Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.

Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity

In this work,the size-dependent buckling of functionally graded(FG)Bernoulli-Euler beams under non-uniform temperature is analyzed based on the stressdriven nonlocal elasticity and nonlocal heat conduction.By utilizing the variational principle of virtual work,the governing equations and the associated standard boundary conditions are systematically extracted,and the thermal effect,equivalent to the induced thermal load,is explicitly assessed by using the nonlocal heat conduction law.The stressdriven constitutive integral equation is equivalently transformed into a differential form with two non-standard constitutive boundary conditions.By employing the eigenvalue method,the critical buckling loads of the beams with different boundary conditions are obtained.The numerically predicted results reveal that the growth of the nonlocal parameter leads to a consistently strengthening effect on the dimensionless critical buckling loads for all boundary cases.Additionally,the effects of the influential factors pertinent to the nonlocal heat conduction on the buckling behavior are carefully examined.

固体力学跨尺度计算若干问题研究

本文展示了固体力学领域跨尺度计算的若干问题和研究概况。(1)建立位错动力学与有限元耦合DDD-FEM的计算模型,实现了能够基于纳米尺度离散位错运动机制计算分析连续介质有限变形晶体塑性问题,提出微纳尺度(200 nm~10μm)晶体塑性流动应力解析公式,结合试验数据揭示了在无应变梯度下强度和变形的尺寸效应;(2)建立具有微相分离结构的纳米尺度粗粒化分子动力学模型CG-MD,计算获得聚脲材料在时域和频域下的存储模量和损耗模量,通过动态加载分析的DMA试验和超声波试验的数据验证,解决了连续介质尺度下微相分离高分子共聚物的设计难题;(3)通过数据驱动关联高分辨率的微米尺度CT影像和临床低分辨率的毫米尺度CT影像的特征值,建立了围关节松质骨小梁的等效模量和结构张量,为骨组织增材制造点阵结构设计和实现个性化骨缺损重建奠定了基础。

2021年青海玛多M_(W)7.4地震震后余滑研究

构建应力驱动震后余滑模型,对2021年青海玛多M_(W)7.4地震的震后余滑效应进行数值模拟,得到震后160 d的GPS形变时间序列。结果表明,余滑主要分布在同震断层显著滑动的下倾和两侧区域,最大滑动量达1.24 m,累积释放地震矩1.08×10^(19)Nm,相当于M_(W)6.62地震,5~15 km深度的震后余滑约占总量的80%。最优拟合模型显示,以13 km深度为界,断层上部和下部的参考滑动速率参数V0分别为6.50 m/a和0.15 m/a,表明玛多地震震后余滑界面的摩擦属性在深度上存在明显差异。

基于物理约束的分布式神经网络三维地应力预测模型

地应力是油气藏全生命周期中井壁稳定分析、水力压裂设计、地层出砂预防、套损预测防治和油气开采措施制定的重要基础参数.针对缺乏三维地震资料情况下的三维地应力场预测问题,以工区已钻井地应力测井解释结果为基础,建立了一种基于物理约束的分布式神经网络三维地应力预测模型.首先,采用测井解释方法获得工区已钻井地应力单井剖面,并通过Kriging插值构建三维地质模型;其次,将测井数据和三维地质模型的三维空间坐标喂入3个并行的全连接神经网络,引入地应力物理约束条件,提出了数据和物理双约束的条件,进而通过三维空间坐标实现三维地应力场的预测;再次,优选了数据和物理双约束的权重参数,与人工神经网络、支持向量回归、随机森林等三种机器学习模型以及克里金插值模型进行了对比;最后,评价了不同机器学习模型预测地应力的效果.研究结果表明:(1)研究区域的地应力满足潜在正断层应力状态,即垂向地应力>最大水平地应力>最小水平地应力;(2)数据和物理双约束权重参数取值对预测结果有显著影响,当权重参数λ=0.2时,三维地应力预测效果最优;(3)与人工神经网络、支持向量回归、随机森林、克里金插值等模型相比,本文模型预测得到的地层三维地应力和孔隙压力更准确,在工区内测试集预测得到的垂向地应力、最大水平地应力、最小水平地应力和地层孔隙压力的最大相对误差分别为0.63%、7.59%、7.16%、3.21%,而且,本文模型能够更加准确捕捉地应力梯度的三维变化特征,水平井段地应力和地层孔隙压力参数的正态分布特征明显.结论认为,物理约束的分布式神经网络模型能有效融合地形构造与地应力之间的联系,提高三维地应力预测的准确性和可解释性,为油田三维地应力场的预测提供了一种新的思路.

应力调控下基于Skyrmion的晶体管特性

研究了不同应力、磁各向异性常数对电流驱动Skyrmion的动力学特性影响。随着施加应力增大,能够产生稳定Skyrmion的各向异性常数取值范围的上下限增大,即外加应力影响电流驱动时Skyrmion运行的稳定性。设计了一种宽-窄-宽型Skyrmion基晶体管,通过调控应力和各向异性常数来调控晶体管的开关特性。仿真结果表明,当极化电流密度、各向异性常数变化时,晶体管导通状态对应的应力范围也随之变化。研究结果为设计Skyrmion基晶体管及相关逻辑功能器件提供了新思路。

浅埋深中厚煤层预掘回撤通道支护技术研究与应用

为进一步提高综采工作面末采回撤速度、确保设备回撤空间,采用理论计算、现场试验相结合的方法对浅埋深中厚煤层预掘回撤通道支护技术进行初步研究,建立了工作面残余煤柱承载力学模型,理论分析得知残余煤柱宽度对煤柱承载性能的时空演化规律具有重要影响,末采期间残余窄煤柱出现区域性脆性破坏失稳状态是导致超前采动应力、顶板岩层断裂线前移的主要原因。现场试验末采段残余煤柱宽度约5 m时,整条窄煤柱在多重载荷作用下发生屈服,进而呈现大面积失稳破碎状态,巷内支护体承载受力急剧增加,锚索最大受力约为225 kN,最大顶底板移近量出现在通道中部靠工作面侧,约为100 mm,结果表明,采用高预应力强力锚杆(索)联合支护结构配合垛式支架外部支撑,可有效控制末采期间预掘回撤通道顶底板之间的闭合位移,为类似条件下预掘回撤通道支护提供工程借鉴。

涡北煤矿842工作面顶板水力压裂转移侧向采动应力分布规律

水力压裂技术是实现工作面采动应力转移的重要手段之一。以涡北煤矿842工作面为研究背景,通过数值模拟研究顶板水力压裂技术对842工作面侧向采动应力转移效果和规律的影响。结果表明,水力压裂技术可使距离采空区30 m范围内支承压力有较显著降低,但对距离采空区超过30 m外的区域卸压效果微弱。基于数值模拟结果,开展842工作面风巷水力压裂现场工程实践,结合现场智能钻孔窥视测试结果,发现水力压裂后老顶砂岩中产生了明显的压裂裂隙,为有效阻隔842工作面侧向采动应力向841工作面沿空掘巷传递提供了良好的条件。研究成果对于指导顶板侧向采动应力转移具有一定的理论与工程意义。

基于数据驱动的轨道车辆焊缝疲劳寿命预测

针对实际运行环境下轨道车辆受力情况复杂、寿命难以预测,而传统寿命预测方法耗时耗力的问题,文章提出了一种基于数据驱动的疲劳寿命预测方法。利用有限元仿真软件建立某地铁车辆三人位座椅的有限元模型,通过结构应力法计算得到座椅的一条关键焊缝在不同载荷下的多组疲劳寿命数据,并以此作为训练数据来训练模型,对座椅的关键焊缝进行试验验证。将使用结构应力法计算得到的疲劳寿命结果与文中所提方法预测的结果做对比,通过均方误差、百分比误差和决定系数三项评价指标对预测结果进行量化,最终结果显示,均方误差均在可接受范围内,百分比误差低至2.87%,决定系数均在0.9以上,表明该方法在轨道车辆焊缝疲劳寿命预测领域可行。

川南深层页岩气水平井压裂窜扰主控因素及诱导机制

基于四川盆地南部(即川南)地区深层页岩气的开发实践,以负面冲击为主的井间压裂窜扰严重影响了开发的效率和效益,对深层页岩气的长效开发提出了较大的挑战。为了预防深层页岩气水平井压裂窜扰问题,以四川盆地南部泸州区块为例,通过储层地应力场反演和天然裂缝识别,明确地应力和天然裂缝的组合特征,及其对水力裂缝扩展的影响。在此基础上,根据已窜扰水平井压裂过程中的微地震监测结果进行对比验证,通过体积缝网形态的展布特征揭示水平井压裂窜扰形成的内在机理。最后,基于UFM模型建立多井复杂裂缝扩展模型,重点分析多簇裂缝的竞争扩展规律,为预防页岩气水平井压裂窜扰提供理论依据。研究结果表明:地层凸起区域具有水平地应力值较小、条状天然裂缝较发育的双重特征,易诱导水力裂缝向该区域扩展,是川南深层页岩气水平井压裂窜扰的关键地质因素;由于多簇裂缝竞争扩展,大尺度条状裂缝对水力裂缝具有明显的诱导和捕获作用,使某簇裂缝或某侧裂缝过度扩展,导致水平井间裂缝沟通、形成窜扰。

肺力咳合剂联合氧驱雾化特布他林对支气管哮喘患儿肺功能的影响

目的探讨肺力咳合剂联合氧驱雾化特布他林对支气管哮喘患儿肺功能及氧化应激等指标的影响。方法选取2020年9月至2022年9月浙江省宁海县妇幼保健院收治的150例支气管哮喘患儿,根据治疗方法分为观察组和对照组各75例,对照组患儿给予氧驱雾化特布他林治疗,观察组患儿在对照组的基础上采用肺力咳合剂联合氧驱雾化特布他林治疗,观察对比2组患儿症状改善、白细胞介素水平(IL-6)、肺功能、氧化应激指标水平、治疗满意度及不良反应。结果对照组患儿咳嗽彻底消失时间、哮鸣音消失时间、喘息消失时间分别为(6.98±1.04)d、(7.53±1.21)d、(5.45±1.05)d,观察组患儿分别为(5.27±1.01)d、(4.64±1.15)d、(3.69±1.01)d,差异有统计学意义(P<0.05)。治疗后对照组患儿IL-6表达水平分别为(68±7)g/L,观察组患儿分别为(62±6)g/L,差异有统计学意义(P<0.05)。治疗后对照组患FEV1、PEF、FVC分别为(2.2±0.4)L、(4.1±0.7)L/s、(2.8±0.5)L,观察组患儿分别为(2.6±0.6)L、(5.5±0.8)L/s、(3.6±0.6)L,差异有统计学意义(P<0.05)。对照组治疗满意度89%(67/75),观察组为97%(73/75),差异有统计学意义(P<0.05)。对照组共出现12例(16%)不良反应,其中剧烈咳嗽7例嘴唇发紫3例,治疗终止2例;观察组共出现4例(5%)不良反应,其中剧烈咳嗽2例,嘴唇发紫1例,治疗终止1例,差异有统计学意义(P<0.05)。结论肺力咳合剂联合氧驱雾化特布他林可以快速缓解支气管哮喘患儿的临床症状,改善血清IL-6水平,提升肺功能,调节氧化应激指标、促进患者康复,并提高患儿及家属对治疗的满意度。

高瓦斯多巷系统回采巷道布置方法研究

为了解决高瓦斯煤层两进两回通风方法中外圈巷道维护困难的问题,综合应用理论分析、数值模拟和现场实测等方法研究分析了:①巷道群及煤柱在掘巷、一侧采动、两侧采动后围岩应力演化规律和巷道变形特征;②煤柱宽度对巷道围岩稳定的影响规律。揭示了在两侧采动条件下、煤柱内巷道及煤柱本身变形稳定机理,提出了一种高瓦斯、厚煤层两进两回回采工作面接续的巷道布置新方法,即:第1个工作面外圈巷道作第2个工作面内圈巷道使用,采用宽煤柱护巷;第1个工作面回采稳定后,在区段宽煤柱内沿采空区边缘布置第2个工作面瓦排巷,采用小煤柱护巷;新布置方法缩短了工作面外圈巷道的服务年限,显著改善了巷道围岩应力环境和维护状况,提高了资源回收率和巷道系统可靠性。现场应用效果表明,新的布置方法有效控制了两侧采动支承压力作用下煤柱内巷道围岩变形。

退火工艺对Fe基薄带纵向驱动应力阻抗效应的影响

采用单辊快淬方法制备了Fe73.5Cu1Nb3S i13.5B9(Fe基合金)非晶薄带,利用HP4294A型阻抗分析仪测量了经不同温度退火的Fe基合金薄带在纵向驱动模式下的应力阻抗效应.实验结果表明:经550℃退火的Fe基纳米晶薄带在2.375 MHz电流驱动下的应力阻抗比高达650%,其应力响应灵敏度达120%/MPa.这种纵向驱动模式下的应力阻抗效应,相比其他获得应力阻抗效应的方法,具有灵敏度高、稳定性好的优点.

带式输送机大型换向滚筒接盘应力计算

为研究带式输送机大型换向滚筒的应力计算问题,在略去换向滚筒所受扭矩的前提下,建立换向滚筒的力学模型,基于弹性力学和超静定问题的求解方法,推导出接盘环形辐板承受弯矩和应力的计算公式.分析表明,接盘环形辐板承受的弯矩是直通轴支承轴承间距、直通轴直径、两接盘间距、接盘辐板厚度、轮毂直径和筒体厚度等6个参数的函数,它们对接盘辐板应力的影响各不相同.在载荷一定的条件下,增大两接盘间距和直通轴直径,对于降低接盘辐板应力,效果最为明显.

秦岭地区礼县—山阳断裂对金矿控制的初步探讨

从礼县—白云—山阳断裂的大地构造背景及演化入手,分析了该断裂带走向上及两侧沉积环境、区域应力场的变化及产生原因;探讨了中秦岭金矿成矿物质来源;对中秦岭金成矿带、矿床(点)的分布特征,矿化类型及成矿规律进行了概括、总结。指出礼县—白云—山阳断裂对中秦岭金成矿具重要控制作用;提出了中秦岭金矿成矿模式、找矿标志等。

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

热带海洋对南亚季风和太平洋信风强迫的几种响应模态

应用动力学分析和数值计算的方法讨论了热带海洋对南亚季风和太平洋信风强迫的几种响应模态。结果表明：对于行星尺度的海洋系统，大气风应力可以激发出比较稳定的风生洋流；而对于天气尺度以下的海洋系统，大气风应力则主要激发出几种不同周期的海洋波动。上述结果既同一些经典理论研究有相似之处，也提出了一些新的观点和看法。

盾构隧道近接下穿既有地铁车站的数值模拟

以北京某盾构法施工的区间隧道下穿附近既有地铁车站工程为背景,在确定了合理的应力释放率并充分考虑了分步开挖及注浆加固区影响的基础上,采用三维有限差分计算软件FLAC3D进行了数值模拟.模型采用地层-结构模型,土体采用摩尔-库仑弹塑性模型.此外,隧道和车站结构采用结构单元模拟,既有车站变形缝采用连接单元模拟.预测盾构隧道施工后既有地铁车站的变形,为邻近既有车站的安全评估工作提供了依据.