基于任意四边形镶嵌的四方连续图案智能化设计技术研究

目的 实现无交叠四方连续图案的快速设计,使图案元素排布均匀、画面紧凑,避免简单复制产生的僵硬感和机械感。方法 利用任意四边形可无缝镶嵌的特性,将待填充图案元素布置在一个四边形内,并绘制四边形包围轮廓。将镶嵌单元从直边四边形拓展到曲边四边形,给出了曲边四边形的可镶嵌性条件及镶嵌处理方案,实现了任意可镶嵌曲边四边形的人机协作快速构建方法,以及由不同图形单元组成的可镶嵌异质复合单元的构建方法。结论 基于平面设计师常用的矢量软件开发了设计工具。案例测试表明,开发的设计工具可准确识别用户绘制的四边形框架,并生成灵活的四方连续图案,非凸四边形和曲边四边形框架的应用增加了生成图案的多样性。开发的设计工具通过智能辨识设计师的手绘曲线进行运行,省去了复杂的界面操作,且交互性更加可靠。     

网格划分对爆破损伤有限元分析的影响

利用ANSYS/LS-DYNA软件对装药在混凝土靶中的爆炸过程进行数值模拟,研究不同网格划分方式对计算结果的影响。通过算例比较了四边形映射网格、四边形自由网格和四边形自由网格局部加密三种网格下靶损伤区、损伤度以及水平径向(X向)不同距离的冲击压力峰值模拟结果,并与相关理论公式比较。结果表明:四边形映射网格和自由网格局部加密方式在研究靶体的损伤区和损伤度得到的结果较为接近。比较靶体上同一测点竖直向(Y向)的应力时程表明映射网格更有助于减少网格划分带来的计算误差,有利于获得更精确的结果。     

混合应用三类四边形面积坐标构造八结点四边形膜元

三类四边形面积坐标已先后提出。如果对三类面积坐标加以混合应用,这将使构造四边形单元的工作更加灵活多样,具有更加广阔的优选空间。该文混合应用三类四边形面积坐标构造一个8结点四边形膜元。新单元具有如下优点:1)新单元具有优异性能,特别是对网格畸变不敏感,优于8结点等参元,显示出三类四边形面积坐标的共同优点;2)新单元的推导过程和主要列式都非常简洁。这是由于巧妙地混合应用三类面积坐标并进行优选而取得的结果。     

网格划分对叉排管束摩擦阻力系数的影响

应用流体计算软件FLUENT,对受限空间内烟气冲刷叉排管束(横竖均为5排,间距比均为1.25)的流动进行了数值模拟研究,主要研究了三角形和四边形非结构化网格及四边形结构化网格划分对流场流动摩擦阻力系数f的影响。结果表明:结构化网格相对于非结构化网格,虽然建模时间较长,但网格生成速度快,计算耗时短,易收敛且精度高;对于同类型网格,网格边界层底层厚度及圆周节点数的选取均对模拟结果存在较大影响。     

任意平面区域的变密度四边形网格生成方法

：基于三角形网格的合并方法,首先生成光滑过渡的变密度三角形网格,然后进行三角形的合并,接着将合并后残留的三角形细分成三个较小的四边形,相应把合并生成的四边形进一步细分成四个较小的四边形,最终生成了光滑过渡的四边形网格。     

NURBS曲面的四边形网格的分割与逼近

介绍了一个用于对NURBS曲面进行四边形网格的分割与逼近的算法。该算法采用二叉树递归分割的方法分割和逼近曲面，所分割的四边形除了在高度方向和曲面边界处满足给定精度外，同时在四边形四条边界满足给定的切矢精度。实例测试结果表明，用本文所述算法生成的四边形网格具有网格逼近原曲面、网格四边形接近于规则四边形等特点。     

任意四边形平面问题的样条有限元法

用三次B样条有限元通过坐标变换和变分法求解任意四边形区域上的平面问题,利用分区势能原理推广到由四边形组成的任意平面区域,推导出了具体的计算公式,为平面问题求解提供了一种高效的计算方法。与普通有限单元相比,该方法计算量小,而且计算结果具有对网格畸变不敏感,精度高等显著特点。     

四边形单元面积坐标的微分和积分公式

构造四边形单元时，应用面积坐标方法有其优点。文献［１］系统地论述了四边形单元面积坐标理论，本文是文献［１］的续篇，补充论述采用四边形单元面积坐标时的微分和积分公式。采用三角形单元面积坐标时的微分和积分公式是其特殊情况。应用面积坐标方法时，易于得出四边形单元刚度矩阵的积分显式，无需依赖于数值积分，这个优点是采用四边形等参坐标时所不具备的。     

三角网格模型上的四边形曲线网生成新方法

四边形网格划分是组合曲面建模技术的首要条件。针对海量流形三角网格数据,提出了基于网格简化技术与调和映射算法的四边形网格生成新方法--映射法。该方法采用基于顶点删除的网格简化技术对三角网格模型进行简化,进而借助调和映射算法将简化网格映射到二维平面上进行四边形划分,并将所获得的平面四边形节点数据逆映射回物理域,采用短程线边界形式最终得到适于组合曲面建模的空间四边形拓扑。该方法简单、实用,运行速度较快,实际的算例也验证了方法的有效性与可行性。     

RTM加工工艺充模过程的计算机模拟

RTM加工工艺是一种先进复合材料加工的方法。但这种加工工艺技术含量高,设计不当非常容易出次品,尤其注射口和溢料口的设计。因此相当多的科技工作者对RTM加工工艺进行了计算机模拟研究,并已得到很大的发展,其计算方法和实验手段已获得广泛认可。由于有限元控制体积法不需要对变界面进行网格的重新划分而获得广泛采用。但是在众多的文献中,绝大多数使用的是三角形有限元网格,对于更加有效的四边形有限元网格没有提及或仅仅一笔带过。本文作者比较详细地阐述三角形和四边形有限元控制体积法的使用和实施,通过例子分析了三角形单元、四边形单元及其混合使用的情况下的计算结果。分析表明,四边形单元计算精度高、速度快,与三角形混合使用情况良好。     

On the decomposition of generalized eigenproblems for the free vibration analysis of cyclically symmetric finite element models

Free vibration analysis is a major part of any dynamic analysis. Natural frequencies and related mode shapes may be obtained from free vibration analysis as the solutions of generalized eigenproblems. Although the eigensolutions of large‐scale structures require large computational efforts, these solutions may be achieved simply for symmetric structures. We present an efficient method for the decomposition of generalized eigenproblems related to finite element models with cyclic symmetry (having nodes at the axis of symmetry) into eigensubproblems with significantly smaller dimensions. This decomposition is obtained by block diagonalization of a matrix with a special pattern known as a block circulant, using the concept of the Kronecker product and similarity transformations. The proposed method is applied to three finite element models discretized by triangular and four‐node quadrilateral plate and shell elements, and its efficiency, accuracy and simplicity are evaluated. Copyright © 2009 John Wiley & Sons, Ltd.     

Quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method (QACM‐II)

A novel strategy for developing low‐order membrane elements with analytical element stiffness matrices is proposed. First, some complete low‐order basic analytical solutions for plane stress problems are given in terms of the new quadrilateral area coordinates method (QACM‐II). Then, these solutions are taken as the trial functions for developing new membrane elements. Thus, the interpolation formulae for displacement fields naturally possess second‐order completeness in physical space (Cartesian coordinates). Finally, by introducing nodal conforming conditions, new 4‐node and 5‐node membrane elements with analytical element stiffness matrices are successfully constructed. The resulting models, denoted as QAC‐ATF4 and QAC‐ATF5, have high computational efficiency since the element stiffness matrices are formulated explicitly and no internal parameter is added. These two elements exhibit excellent performance in various bending problems with mesh distortion. It is demonstrated that the proposed strategy possesses advantages of both the analytical and the discrete method, and the QACM‐II is a powerful tool for constructing high‐performance quadrilateral finite element models. Copyright © 2008 John Wiley & Sons, Ltd.     

An efficient hybrid / mixed element for geometrically nonlinear analysis of plate and shell structures

In this paper, a geometrically nonlinear hybrid/mixed curved quadrilateral shell element (HMSHEL4N) with four nodes is developed based on the modified Hellinger/Reissner variational principles. The performance of element is investigated and tested using some benchmark problems. A number of numerical examples of plate and shell nonlinear deflection problems are included. The results are compared with theoretical solutions and other numerical results. It is shown that HMSHEL4N does not possess spurious zero energy modes and any locking phenomenon, and is convergent and insensitive to the distorted mesh. A good agreement of the results with theoretical solutions, and better performance compared with displacement finite element method, are observed. It is seen that an efficient shell element based on stress and displacement field assumptions in solution and time is obtained.     

Two refined non‐conforming quadrilateral flat shell elements

Two refined quadrilateral flat shell elements named RSQ20 and RSQ24 are constructed in this paper based on the refined non‐conforming element method, and the elements can satisfy the displacement compatibility requirement at the interelement of the non‐planar elements by introducing the common displacements suggested by Chen and Cheung. A refined quadrilateral plate element RPQ4 and a plane quadrilateral isoparametric element are combined to obtain the refined quadrilateral flat shell element RSQ20, and a refined quadrilateral flat shell element RSQ24 is constructed on the basis of a RPQ4 element and a quadrilateral isoparametric element with drilling degrees of freedom. The numerical examples show that the present method can improve the accuracy of shell analysis and that the two new refined quadrilateral flat shell elements are efficient and accurate in the linear analysis of some shell structures. Copyright © 2000 John Wiley & Sons, Ltd.     

Boundary element solution of the transonic integro-differential equation

The transonic integro-differential equation for two-dimensional flows is solved by boundary element methods. In addition to constant and quadrilateral elements we develop hybrid elements based on constant elements in the streamwise direction and variable elements in the transverse direction. Computation is carried out for parabolic-arc and NACA0012 airfoils and the results, which converge fast, compare favourably with finite-difference solutions. The hybrid elements are to be preferred because they yield results which are more accurate than constant elements without the computational complexity associated with quadrilateral elements. Moreover, they can be applied with a small number of nodes by using only one strip of rectangular elements.     

Modified crack closure integral using six-noded isoparametric quadrilateral singular elements

Six-noded, isoparametric serendipity type quadrilateral regular/singular elements are used for the estimation of stress intensity factors (SIF) in linear elastic fracture mechanics (LEFM) problems involving cracks in two-dimensional structural components. The square root singularity is achieved in the six-noded elements by moving the in-side nodes to the quarter point position. The modified crack closure integral (MCCI) method is adopted which could generate accurate estimates of SIF for a relatively coarse mesh. The equations for strain energy release rate and SIF are derived for mixed mode situations using six-noded quadrilateral elements at the crack tip. The model is validated by numerical studies for a centre crack in a finite plate under uniaxial tension, a single edge notched specimen under uniaxial tension, an inclined crack in a finite rectangular plate and cracks emanating from a pin-loaded lug (or lug attachment). The results compare very well with reference solutions available in the literature.     

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions.     

Hybrid displacement function element method: a simple hybrid‐Trefftz stress element method for analysis of Mindlin–Reissner plate

In order to develop robust finite element models for analysis of thin and moderately thick plates, a simple hybrid displacement function element method is presented. First, the variational functional of complementary energy for Mindlin–Reissner plates is modified to be expressed by a displacement function F, which can be used to derive displacement components satisfying all governing equations. Second, the assumed element resultant force fields, which can satisfy all related governing equations, are derived from the fundamental analytical solutions of F. Third, the displacements and shear strains along each element boundary are determined by the locking‐free formulae based on the Timoshenko's beam theory. Finally, by applying the principle of minimum complementary energy, the element stiffness matrix related to the conventional nodal displacement DOFs is obtained. Because the trial functions of the domain stress approximations a priori satisfy governing equations, this method is consistent with the hybrid‐Trefftz stress element method. As an example, a 4‐node, 12‐DOF quadrilateral plate bending element, HDF‐P4‐11 β, is formulated. Numerical benchmark examples have proved that the new model possesses excellent precision. It is also a shape‐free element that performs very well even when a severely distorted mesh containing concave quadrilateral and degenerated triangular elements is employed. Copyright © 2014 John Wiley & Sons, Ltd.