板材成形无网格法模拟中的关键技术处理

针对有限元法费时的网格划分/网格重划问题,提出采用无网格法模拟板材成形.采用约束型再生核子法描述板材成形力学方程,仅用一层节点离散板材,同时对形函数进行改造,所得动可容形函数具有插值性,避免了大变形所导致的不稳定形函数及频繁构造形函数,提出了稀疏矩阵数据结构加快接触搜索方法.基于上述措施建立了板材冲压成形无网格数值模拟...     

金属体积成形过程有限元模拟中六面体网格重划技术的研究

针对金属体积成形过程有限元模拟中的网格重划问题,提出了基于边界构形的有限元网格重划技术,并对其中的一系列技术处理进行了详尽的讨论。将该技术应用于矩形块体镦粗过程的有限元模拟中,较好地解决了六面体网格重划问题。     

三维稳态板轧制过程的再生核质点法模拟

介绍了用再生核质点法求解刚塑性可压缩材料体积成形的基本原理,利用罚函数满足本质边界条件,积分过程采用有限元背景网格,对边界和内部采用不同的高斯积分求解方案,采用砖形影响域的张量积核函数。模拟求解了三维稳定状态板轧制过程,并将模拟结果与文献中的实测值和刚塑性有限元求解结果进行了比较,结果吻合良好,为解决具有网格畸变问题的体积成形过程奠定基础。     

金属体积塑性成形过程数值模拟技术与仿真系统

介绍了金属体积塑性成形过程数值模拟方法、关键应用技术及其仿真系统的构成和国内外相关软件系统,对二维、三维有限元网格自动生成技术进行了较为详细的论述,综述了金属塑性成形过程优化设计方法、有限体积法以及无网格方法的国内外现状.最后给出了目前存在的问题及其将来应努力的方向.     

金属体积塑性成形过程数值模拟技术与仿真系统

介绍了金属体积塑性成形过程数值模拟方法、关键应用技术及其仿真系统的构成和国内外相关软件系统,对二维、三维有限元网格自动生成技术进行了较为详细的论述,综述了金属塑性成形过程优化设计方法、有限体积法以及无网格方法的国内外现状.最后给出了目前存在的问题及其将来应努力的方向.     

面向叶片精锻过程的三维有限元模拟

对刚粘塑性有限元用于模拟分析叶片精锻过程的基本原理进行了论述 ;对模拟中需解决的关键问题提出了相应的算法和处理技术 ;开发了考虑工模具间的摩擦的三维刚粘塑性有限元模拟分析系统 .采用该系统 ,对航空发动机压气机简单叶片和带阻尼台叶片精锻过程进行了三维有限元模拟分析 .模拟过程中对榫头和叶身过渡处采用圆角连接 ,改善了金属的流动性和充填性 ,使叶片锻造三维有限元模拟的建模与分析更接近于实际过程 .结果表明 :采用作者所提出的基于边界构形的网格重划方法 -内缩法 ,进行畸变网格的重划是可行的 ;采用作者所提出的动态边界条件的处理方法以避免模具死锁问题是有效的 ;所开发的软件系统是可靠的 .     

对有限覆盖无网格法中悬挂节点的研究

当前基于Galerkin法的无网格法都只在域内和边界上布置节点。基于无网格方法背景网格独立于节点布置这一性质,该文探讨了无网格域外布置悬挂节点的可行性,提出了一种统一的、均匀的无网格节点布置方案,并设计了相应的背景网格方案,称为有限覆盖无网格法。通过数值算例讨论了悬挂节点对精度的影响,在此基础上讨论了悬挂节点的数目、节点影响域的形状、尺寸以及背景积分方案等对求解精度的影响,并给出了推荐的做法。算例结果表明,悬挂节点能够显著提高求解精度,尤其是边界附近的应力精度。     

空间碎片高速撞击的数值模拟方法评述

计算机数值模拟是实现空间碎片撞击效应地面模拟的重要手段之一。撞击速度增加,撞击的物理机制和效应将发生改变,计算机数值模拟方法也应随之丰富和全面。介绍了基于有网格和无网格方法的高速撞击数值模拟发展历程,并针对数值模拟中常用的有限元法和SPH法进行了分析比较,阐述了高速撞击计算机模拟中无网格法的计算优势,并提出量子力学在未来无网格法数值模拟中的可能应用。为空间碎片高速撞击更加真实可靠的数值模拟提供参考。     

多层抗爆结构冲击响应无网格MPM法分析

在两层钢板中间夹衬泡沫铝等多孔材料构成多层复合结构被应用于抗爆、抗冲击的结构设计中,能够有效地降低冲击载荷对结构的破坏作用。为了研究多层复合结构的抗爆机理和变形破坏过程,使用材料非线性本构模型和无网格物质点法对在高速冲击载荷作用下各层材料的弹塑性大变形进行数值模拟。MPM法利用了欧拉法和拉格朗日法两者的优点,不仅与网格无关,也避免了有限元法中网格畸变,而且在对涉及多物质分界面的问题计算时,因MPM法的耦合条件自动满足,不需要考虑材料界面的变形和破坏,为计算多层抗爆结构的冲击响应建立了一个有效的无网格法数值模拟平台。     

一种基于修正SSPH近似的无网格局部Petrov-Galerkin 法

首先采用奇异权函数对对称光滑粒子流体动力学(SSPH)近似进行了修正,使其构造的形函数近似满足d函数性质,方便无网格法中本质边界条件施加;然后应用修正的SSPH 近似法构造试函数,结合以Heaviside 函数为权函数的局部弱形式,提出了一种新的求解弹性静力问题的无网格局部Petrov-Galerkin 法;最后应用新的无网格法计算了一系列数值算例,结果表明:该方法具有良好的精度和收敛性。     

无网格方法数值结果的可视化方法与实现

科学计算可视化是科学计算中不可缺少的一个组成部分,其主要任务是将数值模拟产生的大量复杂的数据信息通过计算机技术转换成图形、图像信息。无网格方法是一种基于点的数值计算方法,各离散点之间没有联结信息,其数值结果的可视化后处理是一件很困难的事情,尤其当离散点随机分布时,更是如此。Delaunay 三角化是十分理想的散乱数据的可视化工具,它可以根据一组随机分布的离散点数据生成唯一的近似等边三角形。首先介绍了 Voronoi 图与 Delaunay 三角化的基本原理,然后介绍了实现 Delaunay 三角剖分的算法及无网格方法数值结果可视化的实现方法,最后给出了无网格方法可视化的若干应用实例。     

An efficient meshless method for fracture analysis of cracks

This paper presents an efficient meshless method for analyzing linear-elastic cracked structures subject to single- or mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with an exact implementation of essential boundary conditions and a new weight function. The proposed method eliminates the shortcomings of Lagrange multipliers typically used in element-free Galerkin formulations. Numerical examples show that the proposed method yields accurate estimates of stress-intensity factors and near-tip stress field in two-dimensional cracked structures. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing required by finite element method (FEM) is avoided. By sidestepping remeshing requirement, crack-propagation analysis can be dramatically simplified. Example problems on mixed-mode condition are presented to simulate crack propagation. The predicted crack trajectories by the proposed meshless method are in excellent agreement with the FEM or the experimental data. Received 6 March 2000     

Structural shape and topology optimization using a meshless Galerkin level set method

This paper aims to propose a meshless Galerkin level set method for shape and topology optimization of continuum structures. To take advantage of the implicit free boundary representation scheme, the design boundary is represented as the zero level set of a scalar level set function, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and construct the shape functions for meshfree approximations based on a set of unstructured field nodes. The meshless Galerkin method with global weak form is used to implement the discretization of the state equations. This provides a pathway to unify the two different numerical stages in most conventional level set methods: (1) the propagation of discrete level set function on a set of Eulerian grid and (2) the approximation of discrete equations on a set of Lagrangian mesh. The original more difficult shape and topology optimization based on the level set equation is transformed into a relatively easier size optimization, to which many efficient optimization algorithms can be applied. The proposed level set method can describe the moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function in time by solving the size optimization. Several benchmark examples are used to demonstrate the effectiveness of the proposed method. The numerical results show that the proposed method can simplify numerical process and avoid numerical difficulties involved in most conventional level set methods. It is straightforward to apply the proposed method to more advanced shape and topology optimization problems. Copyright © 2011 John Wiley & Sons, Ltd.     

Enriching the finite element method with meshfree particles in structural mechanics

The automatic generation of meshes for the finite element (FE) method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the particles selected in a general domain. This study advances a numerical strategy that blends the FE method with the meshless local Petrov–Galerkin technique in structural mechanics, with the aim at exploiting the most attractive features of each procedure. The idea relies on the use of FEs to compute a background solution that is locally improved by enriching the approximation space with the basis functions associated to a few meshless points, thus taking advantage of the flexibility ensured by the use of particles disconnected from an underlying grid. Adding the meshless particles only where needed avoids the cost of mesh refining, or even of remeshing, without the prohibitive computational cost of a thoroughly meshfree approach. In the present implementation, an efficient integration strategy for the computation of the coefficients taking into account the mutual FE–meshless local Petrov–Galerkin interactions is introduced. Moreover, essential boundary conditions are enforced separately on both FEs and meshless particles, thus allowing for an overall accuracy improvement also when the enriched region is close to the domain boundary. Numerical examples in structural problems show that the proposed approach can significantly improve the solution accuracy at a local level, with no remeshing effort, and at a low computational cost. Copyright © 2016 John Wiley & Sons, Ltd.     

Meshless method for numerical modeling of pulsed eddy currents

Meshless methods have attracted great attention due to their advantage in geometric representation. In this paper, a meshless element-free Galerkin method is applied for the first time to solve pulsed eddy-current problems. Detailed mathematical derivations and the numerical implementation are discussed. The model is validated against analytic solutions for two canonical cases.     

Node‐by‐node meshless approach and its applications to structural analyses

The meshless method is expected to become an effective procedure for realizing a CAD/CAE seamless system for analyses ranging from modelling to computation, because time‐consuming mesh generation processes are not required. In the present study, a new meshless approach, referred to as the Node‐By‐Node Meshless method is proposed, in which only nodal data is utilized to discretize the governing equations, which are derived using either the principle of virtual work or the Galerkin method. In this method, three key methodologies are utilized: (i) nodal integration using stabilization terms, (ii) interpolation by the Moving Least‐Squares Method, and (iii) a node‐by‐node iterative solver. This paper presents the formulation of the proposed method along with numerical results obtained for two‐dimensional elastostatic and eigenvalue problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptiver 3D-Vernetzungsalgorithmus zur FEM-Analyse von Massivumformvorgängen

In the numerical simulation of bulk metal forming process by the finite element method (FEM) extremely degenerated meshes result due to high local deformation. The finite elements distort so much that they lose their regular shape. Remeshing and rezoning techniques are necessary to avoid the resulting numerical problems. For remeshing it is important to create a new mesh with regular elements, and to refine the generated grid in dependency of geometric features. An automatic remeshing-module independent of the FE-code is developed at the Institute of Metal forming and Metal forming Machine tools (IFUM). This program creates a mesh that meets all requirements of the object by combination of adaptive meshing and optimisation of the correct grid distortion. In this paper an algorithm to mesh complex 3D geometries with tetrahedron elements is introduced, by taking into account the specific of metal forming processes and their implication in FE-Analysis.     

On background Cells during the Analysis of Bulk Forming Processes by the Reproducing Kernel Particle Method

The reproducing kernel particle method based on the irreducible flow formulation is utilised to perform the numerical simulation of bulk metal forming processes. Emphasis is given on analysing the influence of employing triangular or quadrilateral background cells on the predictions of material flow, forming load and distribution of strain. A new proposal to smooth the distribution of average stresses during stress computations in the background cells is also included. The effectiveness of the proposed method is discussed by comparing its numerical predictions with a benchmark test case, finite element calculations and experimental data. The benchmark test case is included with the objective of illustrating the influence of several theoretical and numerical subjects such as; order of the basis correction functions, dimension of the compact support and computation of the volume associated to each nodal point. Experimental data was acquired from metal forming controlled laboratory-based tests that were designed so that the proposed method could be tested on its ability to efficiently handle large plastic deformations. It is shown that adaptive arbitrary triangular background cells are capable of efficiently handling large plastic deformations without remeshing.     

Meshless Galerkin least-squares method

Collocation method and Galerkin method have been dominant in the existing meshless methods. Galerkin-based meshless methods are computational intensive, whereas collocation-based meshless methods suffer from instability. A new efficient meshless method, meshless Galerkin lest-squares method (MGLS), is proposed in this paper to combine the advantages of Galerkin method and collocation method. The problem domain is divided into two subdomains, the interior domain and boundary domain. Galerkin method is applied in the boundary domain, whereas the least-squares method is applied in the interior domain.The proposed scheme elliminates the posibilities of spurious solutions as that in the least-square method if an incorrect boundary conditions are used. To investigate the accuracy and efficiency of the proposed method, a cantilevered beam and an infinite plate with a central circular hole are analyzed in detail and numerical results are compared with those obtained by Galerkin-based meshless method (GBMM), collocation-based meshless method (CBMM) and meshless weighted least squares method (MWLS). Numerical studies show that the accuracy of the proposed MGLS is much higher than that of CBMM and is close to, even better than, that of GBMM, while the computational cost is much less than that of GBMM.Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Foundation of China with grant number 10172052.