、隧道变形、螺栓内力的变化规律。结果表明:(1)施工完成后结构内力相比之前有所增大但是依旧在安全范围内;(2)结构的应力及变形在拆撑阶段的变化量最大,内支撑起到了施工期间维护结构安全的作用;(3)破洞后洞口周边衬砌环的内力重分布现象较明显,主要表现在衬砌环开洞口一侧的轴力及弯矩有所增加,距离洞口越近的管片其内力变化越大;(4)破洞后环向螺栓的剪力增加到了450 kN,施工中可以增加特殊管片结构的整体性以减小螺栓内力。

有限元线法通用程序——FEMOL92

介绍了用于线弹性结构分析的有限元线法通用程序—FEMOL92。

考虑SSI的滑坡区输电塔线体系安全性分析

为探究边坡变形对输电塔线体系安全性的影响规律,以位于滑坡体上的某输电塔线体系为研究对象,采用有限元数值计算方法,考虑塔线耦合作用、土-结构相互作用(SSI)以及边坡变形程度与方向的影响,建立了输电塔线体系整体有限元模型,探究了塔线体系受力特性对边坡变形的响应规律,提出了可用于评估滑坡区输电线路安全性的2个参数,即铁塔塔腿支座位移以及塔腿根开变化值。结果表明:在典型边坡变形作用下,上部塔线体系的失效以第一横隔面以及导线悬挂点附近主材、交叉斜材等杆件的屈服为标志;边坡变形角度对塔线体系失效特征的影响不大,但对其抗边坡变形能力的影响显著;总体来看,塔线体系承受一定倾角边坡变形的能力远小于承受水平地表变形的能力,其中大部分情况下只能承受水平地表变形工况下塔腿支座变形的70%~80%,拉伸变形工况下只能承受水平地表变形工况下塔腿支座变形的60%左右。研究结果对滑坡区输电铁塔的安全防治有指导意义。

大跨三片式钢箱桁肋拱桥结构参数敏感性分析

为保证大跨三片式钢箱桁肋拱桥施工过程安全及顺利合龙,成拱线形与理想裸拱线形误差尽可能小,以宜宾至昭通高速公路白水江特大桥为工程背景,通过有限元数值法,研究拱肋自重、拱肋刚度、扣锚索索力、扣锚索刚度、扣塔刚度及温度等结构参数的敏感性,探讨上述参数在单一变量法下,对拱肋成拱线形造成的竖向挠度差。结果表明,拱肋自重、扣锚索索力及温度属于主要敏感参数。大跨三片式钢箱桁肋拱桥拱肋拼装中,要严格复核拱肋质量,控制张拉索力误差,同时要避免极端温差对拱圈线形可能造成的影响,保证合龙顺利及合龙后拱肋线形平顺。

软岩大变形引水隧洞二衬施作时机研究

基于三维有限元方法建立能够综合考虑复杂地质条件下深埋特长引水隧洞开挖进度、初期支护时机效应的仿真模型,以揭示不同二衬实施时机对衬砌结构承载性能的影响规律。研究结果表明:理论上是实施二衬越晚越有利于二衬的长期安全稳定运行。但是当围岩和初衬承担超过90%的开挖荷载时,若初衬的钢支撑产生屈服,围岩塑性区明显增大,就会影响结构安全,而围岩和初衬承担约80%开挖荷载时实施二衬,能更充分发挥初衬与二衬的联合承载性能。

隧道衬砌结构可靠度分析的三阶矩方法

隧道衬砌结构的可靠度分析是隧道工程中的关键研究领域。传统的分析方法主要基于蒙特卡罗有限元法,通过将基本随机变量整合为两个综合变量,然后进行一次二阶矩法或二次二阶矩法来计算可靠度。该方法在处理综合变量之间的相关性时可能存在不足,导致分析结果的精确性受到影响。为了解决这一问题,本文提出了一种新的三阶矩方法来进行隧道衬砌结构的可靠度分析。该方法首先利用基于拉丁超立方抽样的蒙特卡罗有限元法来计算隧道衬砌结构极限状态功能函数的前三阶矩(包括均值、方差和偏度),然后使用三阶矩可靠度指标来估计衬砌结构的失效概率。通过算例验证,该方法不仅简化了计算流程,而且提高了结果的精确性,为隧道衬砌结构及其他隐式功能函数的结构可靠度分析提供了新的研究方法。