Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Evolution of 3D tectonic stress field and fault movement in North China

Based on data of fault movement surveying, we simulate the evolution process of three dimensional stress field in North China by three dimensional finite element method. Evolutional patterns in one-year time scale from 1986 to 1997 have been illustrated and the evolution characteristics of stress field have been analyzed. In comparison with the seismic activity among that time interval in North China, we have primarily discussed the relationship between the evolution of stress field and seismic activity.

Evaluating performance of lignite pillars with 2D approximation techniques and 3D numerical analyses

This paper attempts to investigate the use of approximate 2D numerical simulation techniques for the evaluation of lignite pillar geomechanical response, formed via the room and pillar mining method.Performance and applicability of the developing methodology are assessed through benchmarking with a more direct and accurate 3D numerical model. This analysis utilizes an underground lignite mine which is being developed in soft rock environment. Through the decisions made for the optimum room and pillar layout, the design process highlights the strong points and the weaknesses of 2D finite element analysis, and provides useful recommendations for future reference. The interpretations of results demonstrate that 2D approximation techniques come near quite well to the actual 3D problem.However, external load approximation technique seems to fit even better with the respective outcomes from the 3D analyses.

Numerical simulation of the crustal stress field by using data of deep geophysical exploration in the northern part of North China

DSS data of the last twenty years and more in the northern part of North China are further interpreted, and combined with other geological and geophysical data, the crustal model for the 3 D finite element method is built after straticulate crustal structure and elastic mechanics parameters are obtained. Referring to regional tectonic stress field and taking the effect of gravity into account, the paper constrains properly the model boundary and then computes the displacement of each nodal point and the strain and stress of each element by using the program from the 3 D linear elastic finite method. The relationship between the distribution feature of the crustal stress field and seismicity is discussed on the basis of analyzing contour maps of maximum principal compressive stress in the upper, middle and lower crusts.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

A numerical method for simulating planar 3D multi-fracture propagation in multi-stage fracturing of horizontal wells

To resolve the issue of design for multi-stage and multi-cluster fracturing in multi-zone reservoirs, a new efficient algorithm for the planar 3 D multi-fracture propagation model was proposed. The model considers fluid flow in the wellbore-perforation-fracture system and fluid leak-off into the rock matrix, and uses a 3 D boundary integral equation to describe the solid deformation. The solid-fluid coupling equation is solved by an explicit integration algorithm, and the fracture front is determined by the uniform tip asymptotic solutions and shortest path algorithm. The accuracy of the algorithm is verified by the analytical solution of radial fracture, results of the implicit level set algorithm, and results of organic glass fracturing experiment. Compared with the implicit level set algorithm(ILSA), the new algorithm is much higher in computation speed. The numerical case study is conducted based on a horizontal well in shale gas formation of Zhejiang oilfield. The impact of stress heterogeneity among multiple clusters and perforation number distribution on multi-fracture growth and fluid distribution among multiple fractures are analyzed by numerical simulation. The results show that reducing perforation number in each cluster can counteract the effect of stress contrast among perforation clusters. Adjusting perforation number in each cluster can promote uniform flux among clusters, and the perforation number difference should better be 1-2 among clusters. Increasing perforation number in the cluster with high in situ stress is conducive to uniform fluid partitioning. However, uniform fluid partitioning is not equivalent to uniform fracture geometry. The fracture geometry is controlled by the stress interference and horizontal principal stress profile jointly.

Special hybrid stress element for stress analyses around circular cutouts in laminated composites

A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.

MC CAD/CAM全瓷冠三维有限元应力分析

目的运用三维有限元法分析CAD/CAM全瓷冠受载的应力分布规律,为指导CAD/CAM全瓷冠的临床应用提供理论依据。方法建立下颌第一磨牙MC陶瓷全瓷冠三维有限元模型,全瓷冠设计为单层结构和底层-饰瓷复层结构两种形式,垂直面加载600N,分析不同模型的应力分布。结果全瓷冠在受载时的应力分布形式基本相同,最大应力都在修复体加载点周围,位于面加载点下方,从加载点向周围逐步递减,牙本质内应力较低,分布较均匀,全冠内应力相对较高;两种形式的全瓷冠应力分布无明显差别。结论单层和底层-饰瓷复层两种形式对MC全瓷冠应力分布无明显影响,全瓷冠的面接触点和边缘的强度对其长期应用的完整性影响较大。

30Cr1Mo1V转子钢应力强度因子有限元分析

通过采用20节点solid186退化奇异单元,利用ANSYS软件,对三维断裂参量进行计算和分析,结果表明位移法和J积分法确定应力强度因子是可行的;对一定尺寸的紧凑拉伸试样三维裂纹进行分析,得出30Cr1Mo1V转子钢裂纹尖端KI随裂纹长度和载荷水平改变时的变化规律,为研究汽轮机转子裂纹扩展规律提供了合理、有效的方法.

PPS/CaCO_3复合材料界面应力分布的三维有限元模拟

以碳酸钙粒子（CaCO3）填充聚苯硫醚（PPS）粒子为研究对象，用ANSYS/LS-DYNA软件对复合材料冲击过程中界面应力分布进行了有限元分析。结果表明：在粒子的赤道处，正应力、剪切应力和等效应力均为最大，朝极点方向迅速减小，在距赤道约0.5-2.0μm之间达致最低点，然后趋于平缓或略微回升，并介绍了PPS/CaCO3复合材料在冲击载荷下失效或断裂的主要机理。

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional （3D） hybridfinite-discrete element method （FDEM） to investigate the development of an excavation damaged zone（EDZ） around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibratedagainst standard laboratory experiments, including Brazilian disc test and uniaxial compression test. Theeffect of increasing confining pressure on the mechanical response and fracture propagation of the rockwas quantified under triaxial compression tests. Polyaxial （or true triaxial） simulations highlighted theeffect of the intermediate principal stress （s2） on fracture directions in the model： as the intermediateprincipal stress increased, fractures tended to align in the direction parallel to the plane defined by themajor and intermediate principal stresses. The peak strength was also shown to vary with changing s2. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

300m级超高斜心墙和直心墙堆石坝应力变形分析

为了优化设计和安全评价,对某300 m级超高直心墙堆石坝和作为比较方案的斜心墙堆石坝进行了三维有限元应力变形计算。对坝体堆石料采用邓肯张E-B非线性弹性模型,对高塑性黏土与混凝土结构接触面采用Goodman单元模型,分43级荷载对坝体的施工和蓄水过程进行模拟,比较分析两种坝型在蓄水期坝体和心墙的应力和变形性状。结果表明,相对直心墙方案,斜心墙方案计算所得坝体的最大水平位移相对较小,垂直沉降较大。斜心墙方案下心墙两岸坝肩处高应力水平区域有所减小,可以适当改善心墙上游面单元的应力和变形条件。斜心墙方案下心墙的拱效应相对较弱,其抗水力劈裂的性能稍好。

DBQ系列塔机臂架销轴联接有限元分析

建立了DBQ系列塔机臂架系统中销轴联接的三维实体有限元模型,分析了臂架不同部位销轴联接的应力分布情况,为该类型塔机联接销轴的疲劳设计、可靠性分析提供了数据。

旋转叶轮三维应力分布及其改善措施

利用三维有限元素法对一个实际叶轮进行计算和分析比较 ,并提出了保证叶轮运行安全可靠的改进措施 .研究的目的在于通过提高叶轮机械的转速来扩大其运用范围 ,以满足工程改造或减少设备投资的要求 .转速增加引起的应力过大的情况可通过叶轮结构的变化来改善 .

川滇地区强震序列库仑破裂应力加卸载效应的数值模拟

通过建立较精细的川滇地区三维有限元模型,数值模拟了川滇地区主要活动断裂的强震活动对于其他活动断裂潜在强震孕育进程的库仑破裂应力加卸载效应.模拟结果显示在川滇地区主要活动断裂带的几何学展布形态和运动学性质的构造背景之上,川滇地区强震活动相互影响的主要特征是活动断裂面库仑破裂应力变化大多处于增大状态.其中,金沙江断裂带、小江断裂带、楚雄—建水断裂带、鲜水河断裂带和安宁河断裂带上的强震所产生的加载作用比较强,而丽江—小金河断裂带和腾冲—澜沧断裂带则较弱.1981～2000年川滇地区M≥6.5地震序列的模拟结果显示,后续地震全部位于已发生地震所引起的库仑破裂应力增大区之内.数值模拟结果显示,在川滇地区,一个强震发生之后,发震断层本身强烈卸载的同时,库仑破裂应力的加载效应在其他主要活动断裂带潜在强震孕育进程中占据了主导地位,强震活动之间相互作用的主要效应是应力加载,已发生的强震加速了下一个强震的孕育进程,进而导致一系列地震的发生,直至整个区域所积累的应变能处于较低水平之后,区域地震活动进入一个新的平静期.

北祁连-河西走廊地区垂直形变与构造应力场关系的初步研究——三维有限元拟合结果分析

根据已知的地震地质资料对北祁连 -河西走廊及相邻区进行了三维有限单元剖分 ,在线弹性条件下 ,拟合了其 2 0a来垂直运动的总体趋势。计算表明 ,北祁连 -河西走廊地区垂直形变的拟合结果 ,与背景应力场的约束形式和变化特征密切相关 ,其中采用构造应力场增强作为加载条件以及稳定地块作为位移约束条件得出的拟合结果与该区域 2 0a来垂直运动的整体分布特点相一致。在此基础上 ,进一步得到其背景应力场增强的量值估算 ,其中SN方向的压力变化为 +0 .11MPa(压为正 ) ,EW方向的压力变化为 +0 .0 4MPa(压为正 ) ,EW方向的压力变化量是SN方向的 3倍左右。此外 ,根据计算得到的 10～ 15km深处剪应力增量Δγxy的分布情况 ,对比中强地震震源分布可以看出 ,剪应力增量与震源在空间分布上有一定的关联性。震源往往分布在剪应力增量变化较剧烈处 。

在温度和机械载荷作用下活塞应力与变形的三维有限元分析

根据有限元法解得的温度场，利用微机对ω型燃烧室的柴油机活塞进行温度载荷和机械载荷作用下应力和变形的三维有限元分析。单元网格划分中采用了３１８６个节点、２２１０个８节点六面体等参元，将计算输出的各单元形心的六个应力分量换算为三个主应力分量，再选择合适的插值求得各节点的主应力分布。绘制各截面在温度和机械载荷作用下的变形图和三个主应力分量的等应力曲线图。为了评估计算的可靠性，还进行了沿活塞轴线方向的静力校核。

破裂水泥混凝土路面板沥青加铺层温度应力影响因素

为了防止水泥混凝土路面加铺沥青面层反射裂缝的产生,采用有限元方法,视路面结构为弹性层状体系,建立沥青加铺层、补强层、破裂水泥混凝土路面板和地基组成的空间三维模型,分析了破裂板块平面尺寸、降温幅度、沥青加铺层模量及厚度、结构补强层模量、混凝土路面板厚度等因素对沥青加铺层温度应力的影响。结果表明,对破裂后的旧水泥混凝土路面板块,沥青加铺层温度应力随其板块尺寸的减小而大幅度降低,较大的降温幅度对加铺层温度应力的影响远大于车辆荷载产生的应力;而降低沥青加铺层模量,增大加铺层厚度等技术措施可明显改善破裂板接缝处的应力状况,并能有效地防止沥青加铺层反射裂缝的产生。

腰椎椎弓峡部裂的应力分析

[目的]探讨腰椎椎弓峡部裂发病的力学因素，为治疗与预防腰椎峡部裂提供参考。[方法]采用三维有限元方法建立完整的脊柱腰段（L1-5）有限元模型，分析7种不同姿势下腰段脊柱椎弓峡部的应力分布情况。[结果]各椎弓峡部应力值由L1-5逐渐增大，椎弓峡部在前屈、后伸位均出现明显的应力集中，其中后伸位时应力值最大。[结论]椎弓峡部裂的发生是峡部长期高应力刺激的结果，而且与腰椎后伸关系最为密切。