Eight-node conforming straight-side quadrilateral element with high-order completeness (QH8-C1)

A new eight-node conforming quadrilateral element with high-order completeness, denoted as QH8-C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high-order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8-C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.     

基于灰色关联度的微孔端面机械密封开启力共性影响参数分析

目前微孔端面机械密封采用的几何参数繁多,缺乏明确物理意义。为找出跨孔型的共性几何参数,基于Fluent多相流空化模型,针对矩形孔、菱形孔、椭圆孔端面机械密封,建立密封间隙流体的三维数值计算模型,计算得到144条开启力数据;在分析开启力和几何尺寸之间的关系、额外开启力产生机制的基础上,提出等效长度和等效宽度2个具有物理意义的几何参数;采用灰色关联度分析法,分析和验证等效长度、等效宽度、方向角、面积比对开启力的影响,发现4个因素对3种微孔密封的间隙流体开启力都有影响,但等效长度与等效宽度的影响较方向角、面积比大。     

Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration

This paper performs a comprehensive analysis and calibration on the geometric error of the ultra-precision drum roll lathe with dual-spindle symmetrical structure and cross slider layout. Firstly, the volumetric error model which contains all geometric errors of the dual-spindle ultra-precision drum roll lathe (DSUPDRL) is developed based on the combination of the homogenous transfer matrix (HTM) and multi-body system (MBS) theory. Secondly, sensitivity analysis for the volumetric error model is conducted to identify the sensitive geometric error components of the DSUPDRL using an improved Sobol method based on the quasi-Monte Carlo algorithm. The result of sensitivity analysis laid the foundation for the subsequent geometric error calibration. Then, some sensitive error components along the X and Z directions are calibrated using a laser interferometer and a pair of inductance displacement probes. Besides the volumetric error model, the concentricity error caused by dual-spindle symmetrical structure is proposed and calibrated by the on-machine measurement using a classic reversal method. Finally, a large-scale roller mold with a diameter of 250 mm and a length of 600 mm is machined using the DSUPDRL after calibration. The experimental result shows that 1.4 μm/600 mm generatrix accuracy is obtained, which validate the effectiveness of the geometric error analysis and calibration.     

计及时间相关性的微能源网鲁棒规划方法

微能源网以能源的梯级利用为原则,可实现风、光等多种新能源的高比例消纳,满足区域内电、热、冷等多种能源需求。微能源网中存在新能源出力与冷、热、电负荷的多重不确定性。为增强系统规划结果的鲁棒性,常采用不确定集表述新能源出力与多种用能需求的不确定性,实现针对微能源网的鲁棒规划设计,往往使系统规划结果过于保守,降低系统经济性。为克服以上问题,规避实际运行中不可能发生的场景,降低系统规划结果的保守性,文章提出一种考虑时间相关性的微能源网鲁棒规划模型。该模型在计及多重源荷不确定性的基础上,进一步考虑新能源出力与冷、热、电负荷的时间相关性。通过算例对传统不确定集与所提出的改进不确定集进行对比分析,验证了所提模型及方法的优越性和有效性。     

Structural optimization with an automatic mode identification method for tracking the local vibration mode

Traditional optimization methods, which take a specific order of modal frequency as the design constraint, could fail to obtain the desired solution because of modal substitution. An improved optimization model with continuous sizing variables is established to solve this problem, in which the minimum weight and a given local modal frequency are considered as the objective and the constraint. To capture accurately the expected mode of vibration, a local mode identification technique is proposed based on the strain energy ratio between the local area and the whole structure. With that scheme, an optimization system is developed, in which the local mode can be effectively identified and the constraint can be updated with it in the iteration process. Two numerical examples, of a reinforced plate and a satellite structure, are applied to illustrate the effectiveness and efficacy of the proposed method.     

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method (DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil (e.g. cavity expansion), DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response. Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model, and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation (i.e. cavity expansion), a minimum distance of 11a (a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.     

Supply chain network design under the risk of uncertain disruptions

Facility disruptions in the supply chain often lead to catastrophic consequences, although they occur rarely. The low frequency and non-repeatability of disruptive events also make it impossible to estimate the disruption probability accurately. Therefore, we construct an uncertain programming model to design the three-echelon supply chain network with the disruption risk, in which disruptions are considered as uncertain events. Under the constraint of satisfying customer demands, the model optimises the selection of retailers with uncertain disruptions and the assignment of customers and retailers, in order to minimise the expected total cost of network design. In addition, we simplify the proposed model by analysing its properties and further linearise the simplified model. A Lagrangian relaxation algorithm for the linearised model and a genetic algorithm for the simplified model are developed to solve medium-scale problems and large-scale problems, respectively. Finally, we illustrate the effectiveness of proposed models and algorithms through several numerical examples.     

1000MW等级超超临界锅炉张力板结构的强度计算及优化

张力板是锅炉螺旋管圈水冷壁的重要部件,其主要作用是通过槽型钢、张力板、手指板等一系列结构将螺旋管圈荷载传递至垂直管圈。本文利用有限元计算方法,对1000MW等级超超临界n型布置锅炉张力板及手指板结构强度进行计算分析。并根据计算结果,对该结构提出了优化方案。     

特高砂砾石面板坝流变效应及面板防裂措施

针对高面板坝后期变形导致的面板破坏问题,采用大型室内试验测定了大石峡筑坝料流变力学特性,重点研究了后期流变效应对坝体、防渗体应力变形的影响。评估了各期面板浇筑前坝体沉降速率,复核了面板浇筑前预沉降时间的合理性。研究结果表明,该坝各期面板浇筑前设置的预沉降期可将坝顶沉降率控制在5mm/月以内。大坝蓄水运行后面板应力,尤其是轴向应力,较初次蓄水增加明显,存在挤压破坏的风险。论证了在面板受压区设置柔性缝的面板应力改善措施,结果表明该工程措施对削减面板轴向压应力效果明显。总体上,250m级的特高砂砾石面板坝坝体和防渗体应力变形能满足安全控制要求,通过合理的工程措施可保证大坝施工与运行安全。     

An expectation operator for belief functions in the Dempster–Shafer theory*

ABSTRACT

The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.