三维有限元网格图的高效消隐技术

本文利用三维有限元网格图形的性质和计算数据结构的特点,提出了一种高效的空间立体网格图的消隐方法。该方法以最短的时间确定内部、外部单元面和快速生成不重复单元棱线,从而大大地提高了消隐效率。     

基于刚（粘）塑性流动理论的自然单元法研究

将自然单元法与刚（粘）塑性流动理论相结合,对自然单元法在金属塑性成形过程数值模拟中的应用进行了研究。采用基于Voronoi图和Delaunay三角化结构的Non-Sibsonian插值方法构造近似速度场向量,实现无网格方法中速度边界条件的直接精确施加,提出了基于刚（粘）塑性流动理论的无网格自然单元法。运用不完全广义变分...     

用Voronoi图进行新型自然邻居插值的几何学方法与特性

新的基于Voronoi图的Natural Neighbour插值是自然单元法的数学基础，也是一种新型的几何插值方法，具有与其他传统常用插值不同的构造方法，并表现出一定的优越性。本文介绍了基于Natural Noighbour关系的Sibson插值和non-Sibsonian插值，并与有限元法和无单元法所用的插值方法，就离散插值方案和网格总体特性、形函数支撑域、本征边界条件、空间维数扩展与计算工作量等诸问题进行了比较分析。     

一种基于单元几何变形的网格修匀方法

基于单元几何变形操作提出一种高效的非结构网格质量修匀方法。其基本过程是先对每个单元独立地进行拉伸-收缩操作以优化单元的形状,然后在整个网格中通过对各单元的节点位置进行加权平均来获得改善后的网格。为进一步提高修匀方法对网格质量的优化效果,并使得该方法具备一定的网格调整能力,结合动网格技术提出了对单元进行大范围和较大幅度移动的策略;在修匀过程中还通过适当算法调整单元形心位置和单元尺寸,进一步增强了修匀方法对网格局部进行疏密调节的能力。本文方法可适用于平面和三维非结构网格的质量改善及网格调整。若干算例表明了方法的有效性。     

Kirchhoff-Love壳的等几何分析

论文利用等几何分析研究了基于Kirchhoff-Love理论的薄壳的静态问题.等几何分析采用等参思想,将精确描述几何形状的NURBS基函数同时作为场变量的插值函数,保证了在分析和网格优化过程中模型的几何精确性,并可以轻易地构造任意高阶连续的单元.该方法具有很高的数值精度.计算结果表明,在等几何分析中,NURBS单元的阶次越高,网格数越多,计算结果越精确.     

封面故事

<正>图片为Trefftz基本解有限元法分析轴对称热传导问题的应用实例。带孔圆环内壁恒温外壁绝热,其几何参数如图Ⅰ所示。分析中采用8节点8源点Trefftz基本解环单元(图Ⅱa)进行网格划分,ABAQUS温度云图如图Ⅱb所示。同时,图Ⅲ给出了Trefftz有限元与ABAQUS的等温线对比,     

OPS算法优化效果影响因素分析

OPS算法中目标函数以及如何获取目标函数最优解是决定算法优劣的重要因素。对比分析了4种目标函数和10种求最优解方法在网格数、初始点位置、迭代次数以及需求精度等因素变化时对OPS算法优化效果的影响。结果表明,在顶点移动过程中目标函数f1和f4变化较为光滑。采用不同目标函数时,随着网格数的增加优化时间随之增加,但优化后最差单元质量并无此规律;随着需求精度的增加,网格中最差单元质量和优化时间都有所增加,迭代次数变化对于优化时间和优化效果的影响可以忽略不计。采用变尺度法求解目标函数下降方向以及二次插值法进行一维搜索的第6种方法,在耗费时间、优化效果以及收敛速度等方面都显示出了较好的优势。     

岩石、混凝土类材料断裂破坏有限元数值模拟中的有效方法

岩石、混凝土类材料断裂破坏有限元数值模拟中的网格重划,依据单元畸变和裂缝介质间的单元干涉作为网格重划判据,采用几何体重构技术把几何实体分解成能在ANSYS上实现六面体网格划分的几个部分,利用体积判断法确定新结点在旧单元的单元编号,在场量传递上采用基于解析性质的等参有限元逆变换,把旧网格场量信息传递到新网格中。本文对ANSYS进行二次开发,实现了三维网格重划,网格重划采用单元畸变和界面干涉两个判据,在网格再划分前进行几何体重构,提取变形后的点线面信息重新生成实体,充分利用AN-SYS的函数和体积判断法找到新结点在旧网格中的位置,在新旧网格间的场量传递中采用基于解析逆等参单元法。在平台上实现了三维有限元网格重划技术,最后利用方料的单轴压缩断裂模拟计算检验了传递前后等效塑性应变分布用载荷信息的变化,证明了所开发系统的正确性。     

自然单元法在Winkler地基薄板计算中的应用

自然单元法是一种基于Voronoi图及Delaunay三角形剖分图,以自然邻接点插值为试函数的一种无网格数值方法.本文以目前该方法中自然邻接点的Laplace插值形函数为基础,求出了其一阶及二阶导函数,建立了Winkler地基上薄板弯曲挠度的自然单元法求解控制方程,并编制了相应的计算程序,通过算例分析表明了本文方法的可行性和有效性.     

Delaunay多边形单元的有理函数插值格式

本文提出了基于Delaunay多边形化的多边形单元有理函数插值格式。给出了Delaunay多边形化的概念和Delaunay多边形单元有理函数插值形函数的计算表达式。与Delaunay三角化网格不同，Delaunay多边形化网格形成对区域的唯一剖分。Delaunay多边形单元有理函数插值是以Delaunay多边形的顶点作为插值点，构造的有理函数形式插值。Delaunay多边形单元有理函数插值克服了有限元方法中难以构造边数大于4单元多项式形式位移插值的困难。有理函数插值形函数在多边形单元的内部是无穷次光滑的，在多边形的边界上是线性的。在三角形单元和矩形单元上，有理函数插值分别等价于有限元的三角形面积坐标插值和四边形双线性插值。给出了Delaunay多边形有理函数插值在圆域温度分布插值近似中的两个算例。     

Application of the 2-D constant strain assumption to FEM elements consisting of an arbitrary number of nodes

The formulation for the constant strain element is revisited to develop multi-noded elements that can be used as transition elements in a finite element mesh. Although the constant strain approach is computationally attractive, spurious force-free displacement modes arise for elements consisting of more than three nodes. These unstable mode shapes are typified by “hourglassing” which develops in quadrilateral elements when constant strain is assumed within the element. The means for stabilizing spurious mode shapes for quadrilateral elements is well documented in the literature, however, in this paper, a general formulation for stabilizing forces is presented for elements having an arbitrary number of nodes and therefore is not restricted to quadrilateral elements. This paper examines the use of meshes consisting of constant strain elements created from polygons having differing numbers of element nodes. The effectiveness of the stabilization procedure is illustrated along with “patch test” examples to assess the consistency of the approximation. The elements are shown to be surprisingly robust, yielding reasonable results even when poorly designed mesh transitions are used.     

Shape optimization of a body located in incompressible flow using adjoint method and partial control algorithm

The purpose of this study is to obtain an optimal shape of a body located in an incompressible viscous flow. The optimal shape of the body is defined so as to minimize the fluid forces acting on it by determining the surface coordinates based on the finite element method and the optimal control theory. The performance function, which is used to judge the optimality of a shape, is defined as the square sum of the drag and lift forces. The minimization problem is solved using an adjoint equation method. The gradient in the adjoint equation is affected by the finite element configuration. The use of a finite element mesh whose shape is appropriate for the procedure is important in shape optimization. If the finite element mesh used is not suitable for computations, the exact gradient is not calculated. Therefore, a structured mesh is used for the adjacent area of the body and all finite element meshes are refined using the Delaunay triangulation at each iteration computation. The weighted gradient method is applied as the minimization technique. Using an algorithm in which all nodal coordinates on the surface of the body are employed and starting from a circle as an initial shape, a front‐edged and rear‐round shape is obtained because of the vortices at the back of the body. To overcome this difficulty, we introduced the partial control algorithm, in which some of the nodal coordinates on the surface of the body are updated. From four cases of computational studies, we reveal that the optimal shape has both sharp front and sharp rear edges. All computations are conducted at Reynolds number Re=250. The minimum value of the performance function is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Anisotropic adaptive stabilized finite element solver for RANS models

Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge‐based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A variational multiscale‐stabilized finite element method is used to solve the incompressible Navier‐Stokes equations. Finally, the Spalart‐Allmaras turbulence model is solved using the streamline upwind Petrov‐Galerkin method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases.     

Effect of mesh phase on wave vibration of spur planetary ring gear

The distinctive wave vibration of a ring gear affected by mesh effect is investigated based on the inherent symmetry of spur planetary gears. Compared to prior analysis, this work mainly examines the forced flexural and extensional vibrations. The superposition principle and the Fourier series are introduced to jointly deal with the wave vibrations. The dynamics of the ring gear shows that the effect of the mesh phase on the wave vibration is mainly embodied by the specific relationships between the tooth number, the planet number, the largest common factor of them, the planets’ circumferential position, and the excited wave numbers in the typical rotational, translational and planet modes. For the equal systems, the three modes can be possibly excited depending on the specific mesh phase. And the dominant vibration orders of them are 0, 1 and 2, respectively. The non-zero lowest order is equal to the largest common factor of the two numbers. But for the diametrical ones, only the first two modes can be excited, and the dominant orders of them are 0 and 1, respectively. And the lowest non-zero wave number is 2 for even tooth number and 1 for odd tooth number. As a typical application, these relationships can be used to predict and suppress some potential wave resonances of the ring gear by optimizing the ring-planet mesh phase. The main results are demonstrated with finite element examples and comparisons with the existing literature.     

用逐点插入法生成Delaunay四面体自适应网格

介绍一种基于Delaunay算法的四面体自适应网格的自动划分方法。该方法用单元尺度场控制生成网格的疏密分布,在不满足尺度场要求的单元面形心处插入新节点,同时计算新节点单元尺寸参数,实现三维实体的Delaunay四面体自动划分。此方法具有几个特点:一是表面网格与体内网格同步划分,无需区分两者;二是结点与单元同时生成;三是生成网格自适应性好,疏密分布任意。另外,还介绍了三维网格划分中两个相关算法:一个是约束面恢复算法,该算法基于约束面不允许有单元边与之相交的性质而提出的;另一个是将二维射线法推广至三维空间,判断一个点是否在一多面体内,实现了凹多面体的划分。最后通过算例对单元质量进行了评价。本文所述方法是一种有效的四面体自适应单元生成算法。     

Adaptive shape functions and internal mesh adaptation for modeling progressive failure in adhesively bonded joints

Macroscopic finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.     

Hypersonic viscous flow over large roughness elements

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar?Cturbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier?CStokes code based on the space?Ctime conservation element, solution element (CESE) method is used to perform time-accurate Navier?CStokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.     

Converged solutions of the Newtonian extrudate‐swell problem

Both the axisymmetric and the planar Newtonian extrudate‐swell problems are solved using the standard and the singular finite element methods. In the latter method, special elements that incorporate the radial form of the stress singularity are used around the exit of the die. The convergence of each of the two methods with mesh refinement is studied for various values of the Reynolds and the capillary numbers. The numerical results show that the singular finite elements perform well if coarse or moderately refined meshes are used, and appear to be superior to the standard finite elements only when the Reynolds number is low and the surface tension is not large. The standard finite elements perform better as the surface tension or the Reynolds number are increased. This implies that the effect of the stress singularity on the accuracy of the numerical solution in the neighborhood of the die exit becomes less significant when the Reynolds number is high or the surface tension is large. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive h-refinement on 3D unstructured grids for transient problems

An adaptive finite element scheme for transient problems is presented. The classic h-enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre-sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock-shock and shock-object interaction runs in a production mode. A typical example of this class of problems is given.