一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

Fracture toughness of high strength seamless pipe steel from SE(T) and SE(B) specimens evaluated by different standards

Recently released, BS 8571:2014 standard offers an alternative for the experimental determination of fracture toughness and resistance curves of metallic materials from SE(T) specimens. Similar in stress conditions and constraint to cracked tubes, specimens in SE(T) geometry should yield less conservative toughness values than conventional high‐constraint specimens, such as SE(B) geometry. However, the convention to determine the J‐integral fracture toughness proposed in the new BS standard is different from ASTM standards. In this work, SE(T) and SE(B) specimens of similar dimensions of a tough high‐strength seamless pipe steel were tested following the BS 8571:2014 and ASTM E1820‐16 standards, respectively. Because of the different standardized definitions, SE(T) specimens yield lower fracture toughness than SE(B) specimens, which could lead to more conservative results in structural integrity analysis. This investigation also suggests the introduction of the blunting line concept in the BS 8571:2014 standard in order to minimize this problem.     

On the numerical solution of Fredholm integral equations utilizing the local radial basis function method

The current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method.     

定向长钻孔整体水力压裂增透技术在赵固二矿的应用

针对赵固二矿煤层透气性低、钻孔有效影响半径小，实施定向长钻孔代替底板岩巷进行区域瓦斯治理期间钻孔工程量大、瓦斯抽采效果不理想的问题。结合煤层赋存特征及钻孔施工情况，采用定向长钻孔整体水力压裂增透技术，理论分析了合理坐封位置、压裂参数，完成200 m煤巷条带一次整体压裂，最大泵注压力24.3 MPa、累计注水量1 613 m³。并基于煤层全水分变化，考察确定了单个钻孔压裂影响范围达到巷道两帮30 m，有效改善了煤体储层特性，提高了煤层瓦斯抽采效率。在实现定向钻孔对预抽煤巷条带可靠控制的同时，最大程度降低了钻孔工程量、缩短了瓦斯治理周期，为实现矿区“以孔代巷”及高效安全开采提供了技术支撑。     

整体壁板离散填料滚弯成形有限元模拟

具有一定曲率外形的铝合金整体壁板属于典型的多筋零部件,传统弯曲成形工艺成形困难,容易产生多种缺陷。提出了离散填料辅助滚弯成形整体2A12T4铝合金壁板滚弯工艺,并通过实验与整体填料滚变成形进行了对比,同时采用有限元模拟技术,探究了离散填料辅助整体壁板滚弯成形中的影响因素。研究结果表明:填料数量、上下垫板厚度等因素对成形性能影响较大,填料在3~6块时成形稳定,可以有效地避免筋条屈曲与失稳;随垫板厚度增加,壁板表面圆弧更加光滑、连续,但是回弹性增强;上下垫板分别在10~20 mm厚度时,综合性能较好。通过离散填料辅助滚弯技术可以成形出质量较高的整体壁板。     

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

This paper presents a direct traction boundary integral equation method (DTBIEM) for two-dimensional crack problems of materials. The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces. The displacements and tractions were used as unknowns on the external boundary, while the relative crack opening displacement (RCOD) was chosen as unknowns on either side of crack surfaces to keep the single-domain merit. Only one side of the crack surfaces was concerned and needed to be discretized, thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method (DBEM). A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly, and the SIFs were evaluated by the extrapolation of the RCOD. Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.     

Stress intensity factor evaluations for a curved crack in orthotropic particulate composites using an interaction integral method

This paper develops a domain-independent interaction integral (DII-integral) for extracting mixed-mode stress intensity factors (SIFs) for orthotropic materials with complex interfaces. The DII-integral does not require material property gradients, and moreover its validity is not affected by material interfaces. Combined with the extended finite element method (XFEM), the DII-integral is employed to investigate a straight crack in an orthotropic functionally graded plate and a curved crack in orthotropic particulate composites.     

Research on Chromium Retrieval of Black Soil with Hyperspectral Imagery in Northeast of China#br#

According to the definition of spectral integral，a new spectral characteristic parameter，with the name Reversed Spectral Absorption Integral(RSAI)，is proposed and used to retrieve the chromium content based on the Partial Least Squares Regression(PLSR) model.The contrastive study with other traditional spectral characteristic parameters，including differential transformation，inverse transformation，absorption area，etc.indicates that(1) the first derivation of square root transformed model can predict the chromium content quantitatively in terms of spectral transformations.(2) the stability of the absorption area model is slightly poor，and the chromium content of samples can only be estimated roughly.(3) However，as to the inversed spectral absorption integral model，the adjustment determination coefficient(Ad-R²) of the modeling and verification is 0.73 and 0.77，while the Root Mean Squared Error(RMSE) is 2.63 mg/kg and 2.36 mg/kg respectively with Relative Percent Deviation(RPD) being 3.21，which shows that the RSAI model has excellent prediction ability.So，the inversed spectral absorption integral new model can improve the accuracy and stability used to retrieve the chromium content，which provides a new idea for monitoring the chromium contamination in soil.     

注塑机料筒温度调控和计算机仿真研究

利用模糊控制和比例积分微分(PID)控制相结合的手段对注塑机料筒温度进行了控制,同时以Matlab 6.0软件为仿真平台,对料筒温度控制进行了模拟仿真研究。实验发现,在注塑机料筒升温过程中利用CHR整定的PID控制手段和模糊控制手段,恒温过程中利用人工整定的PID控制手段,可保证快速的料筒升温响应速率和稳定的保温过程。通过实际注塑实验对该仿真结果进行了验证,在十组实验中,料筒温度误差不超过2%,产品翘曲变形量不超过0.059 mm。     

Measurements of thermal-neutron capture cross-section of Cesium-135 by applying mass spectrometry

ABSTRACT

The thermal-neutron capture cross-section (σ₀) and resonance integral (I₀) were measured for the ¹³⁵Cs(n,γ)¹³⁶Cs reaction by an activation method and mass spectrometry. Because of difficulty in the preparation of pure ¹³⁵Cs samples, we used ¹³⁵Cs contained as an impurity in a normally available ¹³⁷Cs standard solution. An isotope ratio of ¹³⁵Cs and ¹³⁷Cs in a standard ¹³⁷Cs solution was measured by mass spectrometry to quantify ¹³⁵Cs. Cesium-135 impurity along with the ¹³⁷Cs standard solution was irradiated at the hydraulic conveyer of the research reactor in the Institute for Integral Radiation and Nuclear Science, Kyoto University. Wires of Co/Al and Au/Al alloys were used as neutron monitors to measure thermal-neutron fluxes and epi-thermal Westcott’s indices at an irradiation position. A gadolinium filter was used to measure the σ₀, and a value of 0.133 eV was taken as the cut-off energy. Gamma-ray spectroscopy was used to measure induced activities of ¹³⁷Cs, ¹³⁶Cs and monitor wires. On the basis of Westcott’s convention, the σ₀ and I₀ values were derived as 8.57 ± 0.25 barn, and 45.3 ± 3.2 barn, respectively. The value of σ₀ obtained in the present study agreed within the limits of uncertainties with the past-reported value of 8.3 ± 0.3 barn.