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。     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

基于微观孔隙结构的特低渗储层分类评价方法——以大庆油田古龙南地区为例

为了搞清研究区不同区块油井产能差异,针对研究区属于低孔￣特低渗储层的特点,将表征储层微观孔隙结构特征的平均孔喉半径作为参数引入储层分类评价中,建立了基于测井曲线的平均孔喉半径解释模型。选取孔隙度、渗透率、平均孔喉半径及有效厚度作为储层评价参数,在单因素储层分类评价的基础上,采用模糊综合评判方法对研究区储层进行综合分类。将研究区各单元储层分为Ⅰ,Ⅱ,Ⅲ类,利用单井产能情况对储层分类结果进行检验。1类井初期日产油量为3.06 t,2类井初期日产油量为1.71 t,3类井初期日产油量仅为0.36 t。初期日产油量是由不同类型单井Ⅰ,Ⅱ类储层所占比例决定的,Ⅰ,Ⅱ类储层所占比例越大,油井初期产油能力越强。该储层分类方法为研究区后期各区块开发调整提供了重要依据。     

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.     

Robust integral of neural network and precision motion control of electrical–optical gyro-stabilized platform with unknown input dead-zones

Parametric uncertainty associated with unmodeled disturbance always exist in physical electrical–optical gyro-stabilized platform systems, and poses great challenges to the controller design. Moreover, the existence of actuator deadzone nonlinearity makes the situation more complicated. By constructing a smooth dead-zone inverse, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback is proposed, in which adaptive law is synthesized to handle parametric uncertainty and RISE robust term to attenuate unmodeled disturbance. In order to reduce the measure noise, a desired compensation method is utilized in controller design, in which the model compensation term depends on the reference signal only. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded (GUUB) tracking stability of servo systems recently. An asymptotic tracking performance in the presence of unknown dead-zone, parametric uncertainties and various disturbances, which is vital for high accuracy tracking, is achieved by the proposed robust adaptive backstepping controller. Extensively comparative experimental results are obtained to verify the effectiveness of the proposed control strategy.