On the need for the use of error‐controlled finite element analyses in structural shape optimization processes

This work analyzes the influence of the discretization error associated with the finite element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of an algorithm for the mesh generation by projection of the discretization error, which reduces the computational cost associated with the adaptive FE analysis of each geometrical configuration and (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process. Copyright © 2011 John Wiley & Sons, Ltd.     

比例边界有限元模拟裂纹和夹杂动力相互作用

基于三角形背景网格,任意结构可用 （ ）边多边形比例边界有限元 （Polygon Scaled Boundary Finite Elements, PSBFE）自动离散。相对以往基于比例边界有限元（SBFEM）的应用,该多边形单元不但继承SBFEM半解析求解裂纹尖端奇异性的特性,而且在模拟复杂结构的网格生成和裂纹扩展上具有更高的通用性。本文首次用该单元模拟了动荷载下复合材料裂纹和夹杂相互作用。动荷载稳定裂纹情况下,PSBFE计算结果同现有文献吻合良好,在此基础上,本文结合基于拓扑的局部网格重剖分方法,模拟了动荷载下夹杂和扩展裂纹相互作用。结果表明,硬质夹杂和软质夹杂对结构的动力应力强度因子分别起到抑制和放大的作用。夹杂尺寸,夹杂大小也会在一定范围内影响动力应力强度因子,尺寸越大距离裂纹越近的夹杂影响越大。     

On a consistent field transfer in non linear inelastic analysis and ultimate load computation

In this work we propose a field transfer operator for remeshing carried out in the course of incremental analysis of a non linear inelastic behavior. The proposed procedure is geared towards the ultimate load computation of a complex structure, where we choose the appropriate mesh grading for each different phase of computations, starting with a coarse mesh for the initial linear response and going towards a more refined mesh for highly nonlinear inelastic response. The proposed projection operator is developed on the basis of diffuse approximation method. The key feature of such an operator is to guarantee the conservation of relevant mechanics quantities which ensures a superior performance of the proposed field transfer with respect to the standard remeshing procedure. We present the illustrative results both for an isotropic damage model and standard plasticity model, indicating very satisfying performance.     

Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in a 2D finite element mesh. The Zienkiewicz-Zhu error estimator is employed in conjunction with a modified SPR technique based on the recovery of gradients using analytical crack-tip fields in order to obtain more accurate estimation of errors. The optimization of crack-tip singular finite element size is achieved through the adaptive mesh strategy. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of computational algorithm in calculation of fracture parameters and prediction of crack path pattern.     

Remeshing for metal forming simulations—Part I: Two‐dimensional quadrilateral remeshing

In this paper, a general framework of practical two‐dimensional quadrilateral remeshing, which includes the determination of remeshing time, automatic quadrilateral mesh generation, and data transfer process, will be formulated. In particular, the current work contains new algorithms of mesh density specification according to the distribution of effective strain‐rate gradients, mesh density smoothing by fast Fourier transform (FFT) and low‐pass filtering techniques, coarsening it by node placement scheme, and a modified Laplacian mesh smoothing technique. The efficiency of the developed remeshing scheme was tested through three practical two‐dimensional metal forming simulations. The results clearly indicate that the algorithms proposed in this study make it possible to simulate two‐dimensional metal forming problems efficiently and automatically. Copyright © 2002 John Wiley & Sons, Ltd.     

全局各向异性四边形主导网格重建方法?

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡。为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格。重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度。该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征。同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格。     

电镦成形过程电热力耦合有限元模拟若干关键技术的处理

电镦成形过程中坯料局部连续地被直接通电加热后变形 ,且变形量非常大。在运用有限元法对成形过程进行电热力耦合数值模拟分析时 ,如何处理电阻热、变形体积的连续增加以及大变形造成网格的畸变等问题 ,是能否获得正确分析结果的关键。作者通过分析坯料变形区域电场的分布 ,采用复合变体积和动态网格划分等方法 ,成功地解决了这些关键技术 ,并将其运用于有限元程序设计中 ,从而获得了满意的分析结果。     

金属塑性成形有限元模拟中的六面体单元再划分技术研究进展

系统分析比较了各种六面体单元网格再划分方法的具体技术思路和优缺点 ,及其在模拟三维金属体积成形过程中的应用。结论指出 ,基于在任意几何形状的三维实体上实现全自动生成满足要求的六面体网格的通用算法非常复杂和困难 ,涉及许多具体的特殊问题的处理 ,而且基于畸变后边界节点生成满足拟合精度的几何实体也是如此。本文提出基于畸变网格的质量优化和局部网格加密 /稀释是最佳的解决方法 ,既可以保持初始网格的拓扑结构 ,还可以有效地避开网格再划分问题     

The Adaptive Finite Element Remeshing in Large Deformation of Metal Forming

The adaptive remeshing technique for quadrilateral elements consists of modules the trigger of remeshing, the new mesh generation, adaptive refinement and interpolation of field variables. The new adaptive mesh generation is the key problem. First, a coarse mesh is created by using “loop algorithm“. Subsequent local mesh adaptive refinement is performed based on effective strain. Finally, a typical example of upsetting is given to test efficient of techniques, from which it is verified that the remeshing algorithm developed here exhibits good performance and has high accuracy.     

A 2D finite element analysis of the effect of numerical parameters on the reliability of Ti6Al4V machining modeling

Abstract

The numerical analysis, based on the finite element modeling (FEM), presents nowadays an efficient computational tool. It allows a better understanding of several thermo-mechanical phenomena involved during the machining process. However, its reliability heavily depends on the accurate definition of the numerical model. In this regard, a FE analysis focused on the 2D modeling of the Ti6Al4V dry orthogonal machining was carried out in this study. The relevance of different numerical meshing approaches and finite elements topologies was studied. The effect of the friction coefficient on the numerical chip morphology, its geometry, the cutting and the feed forces was investigated. The adequacy of several compared adaptive meshing approaches, in terms of the modeling of severe contact conditions taking place around the cutting-edge radius, was underlined in the current study. However, numerical serrated chips, closer to the experimental ones, were only predicted when the pure Lagrangian formulation was adopted and a proper determination of the failure energy was carried out. The definition of different mesh topologies highlighted the efficiency of the 4-node quadrangular mesh, with a suitable edge length, in increasing the agreement with the experimental data, while reducing the computing times.