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伽辽金型无网格法具有精度高、稳定性好的优点,但是实现高阶准确积分过程复杂,计算效率低.配点型无网格法的计算效率高,但是其在求解复杂问题时往往会出现精度和稳定性较差的结果.本文介绍一种新的无网格法-无网格稳定配点法,采用重构核近似作为近似函数,在规则子域内非常容易实现高阶准确积分,既保留了配点型无网格法效率高的特点,又具备伽辽金型无网格法精度高和稳定性好的特点,而且还兼具有限体积法满足局域离散方程守恒的特点.通过弹性力学算例验证了该算法的优越性,未来可将其进一步应用于流体和流固耦合问题分析. 相似文献
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计算效率低的问题长期阻碍着无网格伽辽金法(element-free Galerkin method, EFGM) 的深入发展. 为了提高EFGM 的计算速度, 本文提出一种求解二维弹性力学问题的光滑无网格伽辽金法. 该方法在问题域内采用滑动最小二乘法(moving least square, MLS)近似、在域边界上采用线性插值建立位移场函数; 基于广义梯度光滑算子得到两层嵌套光滑三角形背景网格上的光滑应变, 根据广义光滑伽辽金弱形式建立系统离散方程. 两层嵌套光滑三角形网格是由三角形背景网格本身以及四个等面积三角形子网格组成. 为了提高方法的精度, 由Richardson外推法确定两层光滑网格上的最优光滑应变. 几个数值算例验证了该方法的精度和计算效率. 数值结果表明, 随着光滑积分网格数目的增加, 光滑无网格伽辽金法的计算精度逐步接近EFGM 的, 但计算效率要远远高于EFGM的. 另外, 光滑无网格伽辽金法的边界条件可以像有限元那样直接施加. 从计算精度和效率综合考虑, 光滑无网格伽辽金法比EFGM具有更好的数值表现, 具有十分广阔的发展空间. 相似文献
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无网格法直接通过节点信息构造形函数,不依赖于节点之间的有序单元连接,能够建立任意高阶连续的整体协调形函数。与传统的有限元法相比,无网格法对大变形问题、移动边界问题和高阶问题的求解方面有比较明显的优势。伽辽金型无网格法是目前应用最为广泛的一类无网格法。虽然无网格形函数本身不依赖于单元,但伽辽金型无网格法需要采取合适的方法进行弱形式的数值积分。由于无网格形函数一般不是多项式,具有非插值性且影响域与背景积分网格通常不重合,伽辽金型无网格法通常需要采用高阶的高斯积分进行数值积分,导致了计算效率低下,难于求解大型实际问题。因此,如何通过建立高效积分方法提高无网格法的计算效率成为无网格法研究领域的一个核心问题。本文对无网格法中强制边界条件的施加方法进行了简要归纳,总结了伽辽金型无网格法中若干常用的数值积分方法,并对伽辽金型无网格法的数值积分方法领域存在的一些问题进行了探讨。 相似文献
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稳态蠕变是高温环境下材料的一个重要的考虑问题,它也是材料破坏的一种重要形式。由于存在划分网格,利用传统有限元法模拟稳态蠕变有一定的不足之处。作为一种新兴的数值模拟方法,无网格法不需要划分单元,只需将求解问题离散成独立的结点,计算过程可以局部细化。利用连续介质的虚功原理,将无网格伽辽金法应用于稳态蠕变的数值模拟,推导了稳态蠕变的无网格伽辽金法控制方程。利用罚参数来实现稳态蠕变的不可压缩条件和本质边界条件,能够保证求解过程中刚度矩阵的对称正定性。通过实例的计算结果表明,无网格伽辽金法在求解稳态蠕变时具有较高的计算精度,结果与理论解结果吻合,而且前后处理较为简单。 相似文献
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为提高含裂纹压电柔性臂在断裂分析中的求解精度,基于压电材料断裂力学理论,建立了压电柔性臂的力学分析模型。将描述裂纹尖端奇异性的位移场函数和电场函数引入到传统无网格伽辽金法中,提出了力电耦合扩展无网格伽辽金法。与传统无网格伽辽金法相比,本方法只需要较小的影响域来描述裂尖奇异场,并且节点影响域不会被裂纹线影响,不要可视准则和衍射准则,提高了计算精度。由虚拟裂纹闭合法推导了压电材料能量释放率,讨论了不同高斯点密度对强计算结果的影响。与解析解、有限元法的计算结果进行了比较,在高斯点个数为6×6时,扩展无网格伽辽金法的计算误差为1.88%,明显好于有限元的计算误差2.5%。数值算例结果表明本方法具有较高的计算精度。 相似文献
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计算效率低的问题长期阻碍着无网格伽辽金法(element-free Galerkin method, EFGM)的深入发展.为了提高EFGM的计算速度,本文提出一种求解二维弹性力学问题的光滑无网格伽辽金法.该方法在问题域内采用滑动最小二乘法(moving least square, MLS)近似、在域边界上采用线性插值建立位移场函数;基于广义梯度光滑算子得到两层嵌套光滑三角形背景网格上的光滑应变,根据广义光滑伽辽金弱形式建立系统离散方程.两层嵌套光滑三角形网格是由三角形背景网格本身以及四个等面积三角形子网格组成.为了提高方法的精度,由Richardson外推法确定两层光滑网格上的最优光滑应变.几个数值算例验证了该方法的精度和计算效率.数值结果表明,随着光滑积分网格数目的增加,光滑无网格伽辽金法的计算精度逐步接近EFGM的,但计算效率要远远高于EFGM的.另外,光滑无网格伽辽金法的边界条件可以像有限元那样直接施加.从计算精度和效率综合考虑,光滑无网格伽辽金法比EFGM具有更好的数值表现,具有十分广阔的发展空间. 相似文献
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利用传统有限元法求解声压分布问题常常受到污染误差和色散误差的困扰。加权最小二乘无网格法(MWLS)是一种基于移动最小二乘(MLS)近似的无网格方法,求解声腔声压分布问题具有低色散、高精度的特点。然而传统的MLS近似有时容易产生病态矩阵,利用加权正交基函数构建改进的移动最小二乘(IMLS)近似,得到的系统方程为非病态的。本文基于改进的加权最小二乘无网格法(IMWLS)求解三维声腔内部声压分布。计算得到的声压分布和声压频响曲线都与参考值十分吻合,峰值误差和污染误差都比FEM的小,计算成本相比无单元伽辽金法显著降低。计算结果表明IMWLS相比传统的FEM,能在更高的频段内达到高精度,并且相比EFGM能大幅提高计算效率。 相似文献
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基于局部搜索算法的自然邻接点方法 总被引:9,自引:0,他引:9
自然邻接点方法(NNM)采用自然邻接点形函数进行插值,其插值形函数具有严格定义,且与
有限元形函数一样形式简洁、性能优良,因而避免了EFG法里难以准确施加位移边界条件和
材料不连续条件等诸多主要困难. 但是从形式上看自然邻接点方法仍然属于有网格的方法,
其研究和应用受到了较大的限制. 为了克服这个缺点,对于任意给定的数值积分点,提出了
一种基于局部搜索自然邻接点的寻找算法对NNM进行改进. 改进后的NNM与无单元伽辽金法
(EFG)的插值和求解过程类似,兼具有EFG的真正无网格特性及NNM的便于处理边界和材料
不连续条件等优点. 所得计算结果表明,改进后的NNM的计算精度和计算时间与NNM相当,
是一种比较理想的数值求解方法. 相似文献
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在无单元伽辽金法(EFG)里,由于其滑动最小二乘近似位移函数不满足Kronecker条件,使得它不能准确地施加本质边界条件和材料不连续条件,从而极大地限制了EFG法的发展和进一步应用。本文在位移边界和不同材料交界面的离散结点上采用实际的结点位移值,提出了一种准确施加位移边界和材料不连续条件的方法,该方法实施简单、稳定、求解精度高,而且其推导得出的整体刚度矩阵具有正定、对称和带状分布的特点,可以和有限单元法一样,直接利用各种成熟、高效的线性方程组解法求解系统平衡方程。数值算例结果表明了文中理论和方法的正确性和可靠性。 相似文献
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In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases. 相似文献
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基于单位分解法的无网格数值流形方法 总被引:19,自引:1,他引:19
在数值流形方法和单位分解法的基础上,提出了无网格数值流形方法. 无网格数值流形
方法在分析时采用了双重覆盖系统,即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解
域的有限覆盖和单位分解函数;而物理覆盖描述问题的几何区域及其域内不连续性. 与原有
的数值流形方法相比,无网格数值流形方法的数学覆盖形状更加灵活,可以用一系列节点的
影响域来建立数学覆盖和单位分解函数,具有无网格方法的特性,从而摆脱了传统的数值流
形方法中网格所带来的困难. 与无网格方法相比,由于采用了有限覆盖技术,试函数的构造
不受域内不连续的影响,克服了原有的无网格方法在处理不连续问题时所遇到的困难.
详细推导了无网格数值流形方法的试函数和求解方程,最后给出了算例,验证了该方法的正
确性. 相似文献
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This paper presents the thermal solution of cylindrical composite systems using meshless element free Galerkin (EFG) method. The EFG method utilizes the moving least square approximants, which are constructed by using a weight function, a basis function and a set of non-constant coefficients to approximate the unknown function of temperature. Dirichlet (essential) boundary conditions have been enforced using Lagrange multiplier and penalty methods. Existing rational weight function has been modified and used in the present analysis. MATLAB codes have been developed to obtain the numerical solution. The EFG results have been obtained using cubicspline, quarticspline, Gaussian, quadratic, hyperbolic, exponential, rational and cosine weight functions for a model problem. The results obtained using different EFG weight functions are also compared with those obtained by finite element method. The effect of scaling and penalty parameters has also been studied in detail. 相似文献
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The meshless manifold method is based on the partition of unity method and the finite cover approximation theory which provides a unified framework for solving problems dealing with both continuum with and without discontinuities. The meshless manifold method employs two cover systems. The mathematical cover system provides the nodes for forming finite covers of the solution domain and the partition of unity functions. And the physical cover system describes geometry of the domain and the discontinuous surfaces in the domain. The shape functions are derived by the partition of unity and the finite covers approximation theory. In meshless manifold method, the mathematical finite cover approximation theory is used to model cracks that lead to interior discontinuities in the displacement. Therefore, the discontinuity is treated mathematically instead of empirically by the existing methods. However, one cover of a node is divided into two irregular sub-covers when the meshless manifold method is used to model the discontinuity. As a result, the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the meshless manifold method, the enriched methods are introduced in this work for crack problems. 相似文献
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Xianghua Guo Daining Fang Ai Kah Soh Hyun Chul KIM Jung Ju Lee 《Acta Mechanica Sinica》2006,22(1):34-39
This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and
electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special
shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation
approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since
the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional
finite element method (FEM) is avoided. The numerical results show that the proposed method can yield an accurate near-tip
stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer
actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround
the abrupt end of an internal electrode.
The project supported by the National Natural Science Foundation of China (10025209, 10132010, and 90208002), and the Research
Grants Council of the Hong Kong Special Administrative Region, China (HKU 7203/03E). The English text was polished by Yunming
Chen. 相似文献
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Node generation plays an important role in meshless methods for seepage analysis with a free surface. A probabilistic algorithm based on a combination of simulated annealing and the generalized probabilistic Lloyd's method, which is related to centroidal Voronoi tessellations (CVTs), is used in seepage analyses with the element-free Galerkin method (EFG). The applications in this paper involve analyzing steady seepage in a rectangular dam, a dam with an inclined slope surface, and a dam with a horizontal drain. The results show that the algorithm can easily fit and update the changeable free surface, and obtains higher-quality node sets, particularly when simulating physical domains with complex geometrical boundaries. 相似文献
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三维弹塑性自然单元法算法实现 总被引:1,自引:0,他引:1
自然单元法是一种新兴的无网格数值计算方法,其实质是基于自然相邻插值(C∞)的伽辽金法。该方法计算精度与四边形或六面体单元有限元法相当,自然相邻插值函数比其他无网格法插值函数的计算速度快。由于自然相邻插值在凸域的边界上的相邻点之间是严格线性的,所以自然单元法在边界面的处理也相当简单。本文研究了在自然单元法中采用Von.Mises,Mohr-Coulomb和Drucker-Prager屈服准则解决三维弹塑性问题,并编制了相应计算程序,最后通过算例验证算法的正确性。 相似文献