不锈钢焊接温度场的三维无网格对称粒子法模拟

提出了模拟焊接温度场的无网格对称粒子法,编制了相应的计算程序。建立了不锈钢钨极氩弧焊的三维数值模型,应用无网格对称粒子法进行求解,得到了焊件的温度分布和焊接熔池的形状、尺寸,将模拟结果与有限元法的结果和试验结果进行对比,结果表明无网格对称粒子法与有限元法的精度相近,而前者的效率更高。建立并应用渐进变化的非均匀无网格粒子模型对焊接温度场进行了模拟,计算效率得到了进一步提高。在此基础上,研究了高斯热源模型和双椭球形热源模型对模拟结果的影响,数值结果表明基于后者能给出与试验更相符的熔池形状。     

An efficient meshless method based on a new shape function

Although, the finite element method numerically is efficient it exhibits difficulties whenever the remeshing of the analysis domain must be performed. For such problems, utilizing meshless computation methods is very promising. But, their large computational cost, which arises from following a time‐consuming process to find shape functions, is one of the most important factors limiting the use of these methods. In this paper, we introduce a direct approach, based on properties required for any shape function, to prepare the shape function and propose a new meshless method. The proposed method does not need any predetermined basis or weighting functions and can be performed faster and more efficiently. Another advantage of the introduced method is its capability to apply desirable changes to the shape function. Application of the proposed approach for electrostatic field computation and verification of the obtained results using theoretically known solution is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

A Meshless Approach Towards Solution of Macrosegregation Phenomena

The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%Cu alloy in a 2-dimensional rectangular enclosure is tackled in the present paper. Coupled volume-averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial Basis Function Collocation Method (LRBFCM). The involved physical relevant fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The fields are solved through explicit time stepping. The pressure-velocity coupling is calculated through a local pressure correction scheme. The evolution of the solidification process is presented through temperature, velocity, liquid fraction and species concentration histories in four sampling points. The fully solidified state is analyzed through final macrosegregation map in three vertical and three horizontal cross-sections. The results are compared with the classical Finite Volume Method (FVM). A surprisingly good agreement of the numerical solution of both methods is shown and therefore the results can be used as a reference for future verification studies. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in non-uniform node arrangements. The paper probably for the first time shows an application of a meshless method in such a highly non-linear and multi-physics problem.     

A partition of unity‐based ‘FE–Meshfree’ QUAD4 element for geometric non‐linear analysis

The recently published ‘FE–Meshfree’ QUAD4 element is extended to geometrical non‐linear analysis. The shape functions for this element are obtained by combining meshfree and finite element shape functions. The concept of partition of unity (PU) is employed for the purpose. The new shape functions inherit their higher order completeness properties from the meshfree shape functions and the mesh‐distortion tolerant compatibility properties from the finite element (FE) shape functions. Updated Lagrangian formulation is adopted for the non‐linear solution. Several numerical example problems are solved and the performance of the element is compared with that of the well‐known Q4, QM6 and Q8 elements. The results show that, for regular meshes, the performance of the element is comparable to that of QM6 and Q8 elements, and superior to that of Q4 element. For distorted meshes, the present element has better mesh‐distortion tolerance than Q4, QM6 and Q8 elements. Copyright © 2009 John Wiley & Sons, Ltd.     

基于水平集坐标的二维压剪节理动态扩展过程无网格法模拟研究

 发展能有效模拟岩体节理拉压破坏动态扩展过程的无网格模拟方法,构造岩体节理张开和闭合接触摩擦行为的无网格法近似函数,采用水平集坐标描述和捕捉节理在扩展过程中的几何信息。当节理张开时,引入断裂线,并采用衍射准则引入位移跳跃项。当节理闭合时,提出类似于Goodman接触摩擦单元的无网格近似函数构造方法,考虑节理面上、下两侧的相对滑动和法向接触。与Goodman单元或以往的无网格模拟不同,本文的接触方法基于材料点而非结点,并与水平集坐标更新算法结合,在处理节理模型生成和动态扩展后的模型更新上更灵活、简便,且具有通用性。通过测试拉剪、压剪破坏单节理和雁行节理的静态和动态破坏扩展过程的算例,验证了本文方法的正确性和有效性。     

Application of localized meshless methods to 2D shallow water equation problems

This study aims to apply the meshless local radial-basis-function differential quadrature (LRBFDQ) method to solve the shallow water equations (SWE). This localized approach is developed from the differential quadrature (DQ) method by employing the radial-basis functions (RBFs) as the trial functions. Comparing with global-type meshless methods, the present method is more appropriate to large-scale problems with complex shapes. Moreover the drawbacks rising from the poor selection of shape parameter and also the full resultant matrix with high condition number are reduced. For real hydraulic-engineering applications located in irregular domains, the LRBFDQ method is very suitable to solve these kinds of shallow-water problems. In this work, the numerical models are applied to simulate three typical 2D SWE problems: (1) a tidal-wave propagation, (2) a dam-break problem and (3) an inverse engineering problem: the numerical analysis of the inflow discharge of the Yuanshantze Flood Diversion (YFD) project in Taiwan. As a result, the adopted meshless method not only shows its algorithm superiority over other mesh-dependent numerical schemes, but also brings more efficiency than several conventional mesh or meshless methods. The application of YFD project also delivers its applicability of this meshless scheme to solve real-world engineering projects.     

The natural radial element method

In this work an innovative numerical approach is proposed, which combines the simplicity of low‐order finite elements connectivity with the geometric flexibility of meshless methods. The natural neighbour concept is applied to enforce the nodal connectivity. Resorting to the Delaunay triangulation a background integration mesh is constructed, completely dependent on the nodal mesh. The nodal connectivity is imposed through nodal sets with reduce size, reducing significantly the test function construction cost. The interpolations functions, constructed using Euclidian norms, are easily obtained. To prove the good behaviour of the proposed interpolation function several data‐fitting examples and first‐order partial differential equations are solved. The proposed numerical method is also extended to the elastostatic analysis, where classic solid mechanics benchmark examples are solved. Copyright © 2013 John Wiley & Sons, Ltd.     

Direct strain tensor approximation for full‐field strain measurement methods

Full‐field strain measurement techniques are based on computing the spatial derivatives of numerical or functional approximations of the underlying displacement fields extracted from digital imaging methods. These methods implicitly assume that the medium satisfies the strain compatibility conditions, which are only true in the case of a continuum body that remains continuum throughout its deformation history. In the present work, we introduce a method that can be used to calculate the strain components directly from typical digital imaging data, without the need of the continuum hypothesis and the need for displacement field differentiation. Thus, it enables the measurement of strain fields from imaged surfaces that may or may not contain discontinuities. Numerical comparisons are performed on the basis synthetic data produced from an analytical solution for an elastically orthotropic open‐hole domain in tension. For performance comparison purposes, the mean absolute error distributions are calculated for the cases of both the traditional meshless random grid method, and the direct strain method introduced herein. It is established that the more refined representation of strain provided by our present approach is more accurate everywhere in the domain, but most importantly, near its boundaries. Published 2013. This article is a US Government work and is in the public domain in the USA.     

无网格法计算中一种新的积分点搜索算法

 无网格法计算中常采用背景网格积分法进行数值积分,需判断积分点与分析域的关系,当工程问题域边界较复杂时,虽可采用常用的射线法判断积分点与分析域的关系,但当分析域边界线段处于同一直线时,算法的复杂性大大增加,使其效率不高。为此,提出采用矩阵法判断积分点与分析域的关系,在此基础上,为加快搜索速度,提出并建立一种新的数据结构——稀疏矩阵,该矩阵中的元素记录各节点的信息,包括节点与其相邻节点的距离、节点编号和节点影响域尺寸等,通过稀疏矩阵可快速计算矩阵的行列式,从而给出一种积分点搜索速度更快的算法。算例表明,该算法大大加快积分点的搜索速度,提高无网格法的计算效率。     

用无网格法进行大变形柔性机构拓扑优化设

基于连续体结构的拓扑优化理论,将无网格伽辽金数值方法引入分布式大变形柔性机构拓扑优化设计,并解决了优化中的几何非线性问题。在优化问题中,基于各向同性固体材料惩罚模型（solidisotropic material with penalization,SIMP)和折衷规划法,同时考虑结构的柔性和刚度要求,建立了柔性机构拓扑优化的多准则优化模型,并利用优化准则法求解。采用无网格伽辽金法将求解域离散成节点,避免了有限元方法在处理大变形问题时由于使用网格而产生网格畸变等问题。求解经典算例,与基于线性理论的优化结果相比较分析,说明了该方法的正确性和有效性。