The orthogonal meshless finite volume method for solving Euler–Bernoulli beam and thin plate problems

In this paper a new method untitled “orthogonal meshless finite volume method” (OMFVM) is developed for solving elastostatic problems in Euler–Bernoulli beam and thin plate. In this method, the weak formulation of a conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual finite volume approach, the test functions are not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a Heaviside step function. The present approach eliminates the expensive process of directly differentiating the OMLS interpolations in the entire domain. This method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions. Numerical examples demonstrate the advantages of the present methods: (i) lower-order polynomial basis can be used in the OMLS interpolations; (ii) smaller support sizes can be used in the OMFVM approach; and (iii) higher accuracies and computational efficiencies are obtained.     

Orthogonal meshless finite volume method in elastodynamics

In this paper, the orthogonal meshless finite volume method (OMFVM) is developed to solve elastodynamic problems. Convergence and stability of the new method is verified. Good convergence and stability are achieved. This method is applied to some examples; the performance of the OMFVM is illustrated.     

Orthogonal meshless finite volume method in elasticity

An orthogonal meshless finite volume method has been presented to solve some problems in elasticity. An orthogonal weighted basis function is used to construct shape function so there is no problem of singularity in this new form. High computational efficiency and precision are other benefits of the method. Solving some sample problems of thin-walled structures show a good performance of this method.     

An assumed hybrid displacement finite element model for elastodynamic cracked problems

This paper presents an assumed hybrid displacement finite element model to deal with elastodynamic cracked problems. Based on a modified Hamilton's principle with relaxed continuity requirements for displacements at the inter-element boundary, the mass and stiffness matrix of singular elements embedded with proper singularity near the crack-tip are derived. The inter-element compatibility is satisfied through the use of a Lagrangian multiplier technique. The dynamic stress intensity factors which oscillate with time can be solved directly. The utility of the formulation is successfully demonstrated through the numerical solutions of the same problem solved in the literature. The phenomena concerning the contact behaviours of crack surfaces which have never been noted before due to inertia effects are studied. Good correlations between the computed results and referenced data can be drawn.     

有限积分法与有限差分法在弹性波数值模拟中的对比分析

弹性动力学有限积分法被认为对非均匀介质具有较好的适应性,从而应用于混凝土等不均匀介质的弹性波数值模拟。有限差分法作为目前常用的弹性波数值模拟方法,在计算精度和计算效率方面具有独特优势。对比分析2种不同的数值方法在弹性波数值模拟中的异同点,为数值模拟方法的选取提供参考。从理论上对方法原理进行了对比分析,并设计2种非均匀层状介质模型,对比了其数值模拟结果。结果显示:弹性动力学有限积分法离散公式等价于空间二阶精度的有限差分法;在物性参数不同的弹性介质的分界面上,弹性动力学有限积分法与二阶空间精度的有限差分法数值模拟结果相同;在自由界面上,有限差分法使用声学-弹性介质近似自由地表,比弹性动力学有限积分法更加精确。     

Numerical study on crack problems in segments of shield tunnel using finite element method

Crack problems of segments of shield tunnel are analyzed under the conditions of construction stage and service stage. 3D finite element method was adapted to establish elaborate numerical models of segments. For crack problems in construction stage, two models were used to analyze the following contents: (1) crack states of segments under jacking forces; (2) crack states of segments when two segments relatively twist. For crack problems in service stage, first, different external forces acting on segments are abstracted to seven computational models, then crack distribution of these models were analyzed. The analysis results indicate, in construction stage and service stage, cracks mainly appear in circumferential seam, bolt holes and hand holes of segments. Under normal load level, no cracks appear in inner arc and outer arc of segment surfaces. Improving the anti-crack performance of concrete near hand holes and bolt holes, the probability of crack and breakage can be effectively reduced, which can save maintenance expense in service period.     

Large deflection analysis of flexible plates by the meshless finite point method

The classical finite difference technique and methods based on series expansions can only be adopted for solving plates with simple geometry, loading and boundary conditions. In contrast, the finite element method has been widely used for general analysis of bending and flexible plates (coupled bending and in-plane effects). Lack of stress continuity and relatively expensive mesh generation and remeshing schemes have led to the emergence of meshless methods, such as the finite point method (FPM). FPM is a strong form solution which combines the moving least square interpolation technique on a domain of irregularly distributed points with a point collocation scheme to derive system governing equations. In this study, coupled nonlinear partial differential equations of fourth order are solved to analyse large deflection behaviour of plates subjected to lateral and in-plane loadings. Several plate problems are solved and compared with analytical solution and other available numerical results to assess the performance of the proposed approach.     

基于DIC技术和无网格法的裂尖应变场分析方法

针对数字图像相关(DIC)技术难以获得精准的裂纹尖端应变场问题,提出一种基于DIC技术和伽辽金无网格法(EFG)的混合方法来分析裂尖应变场。该方法基于DIC技术导出场节点建立无网格模型,采用EFG法结合衍射法表示裂纹不连续性,进而计算全场应变值。以Q235qE钢材制成的紧凑拉伸(CT)试样为例开展了准静态循环拉伸试验,通过比较裂尖应变解析解和试验结果,证明该方法的有效性和稳定性。进一步研究DIC-EFG法在裂尖塑性区域和应力强度因子(SIF)计算等方面的应用。研究结果表明:DIC-EFG混合方法建模简单,不需要荷载和约束条件,能够获得准确的包括裂尖在内的全平面应变场。相较于传统DIC技术,DIC-EFG混合方法解决疲劳裂纹附近结果缺失的问题,结合J积分法计算SIF结果更为精准,可应用于疲劳裂纹的塑性区域和SIF计算等断裂性能研究。     

无网格法与有限元法处理边界条件的比较

介绍了无网格法和有限元法各自的特点，从加权余量法出发，阐述了无网格法处理本质边界条件的方法及其与有限元法的异同点，并通过算例证明了各种处理方法的可行性。     

Thermo-hydro-mechanical-air coupling finite element method and itsapplication to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.     

Concurrent fatigue crack growth simulation using extended finite element method

In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.     

Concurrent fatigue crack growth simulation using extended finite element method

In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.     

改进无网格法求解断裂力学参数

结合无网格法(element free galerkin,EFG)和单位分解思想的特点,在不连续位移模式中引入跳跃函数和渐进位移场函数对无网格法进行改进,建立不连续近似函数的离散方程,求解裂尖附近的场变量,研究了改进无网格中参数选取对I型裂纹应力强度因子的影响,验证了改进无网格法的可靠性和精确性。     

碾压混凝土拱坝诱导缝的半解析有限元计算

在碾压混凝土诱导缝缝端建立奇异超级解析单元，将该解析元与有限元相结合，在单裂纹平面半解析有限元基础上，建立了多裂纹平面半解析有限元程序，计算了碾压混凝土三点弯曲梁断裂参数和拱坝诱导缝等效强度随高程、缝大小和间距等的变化情况，并同其他文献结论和计算模型进行了对比和验证。     

Schwarz-Christoffel transformation applied to steady-state ground-coupling problems

The Schwarz-Christoffel transformation is used to find closed form solutions of two-dimensional steady-state temperature distributions around uninsulated slab-on-grade and rectangular basement geometries. The distribution of the heat flux is also determined. Superposition is used to investigate the behavior of adjacent slabs at different temperatures, such as a house and attached garage, and the influence of a fixed-temperature water table below a basement is examined. Temperature and flux distributions are shown for several cases.     

水工结构接触问题的多体有限元法

针对水工结构中的局部接触问题,提出了一种新的数值分析方法—多体有限元法。基于DDA方法的分析思路,以结构面切割而成的块体作为分析单元,每一块体均可允许自身有独立的位移和变形,通过块体间的接触和几何关系形成一个完整的块体系统。块体内部采用有限元法求解,块体之间通过接触力相互联系,且在接触界面上引入变形协调条件,保证了多个块体互相接触作用时块体位移和应力状态的连续性,从而使得计算更加符合实际情况。该方法接触求解过程中无需指定法向刚度及切向刚度等参数,避免了DDA方法因引入刚性弹簧而出现的嵌入问题,同时提高了块体内部变形的求解精度。推导了多体有限元法求解接触问题的支配方程,并给出了其增量形式的定解条件和判定条件。最后通过3个数值算例验证了本文方法的正确性和有效性。     

Coupling analysis of finite element and finite volume method for the design and construction of FPSO crane

The aim of this study is to establish a procedure for systematic design and performance evaluation of an offshore platform (FPSO; Floating, Production, Storage and Offloading) crane using a computational approach. Coupling analyses of the finite element and finite volume methods, which are applicable for ensuring robust design under the consideration of nonlinear environmental effects, were carried out. In order to investigate the effects of dynamic loading, the boundary conditions of an offshore platform crane having a lifting capacity of 100 tons were studied. In the finite volume method, a series of analyses were carried out using the computational fluid dynamics code, FLUENT. The crane's weight, maximum lifting load, calculated wind pressure and boundary conditions such as the inclination of the deck due to the extreme roll motion of FPSO were also considered in the finite element analyses using the commercial code, MSC/NASTRAN. Deformation, stress distribution, as well as fatigue life estimation were conducted under the unified computational environment. An advanced procedure for evaluating design concept validation was proposed for the application of FPSO design and construction.     

基于扩展有限元的巴西圆盘动态裂缝扩展分析

应用ABAQUS扩展有限元方法模拟了冲击荷载下含预设裂纹混凝土巴西圆盘的裂纹扩展、贯通情况,分析了其应力场分布规律和不同网格算法对裂纹扩展路径的影响.算例表明：含有初始切槽的巴西圆盘Ⅰ型裂纹从裂尖最先起裂沿着直径方向扩展,网格算法对扩展路径几乎没有影响,离散性较小;ABAQUS平台的XFEM能够正确捕捉裂纹开裂的位置以及扩展的路径,具有广阔的工程应用前景.     

粉体填料在塑料中应用面临的几个问题

塑料是粉体填料应用的大市场,而且具有巨大的市场潜力,但如果粉体填料的加工脱离了塑料工业整体技术水平,脱离了塑料制品(或材料)对粉体填料性能与价格的综合需求,就会给粉体工业的发展带来不良的后果,因此将粉体填料在塑料中应用所面临的几个问题提出来讨论十分必要.     

无单元法位移模式及断裂问题分析

研究了无单元法中一些严重制约其发展的关键问题,诸如本质边界条件处理,太多的求逆矩阵运算等。借着有限覆盖技术,利用shepard插值及Taylor展开理论,构造出了新的形函数,解决了上述问题并分析了有关断裂及岩土工程问题。