On the incompressible constraint of the 4-node quadrilateral element

The standard plane 4-node element is written as the summation of a constant gradient matrix, usually obtained from underintegration, and a stabilization matrix. The split is based on a Taylor series expansion of element basis functions. In the incompressible limit, the ‘locking’-effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher-order term in the Taylor series. The incompressibility condition is formulated in a weak sense so that the element displacement field is divergence-free when integrated over the element volume. The resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first-order terms of the Taylor series. The corresponding eigenvalue enforces incompressibility implicitly by means of a penalty-constraint. Analytical expressions for that constant-dilatation eigenpair are derived for arbitrary element geometries. It is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner. For several classical and recent elements, the eigensystems are analysed numerically. It is shown that most of the formulations reflect the incompressible constraint identically. In the incompressible limit, the numerical accuracies of the elements are compared.     

高含水期油藏多轮次调剖数值模拟研究

在水驱油田开发中后期,多轮次调剖足一项重要的稳油控水措施。本文提出了高含水期油藏三维三相多轮次调剖数学模型,研制出多轮次调剖模拟器。模拟器中给定考虑了堵剂驱油过程中的物理特性,并使用了局部网络加密技术,为高含水期油藏进行多轮次调剖油藏工程方案研究提供了有力的工具。并结合实际生产情况,对一试验区块进行了多轮次调剖油藏工程方案研究,研究了调剖时机,堵剂用量对调剂效果的影响。     

离散全球格网模型几何均匀性研究

在深入分析离散格网模型系统几何形变的研究现状与不足的基础上,提出了通过研究格网中单个结点与拓扑邻近结点间空间格局,对格网结点空间的均匀性进行评价的新的研究思路.提出了几种新的评价指标,包括邻近点间距离的最大值与最小值比值、邻近点间张角的最大值与最小值比值以及所有结点相互之间边长的标准差.采用上述指标,对6种代表不同类型的全球离散格网模型进行了研究,分析了各种格网模型结点均匀性的变化规律.     

On using different finite elements with an automatic adaptive refinement procedure for the solution of 2-D stress analysis problems

A series of numerical tests is carried out employing some commonly used finite elements for the solution of 2-D elastostatic stress analysis problems with an automatic adaptive refinement procedure. Different kinds of elements including Lagrangian quadrilateral and triangular elements, serendipity quadrilaterals, incompatible elements and hybrid elements have been tested. It is found that for a general problem involving compressible material and when a moderate accuracy of the final solution is sought, the nine-node Lagrangian (L9) element will be the most effective element, while when an extremely accurate solution is needed, higher order Lagrangian quadrilaterals or triangles will be a suitable choice. However, if only linear elements are available, the well known 5βI linear hybrid element is the best choice. © 1997 John Wiley & Sons, Ltd.     

On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations

In this note we describe the maximal and the minimal values of Lyapunov exponents for second-order discrete time-invariant linear system perturbed by time-varying bounded perturbations. An interpretation of the results in terms of generalized spectral radius is given. An application of obtained formulas to the robust stability problem is demonstrated on a numerical example.     

On the bottleneck of adopting 3D printing in manufacturing

A timely book, titled ‘Standards, Quality Control, and Measurement Sciences in 3D Printing and Additive Manufacturing’ has been published to discuss the bottleneck issues when adopting 3D printing in manufacturing. This book review provides some personal thoughts and discussions on the new book.     

On the Use of the Transient Hot-Strip Method for Measuring the Thermal Conductivity of High-Conducting Thin Bars

The thermal conductivity of thin, high-conducting ceramic bars—commonly used in mechanical tensile testing—is measured using a variant of the short transient hot-strip technique. As with similar contact transient methods, the influence from the thermal contact resistance between the sensor and the sample is accurately recorded and filtered out from the analysis—a specific advantage that enables sensitive measurements of the bulk properties of the sample material. The present concept requires sensors that are square in shape with one side having the same width as the bar to be studied. As long as this requirement is fulfilled, the particular size of the thin bar can be selected at will. This paper presents an application where the present technique is applied to study structural changes or degradation in reinforced carbon–carbon (RCC) bars exposed to thermal cycling. Simultaneously, tensile testing and monitoring of mass loss are conducted. The results indicate that the present approach may be utilized as a non-destructive quality control instrument to monitor local structural changes in RCC panels.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Application of a sensitivity equation method to the <Emphasis Type="Italic">k</Emphasis>–<Emphasis Type="Italic">ε</Emphasis> model of turbulence

In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k–ε model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.