Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To solve this problem,a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term.The singular domain integral is transformed into a boundary integral using the radial integration method.Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates.The regular domain integral,after expressing the displacements in terms of the radial basis functions,is also transformed to the boundary using the radial integration method.Finally,a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

多模式整合教学法在麻醉科实习护士中的应用价值

目的探讨多模式整合教学法对麻醉科护生综合能力及核心能力的影响。方法选取2022年1—6月于广州中医药大学第一附属医院麻醉科实习的25名护生为对照组,另选取2022年7月—2023年1月于广州中医药大学第一附属医院麻醉科实习的25名护生为观察组。对照组采取常规教学模式,观察组采用多模式整合教学法,对2组护生的理论成绩能力、综合能力及核心能力进行比较。结果观察组护生出科时的理论成绩能力、技能操作成绩、案例分析成绩均高于对照组(P<0.001);观察组护生护理评估能力、解决问题能力、技术操作能力、护患沟通能力、病情观察能力评分均高于对照组(P<0.001);观察组领导能力、临床护理、专业发展、教育咨询、人际关系、批判性思维与科研、法律伦理实践等核心能力评分高于对照组(P<0.001);观察组护生成绩总合格率为100%,较对照组的72.00%高,差异有统计学意义(P<0.05)。结论多模式整合教学法不仅能够提高麻醉科护生的理论成绩,还能增强综合能力及核心能力。

Winkler弹性介质中多孔功能梯度材料截锥壳的弯曲

弹性介质中板壳结构的力学特性研究,大都假设结构体在变形过程中始终与介质紧密接触。为研究可脱离的Winkler弹性介质中含孔隙功能梯度材料截锥壳在环向荷载作用下的弯曲问题,以陶瓷材料质量分数、体积指数和孔隙率为控制参数,根据混合律计算含均匀孔隙功能梯度材料的物性参数。基于Donnell经典薄壳理论和Hamilton原理,建立Winkler弹性介质和环向荷载共同作用下截锥壳的平衡方程和变形协调方程。考虑锥壳两端简支边界条件,采用Galerkin积分法求解得到截锥壳弯曲挠度的解析解。研究在弹性介质与壳体接触和脱离两种情况下,孔隙率、功能梯度材料组成和截锥壳尺寸等因素对壳体挠度值的影响。结果表明,截锥壳挠度值随着孔隙率、体积指数、壳体长径比、径厚比和半锥角的增大而增大,随着陶瓷质量分数的增大而减小。截锥壳与Winkler弹性介质接触时的挠度值比脱离时小,这是因弹性介质对壳体有一定的反作用力。在截锥壳母线方向上,其中部的挠度值较大,而由中部到两端的挠度值逐渐减小;在截锥壳环向方向上,其挠度值呈现周期变化。分析多孔FGM截锥壳在弹性介质和环向荷载作用下的弯曲问题,为FGM截锥壳在工程领域中的应用提供了理论基础。

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric materials subjected to an anti-plane shear loading

The behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric materials subjected to an anti-plane shear loading was investigated. To make the analysis tractable, it was assumed that the material properties varied exponentially with coordinate vertical to the crack. By using the Fourier transform, the problem could be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. The normalized stress and electrical displacement intensity factors were determined for different geometric and property parameters for permeable electric boundary conditions. Numerical examples were provided to show the effect of the geometry of the interacting cracks and the functionally graded material parameter upon the stress intensity factors of cracks.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

采动覆岩离层注浆地表沉陷“四区”控制模型及应用

覆岩离层注浆技术已被证实是一种能够满足矿井无损开采与固废减排的新方法。为了有效控制采动引起的地面构筑物沉降,以关键层理论为基础对离层注浆开采全过程进行稳态分析。首次提出了采动覆岩离层注浆地表沉陷“四区”控制模型,分别为常规区、过渡区、注浆区和控制区,并推导出“四区”范围的计算公式。以3501工作面控制地面焦化厂沉降为工程背景,结合相似模拟与现场实测的沉陷观测数据对提出的“四区”模型进行验证,结果表明:相似模拟离层注浆地表沉陷曲线呈不规则的“V”字形,工作面地表下沉量先快速增大,到达最大下沉点后,地表下沉量先快速减小,随后减小速率逐渐变缓,沉陷曲线表现出明显的“四区”分布,最大下沉量为1589 mm,出现在常规区与过渡区的接触边界,过渡区与注浆区接触边界下沉量为497.94 mm,控制区内基本无下沉;基于概率积分法预测的注浆条件下采动引起的地表下沉量、水平变形、倾斜和曲率与现场实测结果相符,但明显小于未注浆条件下的预测值,确定了注浆条件下地表变形满足构筑物Ⅰ级损坏等级的要求;结合矿井的实际工程地质及实际观测数据,得到常规区范围为261.19 m,过渡区范围为246.09 m,注浆区范围为655.25 m,控制区范围为199.53 m。提出的“四区”控制模型为研究离层注浆开采沉陷问题提供了基础理论依据。

数字经济与实体经济融合发展测度及差异研究

数字经济与实体经济融合(以下简称数实融合)已成为中国经济发展的新动力。为探究当前中国数实融合发展的现状和区域差异,首先在剖析数实融合发展内涵及机理的基础上,从融合条件、融合应用、融合效益三个维度构建评价指标体系,其次利用纵横向拉开档次法对中国30个省区市2013—2020年数实融合发展水平进行测度,最后结合基尼系数与探索性空间数据分析法(exploratory spatial data analysis,ESDA)研究区域间融合发展的时空差异。实证研究结果表明:近几年中国数实融合发展水平持续上升,整体具有向好的发展态势;区域间发展差异明显,发展水平从东向西依次递减,融合发展水平最高的是广东,最低的是青海;在发展过程中,融合应用能力不足是制约发展的关键原因且地域间缺乏融合互动,在空间上表现出明显的正向集聚特征。本研究从战略指引、应用强化和区域合作等方面提出对策建议,可为各部门制定数实融合发展的相关计划提供参考。

ERROR ANALYSIS FOR A FAST NUMERICAL METHOD TO A BOUNDARY INTEGRAL EQUATION OF THE FIRST KIND

For two-dimensional boundary integral equations of the first kind with logarithmic kernels, the use of the conventional boundary element methods gives linear systems with dense matrix. In a recent work [J. Comput. Math., 22 （2004）, pp. 287-298], it is demonstrated that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. The numerical experiments also indicate that the proposed numerical methods require less computational time than the conventional ones while the formal rate of convergence can be preserved. The purpose of this work is to establish a stability and convergence theory for this fast numerical method. The stability analysis depends on a decomposition of the coefficient matrix for the collocation equation. The formal orders of convergence observed in the numerical experiments are proved rigorously.

无网格法与有限元法的耦合及其对功能梯度材料断裂计算的应用

提出了采用无网格Galerkin法与有限元耦合的方法来计算功能梯度材料中的J积分 .这种耦合的方法不仅解决了无网格Galerkin法力学边界条件施加的难点 ,而且还克服了无网格Galerkin法耗时较多的缺点 .此外 ,文中还给出了一个修正的适合功能梯度材料的J积分 ,它在功能梯度材料中是独立于积分路径的 .在计算过程中 ,取积分网格中高斯点的材料常数来模拟材料特性的变化 .

功能梯度压电压磁材料中断裂问题分析

分析了功能梯度压电/压磁材料中裂纹在反平面剪切载荷下的断裂问题．为了便于分析，假设材料性质沿着裂纹的法线方向呈指数变化．利用 Fourier 变换，问题可以转化为对未知数是裂纹表面张开位移的一对对偶积分方程的求解，此对偶积分方程采用 Schmidt 方法求解．最后分析了裂纹长度及表征功能梯度材料的参数βl 对应力，电位移和磁通量强度因子的影响．

基于自然元法和精细积分法的功能梯度材料瞬态热传导问题求解

为促进无网格法分析技术在热传导分析中的应用,提出空间离散采用自然单元法、时间离散采用精细积分法求解功能梯度材料瞬态热传导问题的数值计算方法.在计算过程中,取高斯点的材料参数模拟功能梯度材料特性的变化.温度场采用自然邻接点插值形函数进行离散插值.数值算例验证该数值算法的正确性和有效性.

水电站植被混凝土边坡生态防护工程基材土壤肥力隔年变化分析

针对水电站边坡植被混凝土生态防护工程基材土壤主要肥力因子的逐年变化问题,采集了四处植被混凝土生态防护边坡的基材土壤样品,对植被混凝土相邻年份(2008年和2009年)土壤主要肥力因子进行定量测定分析。同时,采用标准综合级别法对该四处的肥力水平进行了理化性质方面的综合性评价。结果表明:除样地2外,在一个年循环周期内,其他样地的植被混凝土基材土壤肥力因子各指标值均呈增强趋势,且各样地相邻年份肥力水平表现为隔年增加。这为植被混凝土肥力可持续演替以及植被长期稳定的生长提供了一个良好的营养水平。

功能梯度材料结构的热应力边界元分析

导出了一种新的可对功能梯度材料结构进行二维和三维热应力分析的积分方程,利用该方程并结合多区域边界元三步求解技术,可对由任意多种介质组成的变物性参数复合结构进行热应力分析;采用与弹性模量无关的Kelvin解作为问题的基本解,导出的积分方程含有由材料的非均质性以及温度变化引起的域积分;使用径向积分法将所有的域积分转换成等价的边界积分,从而建立起只需要边界离散的无内部网格边界元算法;最后对两种典型的飞行器防热结构进行二维和三维热应力算例分析,并通过与有限元计算结构对比验证结果的正确性.

考虑缺货的模糊库存模型及其优化求解

研究了考虑缺货时多模糊参数的库存模型优化求解问题。采用梯形模糊数对库存问题进行了描述。当订货量为常数时,基于函数原理,采用梯级平均综合表示法进行了解模糊,对允许适度缺货的库存模型进行了建模和优化求解。当订货量为模糊数时,将扩展拉格朗日法与反证法相结合,解决了不等式约束库存求解问题,结果表明运用模糊数学来解决库存问题是合理可行的。

复杂加载下材料动态响应的数据反演技术

对梯度飞片撞击复杂路径加载实验中,具有冲击加载-斜波加载-斜波卸载的金属铝材料的波剖面信息进行了数据分析和处理,不同加载路径用不同力学响应关系式进行描述,以铝材料\氟化锂窗口界面处的速度剖面作为初始条件,用反积分方法向铝材料内部直至加载面进行了反向计算,所得计算结果与正向计算结果比较吻合较好。计算得到了材料内能、温度、声速及应变率在复杂路径加载中变化规律,并给出了材料的P-V参考线,所得结果可与正向积分计算结果相互校核。

基于多边形网格的变系数问题边界单元法

提出一种用多边形网格计算二维变系数问题域积分的新型边界单元法。首先,构造了由任意多边组成的多边形网格形函数,用于几何与物理量的插值;其次,用径向积分法将多边形域积分转换成沿多边形周边的线积分,有效解决了各类非规则多边形网格的单元积分难题;最后,三个有关功能梯度材料与结构的数值算例结果显示本文提出的算法和常规有限元相比误差小于1%,说明本文方法具有很高的精度,且由于其单元积分时无需对积分函数或者积分域进行三角化等额外处理,该方法具有很高的效率。

基于理想解的复杂系统非线性评估模型

为解决非线性评估中可能存在的层次较多、属性混合且关联性强的问题,提出了一种基于理想解的非线性综合评价法。该方法首先利用灰色关联度法作指标筛选,用熵方法分析各指标重要程度并得到各底层指标的权重值,用AHP法得到底层以上的指标权重;然后,利用改进的TOPSIS方法得到各一级指标的评估分值;再由定义的优先等级隶属函数求得各一级指标的评估矩阵;最后,定义合成函数,利用模糊综合评分法,总合各个一级指标得分,得到被评对象的综合等级。案例分析表明:该方法具有良好的适用性及可操作性。