Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

Clinical significance of three dimensional finite element analysis on humerus fracture

Objective: To treat humerus fracture with three dimensional pattern and finite element analysis, providing mechanical basis for treating humerus fracture. Methods: Humerus pattern was established based on the CT images, and calculation was done by ANSYS5. 6 software. Three dimensional ten-node tetrahedron unit was selected and were divided into 2 729 nodes, 49 041 units. Distribution and amount of axial compression of humerus were analyzed when clip angle was 30°, 45°, 90° between fracture face and axial line with fixed X, Y, Z directions. Results: The distribution of stress was greatly different between fracture face and non fracture face. Stress in fracture part was fairly concentrated with incomplete symmetric distribution around the center of fracture face; Greater stress distributed in the regions 10 mm from fracture face, which was 2-3 times that of other stress regions. Conclusion: Required load must be estimated under various conditions as to select the suitable internal fixation implants during the treatment of humerus fracture, which can provide helpful stress environment for fracture healing.

Three dimensional finite element analysis of anatomic distal radius Nitinol memory connector treating distal radius fracture

Objective: To study the memory biomechanical character of anatomic distal radius Nitinol memory connector (DRMC) in treating distal radius fracture. Methods: Establishing three dimensional model and finite element analysis, we calculated the stress in and around the fracture faces when distal radius fracture was fixated with DRMC. Results: Axial holding stress produced by holding part of DRMC on distal radius was 14.66 MPa. The maximum stress of holding part was 40-70 MPa, the minimum stress was 3-7 MPa,and the stress of compression part was 20-40 MPa. Conclusion: The distribution of stress produced by DRMC around the fracture line is reasonable, and axial holding stress can help stabilize fracture during earlier period. The existence of longitudal compression and memory effect can transfer fixated disused section into developed section and enhance fracture healing.

Three dimensional finite element analysis of acetabulum loaded by static stress and its biomechanical significance

Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress.Methods:By means of computer simulation, acetabular three dimensional model was input into three dimensional finite element analysis software ANSYS7.0. The acetabular mechanical behavior was calculated and the main stress value, stress distribution and acetabular unit displacement in the direction of main stress were analyzed when anterior wall of acetabulum and acetabular crest were loaded by 1 000 N static stress. Results:When acetabular anterior wall loaded by X direction and Z direction composition force, the stress passed along 4 directions: (1)from acetabular anterior wall to pubic symphysis along superior branch of pubis firstly, (2)from acetabular anterior wall to cacroiliac joint along pelvic ring,(3)in the acetabulum,(4)from the suffered point to ischium. When acetabular crest loaded by X direction and Y direction composition force, the stress transmitted to 4 directions: (1)from acetabular crest to ilium firstly, (2)from suffered point to cacroiliac joint along pelvic ring,(3) in the acetabulum ,(4)along the pubic branch,but no stress transmitted to the ischium branch.Conclusion:Analyzing the stress distribution of acetabulum and units displacement when static stress loaded can provide internal fixation point for acetabular fracture treatment and help understand the stress distribution of acetabulum.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Stress Distribution in Maxillary Central Incisors without Ferrules: A Finite Element Analysis of Post and Core Systems

Purpose: The purpose of this study was to identify optimal post and core materials for central incisors without ferrules using three-dimensional finite element analysis and three-point bending tests. Methods: Stress analyses were performed with six models: cast metal post and core (MP), composite resin core alone, straight fiber-reinforced post-composite resin core (FSR), tapered fiber-reinforced post-composite resin core, straight titanium post-composite resin core (TSR), and tapered titanium post-composite resin core (TTR). A 100-N load was applied to the lingual surface at a 45° angle to the long axis of the tooth. Maximum von Mises stress distributions were calculated with finite element analysis software. Five samples each of composite resin, straight fiber-reinforced post, straight titanium post, straight fiber-reinforced post and composite resin, and straight titanium post and composite resin were subjected to three-point bending tests, followed by analysis of variance and Tukey’s multiple comparison test. Results: Stress distribution was optimal on TTR. Maximum von Mises stress on the cervical side of the post was greatest in TSR (693 MPa) and TTR (556 MPa). Maximum stress on the apical side of the post was greatest in MP (110 MPa). Maximum stress in surrounding dentin was lowest in MP (203 MPa) and TTR (250 MPa). Gap distance was smallest in MP (0.09 mm) and largest in FSR (0.26 mm). Mean maximum three-point bending force was lowest in composite resin (26.9 N/mm) and highest in titanium post and composite resin (97.1 N/mm). Titanium post bending strength was consistently greater than that of the fiber-reinforced post (p < 0.01). Conclusion: These results revealed optimal stress distribution and high bending strength with the tapered titanium post and resin combination, suggesting that this combination can most effectively prevent root or post fracture in an anterior tooth without a ferrule.

Numerical and Dimensional Analysis for Prediction of Line Heating Residual Deformations

Line heating process is a very complex phenomenon as a variety of factors affects the amount of residual deformations. Numerical thermal and mechanical analysis of line heating for prediction of residual deformation is time consuming. In the present work dimensional analysis has been presented to obtain a new relationship between input parameters and resulting residual deformations during line heating process. The temperature distribution and residual deformations for 6 mm, 8 mm, 10 mm and 12 mm thick steel plates were numerically estimated and compared with experimental and published results. Extensive data generated through a validated FE model were used to find co-relationship between the input parameters and the resulting residual deformation by multiple regression analysis. The results obtained from the deformation equations developed in this work compared well with those of the FE analysis with a drop in the computation time in the order of 100 (computational time required for FE analysis is around 7 200 second to 9 000 seconds and where the time required for getting the residual deformation by developed equations is only 60 to 90 seconds).

Analysis and Optimization of Key Dimensions of Co-Axial Dual-Mechanical-Port Flux-Switching Permanent Magnet Machines for Fuel-Based Extended Range Electric Vehicles

In this paper,key dimensions of a co-axial dual-mechanical-port flux-switching permanent magnet(CADMP-FSPM)machine for fuel-based extended range electric vehicles(ER-EVs),including split ratio,stator/rotor pole arcs,rotor yoke thickness,etc.,are analyzed and optimized.Firstly,the topologies and operation principles of an exampled 3-phase CADMP-FSPM are introduced briefly,in which an inner-rotor FSPM machine with 12-stator-slots/10-rotor-poles for high-speed generation and an outer-rotor FSPM machine with 12-stator-slots/22-rotor-poles for low-speed motoring are assembled co-axially.Then,the relationship between the key dimensions and electromagnetic performance,particularly for electromagnetic torque(power),of the CADMP-FSPM machine is studied by 2D-finite element analysis(FEA).Further,the reasonable matches of split ratio,rotor/stator pole arcs and rotor yoke are determined and the original CADMP-FSPM machine is optimized correspondingly.Finally,the static characteristics,including no-load PM flux-linkage,electro-motive-force(EMF),winding inductances,cogging torques and electromagnetic torques,of the original and optimized machines are compared by 2D-FEA.The results verify that the optimized CADMP-FSPM machine can exhibit improved torque characteristics than the original one,i.e.,the torque ripples of the inner and outer machines can be reduced by 22.7%and 4.7%,respectively,and the average torque of the inner and outer machines can be increased by 0.43Nm and 2Nm,respectively.

Finite Element Simulation of the Polymeric Liquid Flow in Coat-hanger Die

A three - dimenslonal finite element model is developed to deal with the polymeric liquid flow in coat - hanger die. This model is used to predict the flow behavior of the 2％ CMC/watsr solution in the coat - hanger die with linearly taper manifolds and its validity is experimentally verified quantitatively and qualitatively by using Laser Doppler Velocimetry and Particle Image Velocimetry respectively.

Numerical Analysis of the Adhesive Forces in Nano-Scale Structure

Nanohairs, which can be found on the epidermis of Tokay gecko＇s toes, contribute to the adhesion by means of van der Waals force, capillary force, etc. This structure has inspired many researchers to fabricate the attachable nano-scale structures. However, the efficiency of artificial nano-scale structures is not reliable sufficiently. Moreover, the mechanical parameters related to the nano-hair attachment are not yet revealed qualitatively. The mechanical parameters which have influence on the ability of adhesive nano-hairs were investigated through numerical simulation in which only van der Waals force was considered. For the numerical analysis, finite element method was utilized and van der Waals force, assumed as 12-6 Lennard-Jones potential, was implemented as the body force term in the finite element formulation.

MATHEMATICAL MODEL OF MILLING TEMPERATURE AND TEMPERATURE FIELD ANALYSIS FOR THREE-DIMEN-SIONAL COMPLEX GROOVE MILLING INSERT

The mathematical model on the temperature of the waved-edge is constructedaccording to Jaeger's theory of moving solid and based on the used temperature model of the flatinsert. It is possible to forecast the milling temperature through programming. The comparableexperiments have been done between the two new three-dimension groove inserts (waved-edge insert,great edge insert) and flat fake insert. The theoretic forecast is in good agreement with theexperimental result. According to the cutting conditions, the boundary condition of finite elementanalysis on cutting temperature field is established, and the three-dimensional temperature fieldsof inserts with grooves are analyzed by FEM, so as to offer a reference basis for the design andoptimization of insert grooves.

3D FEM analysis for layered rock considering anisotropy of shear strength

An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a transversely isotropic medium and Mohr-Coulomb criterion in which C and Ф vary with directions were employed, and a relative 3D elasto-plastic FEM code was developed, in which the important thing was to adopt a search-trial method to find the orientation angle （p） of shear failure plane （or weakest shear plane） with respect to the major principal stress as well as the corresponding C and Ф Taking an underground opening as the calculation object, the numerical analyses were carried out by using the FEM code for two cases of transversely isotropic rock and isotropic rock, respectively, and the computation results were compared. The results show that when the rock is a transversely isotropic one, the distributions of displacements, plastic zones and stress contours in the surrounding rock will be non-axisymmetric along the tunnel＇s vertical axis, which is very different from that of isotropic rock. The stability of the tunnel in transversely isotropic rock is relatively low.

Friction coefficient in rubber forming process of Ti-15-3 alloy

The forming limit diagram of Ti-15-3 alloy sheet was constituted at room temperature. The effects of different punch and rubber hardness on the limit principal strain distributions were investigated experimentally. Finite element analysis models of the samples with dimensions of 180 mm×180 mm were established to analyze the friction coefficients of different interfaces. Effects of various friction coefficients on the strain distributions were studied in detail. Finally, the friction coefficients in the cold forming were determined by contrasting the strain results between the experimental data and the simulated ones.

种植体-天然牙联合支持的套筒冠义齿修复下颌多牙缺失的三维有限元分析

目的:分析比较仅由天然牙支持的套筒冠覆盖义齿和种植体-天然牙联合支持的套筒冠覆盖义齿修复下颌多数牙缺失时基牙、牙周膜、牙槽骨、义齿及义齿下黏膜的应力分布情况.方法:通过三维有限元分析法,建立2个生物力学模型:仅由2颗尖牙支持的套筒冠义齿修复下颌缺失牙模型(Model 1)和由种植体-天然牙联合支持的套筒冠义齿修复下颌缺失牙模型(Model 2),在垂直载荷下分析比较2种套筒冠义齿基牙、牙周膜、牙槽骨、义齿及义齿下黏膜的应力分布情况.结果:与Model 1相比,Model 2中基牙的位移、基牙及其周围牙周膜、牙槽骨、修复体及修复体下方的黏膜所受的应力均减小,而种植体所受的应力较大.结论:在游离端缺牙区补充性地植入2枚种植体,并与天然牙联合支持套筒冠义齿对多数缺失牙进行修复,可保护余留牙及其周围支持组织,可减轻修复体所承担的应力,从生物力学的角度来说是一种有价值的修复手段.

下颈椎C3-C7活动节段三维有限元的建模和验证

基于CT图像数据结合图像处理软件建立人体下颈椎C3-C7活动节段的三维有限元模型,并验证模型的有效性。选取一名健康志愿者颈椎CT数据,建立包括椎体、后部结构、终板、椎间盘、韧带和关节突等部分的下颈椎C3-C7三维有限元模型,赋予颈椎组织不同成分的材料属性,模拟人体颈椎在正常生理状态下承受扭矩载荷时,前屈、后伸、侧弯和旋转等运动情况下颈椎椎体、椎间盘和小关节的生物力学特性。颈椎C3-C7活动节段在四种工况下的活动范围与前人离体实验和有限元分析的研究结果基本吻合,颈椎椎体、椎间盘和小关节的应力分布符合其生物力学特性。下颈椎C3-C7活动节段的模拟结果符合人体的真实运动规律,为临床颈椎的生理、病理研究以及植入器械的力学性能分析奠定理论基础。

3D打印个性化正畸装置对单根牙垂直移动的三维有限元分析

背景:基于牙齿垂直移动原理,通过数字化设计结合3D打印制作个性化正畸装置,可使个性化正畸装置与单个切牙形成支抗系统。借助微种植体绝对支抗作用可对单根牙在三维方向上进行精准控制。目的:基于生物力学原理设计了牙位11、12、21、22压低移动与伸长移动的个性化正畸装置,通过三维有限元法分析个性化正畸装置的安全性与其对牙齿的移动作用。方法:应用Mimics、Geomagic Wrap、SolidWorks和Ansys Workbench软件分别建立了上颌前牙区(牙位11、12、21、22)牙槽骨-牙周膜-上颌切牙-个性化悬臂微种植体-连接板-个性化托槽的三维有限元模型,每个牙位分别设置个性化压低移动与伸长移动正畸装置,加载300 g拉力或推力,分析个性化正畸装置各部件应力水平,计算牙齿位移与牙周膜应力分布情况。结果与结论:①个性化压低移动正畸装置受到的最大等效应力为162.90 MPa,个性化伸长移动正畸装置受到的最大等效应力239.57 MPa,二者的最大等效应力均位于个性化托槽加力附件的垂直部分,个性化正畸装置各部件所受等效应力均在屈服强度内,均具有良好的安全性;②在个性化正畸装置作用下,牙齿初始位移呈现整体压低或伸长移动的趋势,垂直方向上的位移远远超过在水平方向和矢状方向上的位移;牙周膜根尖或颈部位置出现等效应力峰值,在根尖区牙周膜出现等效应力集中区域;③结果显示,个性化正畸装置可以使牙位11、12、21、22近似达到压低移动或伸长移动的目的,初步证实了个性化垂直移动正畸装置的有效性。

上颌All-on-4修复种植体在不同牙弓形态中应力分布的三维有限元分析

目的:利用有限元法探讨上颌牙列缺失应用All-on-4修复时种植体在3种牙弓形态模型中应力分布的差异,为临床提高种植体成功率提供客观参数。方法:参照3M公司MBTTM牙弓模板,应用SolidWorks 2013软件建立All-on-4种植修复的3种牙弓形态上颌无牙颌有限元模型(尖圆形、方圆形和卵圆形),设定皮质骨层为2mm,种植体长度为13mm,前牙区2颗种植体平行植入,后牙区2颗种植体在颌骨内沿近远中方向与牙长轴成0°、15°、30°和45°4种角度,所有种植体均固定于上部结构。通过2种加载方式在上部结构施加100N压力模拟咀嚼受力,应用有限元软件Abaqus 6.13运算测得种植体在上颌模型的Von-Mises应力值。结果:测得种植体周围Max von-Mises应力值均出现在皮质骨层,不同牙弓形态模型中应力分布不同,方圆形牙弓种植体周围应力随种植体角度增加而增大;卵圆形牙弓后牙区最大应力值出现在种植体倾斜15°时,前牙区应力在种植体倾斜超过15°后明显提高;尖圆形牙弓种植体周围应力在种植体倾斜45°时显著增大。结论:牙弓形态对种植体周围应力分布有显著影响,All-on-4修复上颌牙列缺失时,方圆形牙弓应尽量减少种植倾斜体角度,卵圆形牙弓种植体倾斜角度不宜超过15°,尖圆形牙弓应避免种植体倾斜角度超过30°。

基于个体CT影像的胸主动脉-血管内支架数值仿真初探

目的:通过对胸主动脉和血管内支架的数值仿真,进行主动脉与支架相互作用的有限元分析,企盼阐明支架径向支撑力、弹性回直力及支架源性损伤的作用机制。方法:采用临床患者薄层CT血管造影(CT angiography,CTA)的图像资料,运用MIMICS软件进行主动脉三维数值模型的构建,使用ABAQUS软件对主动脉及支架模型进行有限元建模。对模拟支架在人体内置入及释放的过程通过有限元方法进行分析和运算,获得相关力学数据及其分布。结果:在胸降主动脉近段,由近端向远端截取3个横截面,观察各自周长和截面积的变化。结果显示,原先的周长分别为72.406mm、69.571mm和65.381mm,支架置入后分别增加至77.468mm、75.931mm和71.013mm,分别增长为6.99%、9.14%和8.61%;原先的截面积分别为410.690mm2、379.788mm2和337.648mm2,支架置入后分别增加至469.697mm2、453.749mm2和399.111mm2,增长率分别为14.37%、19.47%和18.20%。在血管支架的两端附近应力相对较大且分布不均,最大的应力靠近支架近端。结论:基于CT影像的主动脉和血管内支架的数值仿真切实可行,初步结果判断与临床表现吻合,有望为血管和支架相互作用的相关研究提供依据。

永磁同步电机匝间短路-退磁耦合故障分析

永磁同步电机存在匝间短路故障、永磁体退磁故障和偏心故障等多种故障类型,对其故障诊断的研究一直集中于单一故障,耦合故障涉及较少。以匝间短路-退磁耦合故障为例,运用有限元法分别建立电机正常条件及不同耦合故障程度的二维模型;通过瞬态磁场求解器求得空载和额定负载两种不同工况下电机在正常以及不同故障程度运行时的磁感线分布云图、转矩曲线图、相反电动势曲线图,并利用傅里叶变换对相反电动势谐波含量进行了分析。结果表明,耦合故障条件下相反电动势的三次谐波含量明显高于正常条件值,相反电动势的三次谐波含量的增加可作为判断该耦合故障的依据。