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.

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).

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.

A combined numerical model of three-dimensional tidal motion and sediment transport in tidal current and its application

A calculation scheme, which combines a horizontal upwind finite element method with vertical implicit differences, is used to establish a three-dimensional mathematical model of tidal motion and sediment transport in tidal current. Compared with those of the relative theoretical formula, the results are satisfactory. The model mentioned above has been applied to the water area of the Lianzhou Bay, Guangxi Province. On the basis of the analysis and comparison with the field data, it shows clearly that the model calculation results are reasonable.

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.

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.

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。

生物可吸收板与微型钛板在不同骨质下颌骨骨折固定中的有限元分析

背景:下颌骨骨折在坚强内固定后的愈合受多种因素影响,包括接骨板的材料、骨折部位以及患者骨密度等,然而,目前对于不同骨质下下颌骨骨折固定稳定性关系的研究相对较少,并且缺乏科学的依据。目的:利用有限元法分析生物可吸收板和微型钛板固定不同骨质条件下颌骨骨折的稳定性。方法:根据ZARB和LEKHOLM提出的骨质分类方法,分别建立Ⅰ-Ⅳ类下颌骨骨折三维有限元模型,每类骨质条件下分别模拟下颌骨正中、体部和下颌角3个部位的骨折模型,采用生物可吸收板(或微型钛板)对上述骨折进行内固定,模拟健侧咬合状态,利用有限元分析骨折段的相对位移与内固定物应力分布情况。结果与结论:①随着骨质等级的增加,内固定物的最大应力值基本呈逐渐增加趋势,微型钛板组、生物可吸收板组下颌体部Ⅳ类骨质下的内固定物最大应力值最高,分别为382.74,96.11 MPa;在相同骨质条件下,钛板组各部位骨折模型的内固定物最大应力值均高于生物可吸收板组。②对于Ⅲ和Ⅳ类下颌骨正中部骨折,微型钛板组、可吸收板固定组骨折断端位移较大,超过了骨愈合极限值(大于150μm);对于Ⅳ类骨质下颌骨体部骨折,生物可吸收板组骨折断端位移超过了愈合极限值,微型钛板组骨折断端位移接近愈合极限值;在相同骨质条件与骨折部位下,微型钛板组骨折断端位移要小于生物可吸收板组。③结果显示,两种内固定物的强度和刚度均足以支持Ⅰ-Ⅳ类骨质下颌骨3种部位骨折的骨愈合,并且生物可吸收板的固定稳定性与微型钛板几乎相同,可以提供骨折早期的愈合条件。在治疗下颌骨骨折时应将下颌骨骨质类型纳入考虑因素,下颌骨骨质等级越高,骨折固定的稳定性越差,术后更易发生骨愈合不良等并发症。

纤维桩联合不同冠部修复方式修复穿髓型非龋性颈部缺损牙体的力学分析

背景:使用纤维桩修复穿髓型非龋性颈部缺损可以改变牙齿的应力分布,显著降低患牙折裂风险,但关于纤维桩改善牙体抗折性的力学机制及穿髓型非龋性颈部缺损的最佳冠部修复方式尚有争论。目的:综述纤维桩修复穿髓型非龋性颈部缺损后的应力分布模式,在各种受力状态下的抗折能力与断裂模式,以及纤维桩联合不同冠部修复方式的最新研究进展。方法:应用计算机在PubMed和中国知网数据库中检索2008年9月至2023年9月发表的相关文献,英文检索词为“non-carious cervical lesions,endodontically treated teeth restoration,endodontically treated teeth stress distribution”,中文检索词为“非龋性颈部缺损,根管治疗后牙体修复,根管治疗后牙齿应力分布”,最终纳入56篇文献进行分析。结果与结论:穿髓型非龋性颈部缺损根管治疗后,应用纤维桩修复可部分改善牙齿颈部应力,同时不会增加牙根纵裂的风险;使应力分布更加均匀,提高牙齿的抗折性。使用纤维桩修复的非龋性颈部缺损牙齿若折断,其断裂模式显示出有利的、可恢复的或可修复的断裂模式。纤维桩联合瓷贴面或贴面式嵌体可能会成为修复穿髓型非龋性颈部缺损的一种较理想微创修复方法。

不同材料种植体修复单颗上前牙缺失的三维有限元分析

背景:种植修复已成为治疗前牙缺失的重要手段,选取合适的种植修复材料尤为重要,但目前临床应用的种植体材料均存在一定的不足,研究者们一直在探索合适的种植体材料。目的:对比不同材料种植体修复单颗上前牙缺失的生物力学特征。方法:将1例单颗上颌中切牙缺失患者的锥形束CT数据导入3-matic软件建立单颗上前牙缺失的三维有限元分析模型,将模型导入Marc Mentat中,根据不同的种植体材料(聚醚醚酮、钛锆合金、钛合金和氧化锆,4种材料的弹性模量依次升高)及松质骨密度(高密度、低密度)共设计8组种植体修复模型,模拟正中咬合时上前牙受力情况,比较分析种植体位移、应力以及骨皮质应力和骨松质应变。结果与结论:(1)随着种植体材料弹性模量的增加,种植体的最大位移逐渐降低,聚醚醚酮组种植体最大位移数值超过了10μm;模型中种植体应力集中于唇侧颈部,随着种植体材料弹性模量的增加,种植体最大应力逐渐增大,其中氧化锆-低密度骨质组模型种植体应力最高,达21.31 MPa;所有模型的皮质骨应力均集中于与种植体交界的唇侧皮质骨,聚醚醚酮-低密度骨质组皮质骨应力最高,为29.90 MPa。(2)从生物力学角度来看,钛锆合金、钛合金、氧化锆均可用作修复单颗上前牙缺失的种植体材料,但单纯聚醚醚酮材料在上前牙区种植修复时可能会引起种植体位移过大,导致种植失败。

不同骨强度下全膝置换过程中发生股骨前皮质切迹的三维有限元分析

背景:全膝关节置换后发生膝关节股骨假体周围骨折是常见并发症之一,目前对不同骨质强度条件下发生膝关节股骨假体周围骨折的生物力学研究欠缺,三维有限元分析可为临床提供生物力学基础。目的:探讨不同骨质强度下全膝关节置换过程中发生股骨前皮质切迹的生物力学变化,为临床预防膝关节置换后发生膝关节股骨假体周围骨折提供力学理论基础。方法:获取健康成年人的股骨CT数据,运用Mimics、Geomagic studio、Solidworks软件建立膝关节股骨侧置换三维模型,然后构建不同深度的股骨前皮质切迹模型,将模型导入到ANSYS软件并分析不同骨强度、不同股骨前皮质切迹深度对股骨髁上生物应力的影响,并分析股骨前皮质切迹骨水泥填补前、后的股骨前髁截面应力变化。结果与结论:①任何骨质强度下,髁上应力都随股骨前皮质切迹深度加深而增加;在正常骨质情况下,当股骨前皮质切迹深度在3 mm和4 mm间有一个应力突变点;在骨质疏松情况下,当股骨前皮质切迹深度在2 mm和3 mm间有一个应力突变点;②膝关节置换过程中发生股骨前皮质切迹且深度超过骨皮质厚度时,随着骨质强度降低,股骨髁上应力逐渐增大;③使用骨水泥填补股骨前皮质切迹深度为3 mm的模型,股骨前髁截面应力下降;④结果显示,膝关节置换过程中应该避免股骨前皮质切迹出现,特别是骨质疏松患者;如术中出现股骨前皮质切迹且深度超过骨皮质厚度时,可以采用骨水泥均匀填充股骨前皮质切迹以降低股骨髁上应力,降低膝关节股骨假体周围骨折的发生率。

椎体骨皮质强化差异对骨质疏松性椎体压缩性骨折生物力学的影响

背景:骨质疏松性椎体压缩性骨折经皮椎体成形过程中骨水泥在椎体内的骨皮质强化区域对脊柱生物力学及临床疗效有重要影响,但以往研究大多局限于二维层面。目的:采用有限元分析法探讨经皮椎体成形过程中骨水泥在椎体三维层面内骨皮质强化差异对骨质疏松性椎体压缩性骨折椎体、邻近椎间盘及终板生物力学分布的影响,以评估其效果。方法:建立T12椎体骨质疏松性压缩性骨折行经皮椎体成形治疗的有限元模型,从横断面、矢状面、冠状面对骨水泥有无皮质强化情况进行分组分析,研究不同体位变化下,骨皮质强化对T12椎体松质骨、皮质骨、T11/T12椎间盘、T12/L1椎间盘、T11下终板、L1上终板生物力学的影响。结果与结论:(1)在垂直压缩力作用下,经皮椎体成形过程中有或无骨水泥皮质强化在不同体位变化下除伤椎皮质骨以外结构应力变化均不明显;(2)伤椎皮质骨Von Mises应力值在人体前屈、左/右侧弯和左/右轴向旋转时差异显著,同一平面内骨皮质完全强化组较无骨皮质强化组最大Von Mises应力值明显变小,随着骨皮质强化越广泛Von Mises应力值整体呈下降趋势;(3)提示行经皮椎体成形治疗时,横断面内骨水泥应尽量广泛对称水平分布于椎体骨皮质边缘,矢状面内骨水泥应广泛纵向分布且靠近上下终板及前后壁,冠状面内骨水泥应广泛分布于中线两侧同时对称接触上下终板及侧壁,可有效避免伤椎再骨折风险且不增加邻椎骨折、残留盘源性疼痛风险。

超短种植体配置下穿颧骨种植定位方案的三维有限元分析

目的:探究上颌窦沟槽(sinus slot,SS)技术和经上颌窦外(extra sinus,ES)技术结合超短种植体行穿颧种植修复后的生物力学分布特点,为功能性修复上颌骨重度萎缩提供理论基础。方法:通过患者的高分辨计算机断层扫描(computed tomography,CT)资料建立有限元分析模型,虚拟化穿颧种植体分别置于SS和ES模型,并结合使用2枚或4枚超短种植体。分析种植体von Mises应力值及牙槽骨中的主应力值。结果:配置2枚超短种植体+2枚ES穿颧种植体的von Mises应力最大(292 MPa);而4枚超短种植体+2枚SS穿颧种植体的最小(184 MPa)。配置2枚超短种植体+2枚SS穿颧种植体的最高主应力值最大(31 MPa);而4枚超短种植体+2枚ES穿颧种植体的最小(12 MPa)。配置4枚超短种植体+2枚SS穿颧种植体的最低主应力值最小(-58 MPa);而2枚超短种植体+2枚ES穿颧种植体的最大(-81 MPa)。结论:2枚SS穿颧种植体结合4枚超短种植体可能在生物力学方面更安全地用于修复重度萎缩的上颌骨。

穿颧骨种植上颌窦区种植体定位方案的三维有限元分析

目的:探究上颌窦沟槽(sinus slot,SS)技术和经上颌窦外(extra sinus,ES)技术结合常规种植体行穿颧种植修复后的生物力学分布特点,为功能性修复上颌骨重度萎缩提供理论基础。方法:通过患者的高分辨计算机断层扫描(computed tomography,CT)资料建立有限元分析(finite element analysis,FEA)模型,虚拟化穿颧种植体(zygomatic implant,ZI)分别置于SS和ES模型,并结合使用2枚或4枚常规种植体。分析种植体von Mises应力值及牙槽骨中的主应力值。结果:配置2枚常规种植体+2枚ES ZI的von Mises应力值最大(292 MPa);而4枚常规种植体+2枚SS ZI的最小(184 MPa)。配置2枚常规种植体+2枚SS ZI的最高主应力值最大(31 MPa);而4枚常规种植体+2枚ES ZI的最小(12 MPa)。配置4枚常规种植体+2枚SS ZI的最低主应力值最小(|-58|MPa);而2枚常规种植体+2枚ES ZI的最大(|-81|MPa)。结论:使用2枚SS ZI和4枚常规种植体联合修复重度萎缩的上颌骨,在生物力学方面安全性更高。

螺栓联接结合面三维分形刚度模型与实验研究

为更准确地分析螺栓联接体的静动态特性,根据三维分形理论,考虑微凸体弹塑性接触在内的4种变形阶段,分别得到螺栓联接结合面的法向载荷与切向载荷,进而建立了螺栓联接结合面法向刚度与切向刚度模型,并分析了各参数对螺栓联接结合面刚度模型的影响关系。开展了有限元分析与实验研究,应用所建立的法向刚度与切向刚度模型,将考虑结合面影响的螺栓联接体有限元分析结果分别与忽略结合面影响的螺栓联接体有限元分析结果以及实验结果对比。研究结果显示,增大预紧力、工作载荷、分形维数、材料特性参数,或是减小分形尺度参数,可增大螺栓联接结合面的刚度;应用所建立结合面刚度模型的螺栓联接体有限元分析结果与实验结果误差在8%以内,远小于忽略结合面影响的有限元分析误差。