An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

EXPERIMENTAL EVALUATION ON MODULUS OF EQUIVALENT HOMOGENEOUS ETTRINGITE

In the present study, the average modulus of delayed ettringite is evaluated by an experimental method combined with theoretical analysis. Firstly, the delayed ettringite crystal is synthesized by chemical reaction of Aluminum sulfate and calcium hydroxide. Secondly, specimens are obtained by compressing the delayed ettringite crystal under different pre-loads. Thirdly, the variation of the modulus of the specimen with different pre-loads is tested using Instron material test machine and the SHPB technique, respectively. It is found that the experimental data may be suitably fitted by Boltzmann Function. Finally, the porosity of the specimen is detected using the saturation method, and the effect of the porosity on the modulus is analyzed by the Eshelby＇s equivalent inclusion method and the Mori-Tanaka＇s scheme. The static and dynamic modulli of the equivalent homogeneous ettringite obtained in present study are approximately 10.64 GPa and 24.61 GPa, respectively.

Influence of random shrinkage porosity on equivalent elastic modulus of casting： A statistical and numerical approach

Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random "cloud-like" configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the "cloud-like" morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity's distribution characteristics, such as area fraction, shape, and relative location on the casting's equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations:(1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%;(2) the average Stress Concentration Factor(SCF) produced by shrinkage porosity is about 2.0;(3) the defect's length across the loading direction plays a more important role in the effective modulus than the length along the loading direction;(4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

THE DETERMINATION OF AN EQUIVALENT ELASTIC MODULUS FOR BODIES WITH CRACKS BY BOUNDARY ELEMENT METHOD

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

Equivalence between Modulus of Smoothness and K-Functional on Rotation Group SO(3)

In this paper we obtain the equivalence between modulus of smoothness and K-functional on rotation group SO(3).

(<i>f</i>, <i>p</i>)-Asymptotically Lacunary Equivalent Sequences with Respect to the Ideal <i>I</i>

In this study, we define (f, p)-Asymptotically Lacunary Equivalent Sequences with respect to the ideal I using a non-trivial ideal , a lacunary sequence , a strictly positive sequence , and a modulus function f, and obtain some revelent connections between these notions.

不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能分析

为研究不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能,制备了硅橡胶填充点阵结构试验件。通过试验和仿真方法研究了硅橡胶填充BCC1或BCC2(加载方向分别与带支柱体心立方点阵的支柱杆方向相同或垂直)两种点阵结构的压缩力学性能,并采用铁摩辛柯梁理论和极限载荷法分析了两种点阵结构的等效弹性模量和压缩平台应力。结果表明:提出的理论模型能够很好地预测两种点阵结构的等效弹性模量和压缩平台应力。经过填充后两种点阵结构的压缩强度和吸能性能均会得到增强,BCC2结构的增强效果更加显著。对于BCC1点阵结构,填充提高了其内部杆件的承载力;而对于BCC2点阵结构,填充减小了其“V”形剪切带附近的杆件弯曲变形。随着点阵结构半径的增大,两种结构的吸能耦合因子均先增大后减小,而BCC1型结构的吸能耦合因子变化更明显。

循环剪切作用下土工袋组合体动力特性试验研究

土工袋具有承载力高、阻尼大、造价低等诸多优点,是一种适用于村镇地区中、低层房屋的减/隔震材料。通过开展室内循环剪切试验对土工袋组合体的剪切应力⁃剪切应变关系、动力特性参数以及抗剪强度进行分析讨论,探究不同竖向应力与剪切应变幅值条件下土工袋组合体动剪切模量与等效阻尼比的变化规律,同时研究了循环次数对土工袋组合体动力特性参数以及抗剪强度参数的影响。试验结果表明:在小变形情况下,土工袋组合体的峰值剪切应力和动剪切模量随着循环次数的增加而逐渐增大,等效阻尼比则随着循环次数的增加而逐渐减小;在大变形情况下,土工袋组合体发生层间滑移并出现界面软化现象,此时的峰值剪切应力(抗剪强度)随着循环次数的增加而逐渐减小,动力特性参数随循环次数的变化与小变形情况下完全相反。随着循环次数的增加,土工袋组合体的抗剪强度参数似摩擦角逐渐减小,似黏聚力逐渐增大并趋于稳定。在剪切应变幅值较大的情况下,土工袋组合体通过袋内土体的剪切变形以及土工袋层间滑移产生摩擦耗能,具有较好的减振消能效果。

沥青混合料动态模量预测模型研究

通过室内试验,并结合时温等效原理,预测更大频率(温度)范围的动态模量值.室内试验中,利用动态剪切流变仪(DSR)对90#基质沥青、SBS改性沥青以及EVA改性沥青进行频率扫描试验,得到不同温度和频率下的动态剪切模量值|G\+|.对这三种沥青的不同级配的沥青混合料进行动态模量试验得到|E\+|,并结合Williams-Landel-Ferry(WLF)方程与Sigmoid函数得到其动态模量主曲线.基于试验数据评价Hirsch模型、人工神经网络模型的预测能力,发现Hirsch模型预测能力较低,并对其做出优化,结果表明:修正后的Hirsch模型预测能力进一步提升.相比经验模型,人工神经网络模型的预测精度较高.

索道用钢丝绳轴向弹性模量有限元仿真研究

轴向弹性模量是索道用钢丝绳重要的力学特性,影响着索道设计中对钢丝绳的选用。应用微分几何理论推导每根钢丝的中心线参数方程,通过Creo建立一个捻距长度的钢丝绳三维模型,将三维模型文件导入Hypermesh中划分网格、设置边界条件,最后利用Abaqus计算得到不同轴向拉力下钢丝绳的变形与等效应力云图,得出钢丝绳拉力与等效弹性模量的关系。结果表明,在拉力较小时,钢丝绳等效弹性模量随拉力增大而增大,当拉力到达一定值后,等效弹性模量稳定在钢丝材料弹性模量的0.64倍。

不同弹性模量计算机辅助设计和计算机辅助制造桩核材料的应力分析

背景:桩核修复是牙体缺损修复的一种常规选择,然而不同桩核材料的修复效果存在差异。目的:利用有限元方法评估不同弹性模量桩核修复模型中桩核与牙根黏结剂部位的应力分布情况。方法:在三维建模软件中构建一个三维根管治疗过的上颌中切牙模型,进行全瓷冠修复,修复中的桩核材料分别使用纳米陶瓷树脂(弹性模量12.8 GPa)、复合树脂(弹性模量16 GPa)、混合陶瓷(弹性模量34.7 GPa)、玻璃陶瓷(弹性模量95 GPa)、钛合金(弹性模量112 GPa)和氧化锆(弹性模量209.3 GPa),将模型约束在皮质骨中,在中切牙牙冠舌侧1/3处加载与牙体长轴呈45°的100 N集中力,通过最大主应力分析修复模型中桩核、牙本质及桩与牙根黏结剂的应力分布。结果与结论:(1)当使用弹性模量较高的桩核材料时,修复模型中的桩核应力较集中;当使用弹性模量接近牙本质的桩核材料(纳米陶瓷树脂和复合树脂)时,桩核的应力分布较均匀;无论桩核材料如何,各修复模型中牙本质上的应力分布相似;使用弹性模量更高的桩核时,修复模型中桩与牙根黏结剂处显示出更多的应力集中。(2)纳米陶瓷树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为31.00,33.21,0.51 MPa,复合树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为36.84,33.14,0.59 MPa,混合陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为64.05,32.83,1.00 MPa,玻璃陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为112.30,32.69,1.73 MPa,钛合金模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为120.00,32.17,1.86 MPa,氧化锆模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为148.80,31.85,2.28 MPa。(3)桩核材料的弹性模量越高,进行桩核修复时桩核处的最大应力值越大,桩核材料弹性模量对修复模型中桩与牙根黏结剂处与牙本质的最大应力值无明显影响。

共固化穿孔纤维增强阻尼薄膜结构面内力学性能研究

共固化穿孔纤维增强阻尼薄膜结构(CCPFRDFE)是一种大阻尼、高层间结合性能的新型阻尼处理模式,在空天技术、尖端武器、快速交通等领域具有广阔的应用前景。但复杂的结构为其力学性能的研究增加了难度,未知的力学性能限制了该新结构的开发与应用。介绍了CCPFRDFE的制作工艺,建立了CCPFRDFE有限元模型,并搭建实验平台对有限元模型进行了验证。利用有限元模型,分别研究了纤维增强阻尼层穿孔孔径、孔距和阻尼材料厚度对CCPFRDFE面内等效弹性参数的影响规律。结果表明,增加穿孔孔径、减小孔距、增加阻尼层厚度有利于提高CCPFRDFE面内等效剪切模量,但不利于提高面内等效弹性模量。所得结果将为非连续阻尼薄复合材料的振动特性研究与大挠度设计奠定基础。

Study of Sands from Bamendou-West Cameroon: Valorization for Concrete Mix Design

Bamendou (West Cameroon), has a huge potential in natural resources, especially sands. However, the use of these materials in civil engineering works leads to the appearance of numerous pathologies which in some cases lead to the total ruin of the works. In order to overcome these infrastructural problems, the main objective of this study is set at the improvement of the service life of structures built in Cameroon using local materials formed under climatic, geological and geotechnical conditions similar to those of materials in Bamendou. Eight sand samples were taken from the most representative and exploited quarries. The identification and classification of the sand taken from the most representative quarries in the study area show that they are mainly clayey, with an average sand equivalent of 57.54. In terms of granulometry, the curves of several sand samples do not fall within the granular range of sands used in the formulation of concrete. The modulus of fineness obtained by particle size analysis varies from 2.91 to 3.92 with an average of 3.31.

碳纤维双边柔性法兰压缩刚度计算方法

综合复合材料细观力学的复合原理、修正复合原理提出了碳纤维(carbon fiber reinforced polymer,CFRP)双边柔性法兰刚度计算方法,基于三维弹性理论推导了复杂铺层法兰的等效材性参数,根据法兰根部的变形协调条件,利用梁弯曲近似微分方程推导了法兰压缩刚度计算表达式。为分析与验证压缩刚度理论模型,基于既有铺层法兰,建立了3组法兰管试件的有限元模型,令管身端部承受均匀分布的压力,求解获得法兰根部的轴向压缩位移继而求得压缩刚度。结果表明,在同样法兰材质和相同荷载作用下,法兰越厚,对应的压缩刚度越小,有限元模型获得的压缩刚度在初始阶段略有增加,在30 MPa左右的压应力时达到稳定,理论模型计算的压缩刚度值则不随荷载变化。3组试件有限元模型与理论模型计算结果误差不超过4%,表明CFRP双边柔性法兰压缩刚度计算方法正确可行。

卜形岔管水压试验结构受力分析

针对某水电站工程项目岔管打压过程中出现的Vonmises等效应力值过高的问题,通过SolidWorks软件进行建模,导入ANSYS软件进行网格化有限元模拟打压工况分析,分析了岔管在施加1MPa、2MPa、3MPa压力下的应力应变情况,并与实际打压数据作对比,最终得出了钢岔管在加强肋与圆钢交接处产生应力集中现象。计算结果与实际水压试验发生应力偏高位置吻合且计算数值与实际数值存在偏差较小,数据基本吻合。因此该岔管不满足设计压力值4.68MPa水压试验无法达到设计要求压力值5.85MPa。最终得出结论:需对岔管进行补强设计。

A new method of estimating the equivalent elastic modulus of RCCD

Based on the composite material mechanic theory, the analysis method for the equivalent elastic moduli which are parallel and vertical to the construction interface of RCCD is studied in this paper. The differences between the equivalent elastic moduli which are vertical to the construction interface of RCCD gotten from different methods are discussed in detail. The variation range of the equivalent elastic modulus which is vertical to the construction interface of RCCD is studied based on the principle of minimum complementary energy and the principle of minimum potential energy. The effect of the related influential factors on the equivalent elastic modulus is analyzed. The estimation formula of the equivalent modulus which is vertical to the construction interface of RCCD is proposed. The feasibility of the approach proposed in this paper is analyzed through an example.

配筋齿槽装配式剪力墙的等效弹性模量研究

基于轴向刚度等效和弯曲刚度等效原理,分别推导了轴向受力和受弯状态下钢筋混凝土构件的等效弹性模量计算公式,采用解析法和有限元方法计算、对比分析了钢筋混凝土构件在轴向受压、受弯和偏心受压下的等效弹性模量,并利用ABAQUS有限元分析软件,以一片配筋齿槽装配式剪力墙为验算示例,分析其荷载-位移曲线、应变分布和齿槽沿高度方向应力分布,论证了合理拆分、分块等效的方法在有限元分析过程中的应用合理性.结果表明:不同受力状态下钢筋混凝土构件的等效弹性模量与截面配筋率呈线性增长关系;利用刚度等效原理推导得到的等效弹性模量计算公式具有较好的可靠度;合理拆分、分块等效的方法可以较好地应用于截面配筋复杂的配筋齿槽装配式剪力墙构件在弹性阶段的有限元分析中.

混动汽车的工况自适应等效燃油消耗最小控制

为了减小混合动力汽车的燃油消耗,提出了驾驶工况自适应的等效燃油消耗最小控制策略。介绍了混合动力系统结构和工作模式,建立了混合动力车辆的实时控制模型。基于庞特里亚金极小值原理和等效燃油消耗最小策略求解了车辆在多个优化目标下的最优控制律;提取了车辆行驶工况特征参数,使用学习矢量量化神经网络构造了驾驶工况智能识别器,实现了驾驶工况精准识别。为了使等效燃油消耗最小策略适用于复杂多变的驾驶工况,提出了等效因子随驾驶工况自适应变化策略。使用由4种标准工况组成的综合工况进行仿真验证,并与文献[6]的智能规则控制、文献[11]的模型预测控制策略进行比较,这里提出的自适应等效燃油消耗最小策略的百公里油耗比智能规则控制减少了7.64%,比模型预测控制减少了4.96%,说明了自适应等效燃油消耗最小策略可以有效减少混合动力汽车的燃油消耗。

考虑多因素耦合效应的冻结兰州黄土动力学参数研究

为了探究多因素耦合效应对冻结兰州黄土动力参数的影响,以分布在我国西部季节冻土区的兰州黄土为研究对象,通过动三轴试验研究了不同围压(0.1、0.2、0.3 MPa)、温度(−1、−3、−5℃)、含水率(14%、16%、18%)及加载频率(1、2、4 Hz)影响下冻结兰州黄土的动力参数变化特征。基于试验结果,分析了冻结兰州黄土最大动弹性模量、等效黏滞阻尼系数、参考应变幅值在温度、围压、含水率、加载频率等多因素耦合影响下的变化规律。结果表明,温度、含水率、加载频率和围压等耦合因素对冻结兰州黄土动弹性模量、参考应变幅值和等效黏滞阻尼系数的影响程度有差异。可以发现,冻结兰州黄土动弹性模量和参考应变幅值随温度变化的影响最显著,等效黏滞阻尼系数随加载频率变化表现最敏感。基于试验数据,对影响冻结兰州黄土的4种因素进行归一化和无量纲化处理,采用多元回归分析方法提出了冻结兰州黄土动力学参数的预测公式,有助于快速预测冻结兰州黄土在多因素耦合效应影响下的动力学参数变化特征。