计及复杂胎面花纹的子午线轮胎结构有限元分析
摘要
鉴于轮胎技术的发展,人们越来越认识到胎面花纹的重要性,计及复杂胎面花纹的轮胎结构有限元分析技术越来越受到工程和学术界的关注;由于难度很大,相关的文献至今仍较为罕见,因此发展计及复杂胎面花纹的高效的轮胎有限元模型及其求解策略成为当前工程与学术界的挑战性课题。本文就是在这一背景下围绕着这一课题展开的。
基于组合模型技术和两种映射方法,分别提出了组合周向保角映射建模法和组合类保角映射簇建模法。两种建模方法均使繁琐的手工建模过程大大简化,能够较方便地模拟复杂的胎面花纹形态,并得到完全的、较高质量的六面体网格。使用组合周向保角映射建模法建立了用于静力学分析的数个均分的组合花纹轮胎模型和非均分的组合花纹轮胎模型;使用组合类保角映射簇建模法建立了用于稳态滚动分析的数个周期性的组合花纹轮胎模型和变节距的组合花纹轮胎模型;并形成了从装配、充气、静负荷、自由滚动到驱动、制动、侧倾滚动和侧偏滚动等工况下的轮胎结构分析策略。通过较充分的对比考评表明,非均分的组合花纹轮胎模型和变节距的组合花纹轮胎模型是最有效的,可以在求解精度基本相同的前提下大大提高计算效率。
在上述基础上,对充气、静负荷、自由滚动、驱动、制动、侧倾滚动和侧偏滚动等工况下的半钢子午线轮胎结构力学特征进行了较系统的分析研究。
较系统地揭示了半钢子午线轮胎骨架结构的受力特征。充气压力和负荷的改变没有影响充气工况和静负荷工况下的轮胎骨架结构受力分布的总体特征;自由滚动工况下的受力分布与静负荷工况基本相同,轮胎接地端附近的胎体层帘线、带束层帘线和胎圈钢丝中均出现了不同程度的受压情况;在驱动和制动工况下的受力分布与自由滚动工况比较接近;在侧倾滚动和侧偏滚动工况下轮胎骨架结构受力分布呈现出明显的左右不对称性,帘线轴力的最大值大幅增加,同时受压情况也更加严重。
较系统地揭示了半钢子午线轮胎橡胶结构的受力变形特征。各种工况下轮胎橡胶的可能危险区域均集中于胎冠部、胎肩部和胎圈部:与充气工况相比,静负荷和自由滚动工况下的橡胶受力变形情况更加复杂,接地端的可能危险区域内的应力应变水平大幅提高;在驱动和制动工况下,轮胎胎面体部分橡胶的受力变形情况与自由滚动工况有比较显著的差异,同时花纹块在接地面附近的区域成为新的可能危险区域;在侧倾和侧偏工况下,尤其是侧偏工况下,轮胎橡胶的受力变形情况与自由滚动工况的差异非常显著,在轮胎一侧的主体部分橡胶的应力应变水平明显增高,同时花纹块底部、胎侧部和胎圈部均出现了新的可能危险区域。
揭示了帘线角的改变对半钢子午线轮胎结构静力学性能的影响。轮胎径向刚度随帘线角的增加而减小,并在帘线角超过某一数值后急剧减小;胎肩部橡胶内危险区域的剪应力、Mises应力和应变能密度等力学量随着帘线角的增加先增加后减小。此外,带束层帘线沿横向变角度铺设的轮胎模型的分析结果表明,这种轮胎具有较好的力学性能,在保证了较高的径向刚度的同时,改善了带束层帘线和胎肩部橡胶的受力状况。
初步地揭示了胎面花纹对充气、静负荷、自由滚动和侧偏滚动工况下的子午线轮胎结构受力变形特征,自由滚动和侧偏滚动工况下的轮胎接地性能,以及侧偏滚动工况下的轮胎力学特性的影响。就轮胎结构的受力变形特征而言,横向花纹和纵向花纹对各种工况下的胎面体部分的橡胶受力变形情况均有明显的影响;尽管胎面花纹没有改变轮胎主体部分橡胶的应力应变场的总体分布特征,但是对各个危险区域的应力应变水平均有不同程度的影响;对轮胎骨架结构受力分布的影响较小。就轮胎接地性能而言,纵向花纹和横向花纹的存在使轮胎的接地包络面面积、接地压力水平以及接地压力分布的不均匀性均有所增加。就侧偏力学特性而言,纵向花纹和横向花纹的存在使轮胎的侧偏刚度及回正刚度均有较明显的降低,临界侧偏角则略有增加。
综上所述,只有计及复杂胎面花纹的轮胎结构有限元分析才能给出更为准确可靠的结果。
With the development of tire technology, more people have recognized the importance of tire tread patterns. And Finite Element Analysis (FEA) for radial tires with complex tread patterns considered draws focused attention from the engineering and academic fields. However, relative literature is fairly rare since it is a very difficult problem. How to develop an efficient finite element tire model with complex tread patterns and the corresponding solving strategy becomes a challenging subject in tire technology. In such a condition, this dissertation presents a systematic research on the above problems.
Based on the combined modeling technique, two modeling procedures with different mapping method, circumferential conformal mapping and quasi-conformal mapping cluster, are given respectively. Both procedures can not only greatly simplify the awkward manual modeling process for detailed tread patterns, but also easily obtain integrated, high-quality hexahedral meshes. Several uniform and non-uniform combined patterned tire models for static analysis are established with the former procedure. Several combined patterned tire models with constant pitch lengths and with varied pitch lengths, which are used for steady rolling analysis, are established respectively with the latter procedure. The FEA solving strategy of tire structure is founded, with the cases of assembly, inflation, static loading, free rolling, traction, braking, inclination and cornering. The evaluation for the four kinds of models shows that the non-uniform models and models with varied pitch lengths are most efficient and can achieve accurate numerical results.
Based on the above models, FEA calculations of the semi steel Passenger Car Radial tire (PCR tire) structure are carried out in the cases of inflation, static loading, free rolling, traction, braking, inclination and cornering, and systematic study on the mechanical behavior of the tire structure is carried out.
The load and deformation characters of the skeleton structure of the semi steel PCR tire is revealed as follows. The variation of inflation pressure and vertical load hardly affect the overall features of the load distribution in the skeleton structure in the cases of inflation and static loading respectively. The load distribution in the free rolling case is almost the same as that in the static loading case. For example, the carcass cords, belts cords and bead steel wires near the tread-ground zone are under compression in both cases. Comparing with the free rolling case, the load distribution of the traction case and the braking case is mostly the same, while inclination case and the cornering case are quite different. In the latter two cases, the distribution is distinctly asymmetric, the maximum cord tension increases significantly, and the compression status exaggerates intensely.
The load and deformation characters of the rubber structure of the semi steel PCR tire is disclosed as follows. Dangerous regions in the rubber structure congregate in the crown area, the shoulder area and the bead area. Comparing with the inflation case, the stress and strain distribution is more complicated in the cases of static loading and free rolling complicate. Also the stress and stain levels are higher in the dangerous regions. Comparing with the free rolling case, the mechanical behavior of tire tread rubber is quite different in the cases of traction and braking, and additional several dangerous regions appear in the bottom of some tread rubber blocks. In cases of inclination and cornering, the stress and stain level increases distinctly and some additional dangerous regions emerge in the bottom of some tread rubber blocks, in the sidewall area and in the bead area.
Effect of belt angle on the static mechanical behavior of the radial tire is discussed as follows. The calculated results indicate that tire radial deformation under inflation and vertical deformation under static load decrease with the increase of the belt angle. However, at the probably dangerous area in tire shoulder, some important parameters such as shear stress, Mises stress and strain energy density, vary non-monotonously with the belt angle and will reach maximums at a critical angle. In addition, the model with non-uniform belt structure has a perfect performance, with a high vertical rigidity and relatively low shear stress, Mises stress and strain energy density in tire shoulder.
Influence of tread patterns on the load and deformation characters of the radial tire structure in cases of inflation, static loading, free rolling and cornering, on the tire/road contact behavior in cases of free rolling and cornering and on the cornering properties are summarized as follows. In regard to the load and deformation characters, the longitudinal and lateral grooves have extraordinary effect on the mechanical behavior of the tire tread rubber, have some effect on the stress and stain level in the dangerous regions in tire rubbe, and have little effect on the load characteristic of the skeleton structure. In regard to the contact behavior, the existence of the longitudinal and lateral grooves increases the enveloping contact area, the contact pressure level and the inhomogeneity of the contact pressure distribution. In regard to the cornering properties, the cornering stiffness and the aligning stiffness decrease obviously with the addition of the longitudinal and lateral grooves, while the critical slip angle increases slightly.
In conclusion, only when the complex tread patterns are considered can the finite element analysis for the radial tire structure give more precise results.
基于组合模型技术和两种映射方法,分别提出了组合周向保角映射建模法和组合类保角映射簇建模法。两种建模方法均使繁琐的手工建模过程大大简化,能够较方便地模拟复杂的胎面花纹形态,并得到完全的、较高质量的六面体网格。使用组合周向保角映射建模法建立了用于静力学分析的数个均分的组合花纹轮胎模型和非均分的组合花纹轮胎模型;使用组合类保角映射簇建模法建立了用于稳态滚动分析的数个周期性的组合花纹轮胎模型和变节距的组合花纹轮胎模型;并形成了从装配、充气、静负荷、自由滚动到驱动、制动、侧倾滚动和侧偏滚动等工况下的轮胎结构分析策略。通过较充分的对比考评表明,非均分的组合花纹轮胎模型和变节距的组合花纹轮胎模型是最有效的,可以在求解精度基本相同的前提下大大提高计算效率。
在上述基础上,对充气、静负荷、自由滚动、驱动、制动、侧倾滚动和侧偏滚动等工况下的半钢子午线轮胎结构力学特征进行了较系统的分析研究。
较系统地揭示了半钢子午线轮胎骨架结构的受力特征。充气压力和负荷的改变没有影响充气工况和静负荷工况下的轮胎骨架结构受力分布的总体特征;自由滚动工况下的受力分布与静负荷工况基本相同,轮胎接地端附近的胎体层帘线、带束层帘线和胎圈钢丝中均出现了不同程度的受压情况;在驱动和制动工况下的受力分布与自由滚动工况比较接近;在侧倾滚动和侧偏滚动工况下轮胎骨架结构受力分布呈现出明显的左右不对称性,帘线轴力的最大值大幅增加,同时受压情况也更加严重。
较系统地揭示了半钢子午线轮胎橡胶结构的受力变形特征。各种工况下轮胎橡胶的可能危险区域均集中于胎冠部、胎肩部和胎圈部:与充气工况相比,静负荷和自由滚动工况下的橡胶受力变形情况更加复杂,接地端的可能危险区域内的应力应变水平大幅提高;在驱动和制动工况下,轮胎胎面体部分橡胶的受力变形情况与自由滚动工况有比较显著的差异,同时花纹块在接地面附近的区域成为新的可能危险区域;在侧倾和侧偏工况下,尤其是侧偏工况下,轮胎橡胶的受力变形情况与自由滚动工况的差异非常显著,在轮胎一侧的主体部分橡胶的应力应变水平明显增高,同时花纹块底部、胎侧部和胎圈部均出现了新的可能危险区域。
揭示了帘线角的改变对半钢子午线轮胎结构静力学性能的影响。轮胎径向刚度随帘线角的增加而减小,并在帘线角超过某一数值后急剧减小;胎肩部橡胶内危险区域的剪应力、Mises应力和应变能密度等力学量随着帘线角的增加先增加后减小。此外,带束层帘线沿横向变角度铺设的轮胎模型的分析结果表明,这种轮胎具有较好的力学性能,在保证了较高的径向刚度的同时,改善了带束层帘线和胎肩部橡胶的受力状况。
初步地揭示了胎面花纹对充气、静负荷、自由滚动和侧偏滚动工况下的子午线轮胎结构受力变形特征,自由滚动和侧偏滚动工况下的轮胎接地性能,以及侧偏滚动工况下的轮胎力学特性的影响。就轮胎结构的受力变形特征而言,横向花纹和纵向花纹对各种工况下的胎面体部分的橡胶受力变形情况均有明显的影响;尽管胎面花纹没有改变轮胎主体部分橡胶的应力应变场的总体分布特征,但是对各个危险区域的应力应变水平均有不同程度的影响;对轮胎骨架结构受力分布的影响较小。就轮胎接地性能而言,纵向花纹和横向花纹的存在使轮胎的接地包络面面积、接地压力水平以及接地压力分布的不均匀性均有所增加。就侧偏力学特性而言,纵向花纹和横向花纹的存在使轮胎的侧偏刚度及回正刚度均有较明显的降低,临界侧偏角则略有增加。
综上所述,只有计及复杂胎面花纹的轮胎结构有限元分析才能给出更为准确可靠的结果。
With the development of tire technology, more people have recognized the importance of tire tread patterns. And Finite Element Analysis (FEA) for radial tires with complex tread patterns considered draws focused attention from the engineering and academic fields. However, relative literature is fairly rare since it is a very difficult problem. How to develop an efficient finite element tire model with complex tread patterns and the corresponding solving strategy becomes a challenging subject in tire technology. In such a condition, this dissertation presents a systematic research on the above problems.
Based on the combined modeling technique, two modeling procedures with different mapping method, circumferential conformal mapping and quasi-conformal mapping cluster, are given respectively. Both procedures can not only greatly simplify the awkward manual modeling process for detailed tread patterns, but also easily obtain integrated, high-quality hexahedral meshes. Several uniform and non-uniform combined patterned tire models for static analysis are established with the former procedure. Several combined patterned tire models with constant pitch lengths and with varied pitch lengths, which are used for steady rolling analysis, are established respectively with the latter procedure. The FEA solving strategy of tire structure is founded, with the cases of assembly, inflation, static loading, free rolling, traction, braking, inclination and cornering. The evaluation for the four kinds of models shows that the non-uniform models and models with varied pitch lengths are most efficient and can achieve accurate numerical results.
Based on the above models, FEA calculations of the semi steel Passenger Car Radial tire (PCR tire) structure are carried out in the cases of inflation, static loading, free rolling, traction, braking, inclination and cornering, and systematic study on the mechanical behavior of the tire structure is carried out.
The load and deformation characters of the skeleton structure of the semi steel PCR tire is revealed as follows. The variation of inflation pressure and vertical load hardly affect the overall features of the load distribution in the skeleton structure in the cases of inflation and static loading respectively. The load distribution in the free rolling case is almost the same as that in the static loading case. For example, the carcass cords, belts cords and bead steel wires near the tread-ground zone are under compression in both cases. Comparing with the free rolling case, the load distribution of the traction case and the braking case is mostly the same, while inclination case and the cornering case are quite different. In the latter two cases, the distribution is distinctly asymmetric, the maximum cord tension increases significantly, and the compression status exaggerates intensely.
The load and deformation characters of the rubber structure of the semi steel PCR tire is disclosed as follows. Dangerous regions in the rubber structure congregate in the crown area, the shoulder area and the bead area. Comparing with the inflation case, the stress and strain distribution is more complicated in the cases of static loading and free rolling complicate. Also the stress and stain levels are higher in the dangerous regions. Comparing with the free rolling case, the mechanical behavior of tire tread rubber is quite different in the cases of traction and braking, and additional several dangerous regions appear in the bottom of some tread rubber blocks. In cases of inclination and cornering, the stress and stain level increases distinctly and some additional dangerous regions emerge in the bottom of some tread rubber blocks, in the sidewall area and in the bead area.
Effect of belt angle on the static mechanical behavior of the radial tire is discussed as follows. The calculated results indicate that tire radial deformation under inflation and vertical deformation under static load decrease with the increase of the belt angle. However, at the probably dangerous area in tire shoulder, some important parameters such as shear stress, Mises stress and strain energy density, vary non-monotonously with the belt angle and will reach maximums at a critical angle. In addition, the model with non-uniform belt structure has a perfect performance, with a high vertical rigidity and relatively low shear stress, Mises stress and strain energy density in tire shoulder.
Influence of tread patterns on the load and deformation characters of the radial tire structure in cases of inflation, static loading, free rolling and cornering, on the tire/road contact behavior in cases of free rolling and cornering and on the cornering properties are summarized as follows. In regard to the load and deformation characters, the longitudinal and lateral grooves have extraordinary effect on the mechanical behavior of the tire tread rubber, have some effect on the stress and stain level in the dangerous regions in tire rubbe, and have little effect on the load characteristic of the skeleton structure. In regard to the contact behavior, the existence of the longitudinal and lateral grooves increases the enveloping contact area, the contact pressure level and the inhomogeneity of the contact pressure distribution. In regard to the cornering properties, the cornering stiffness and the aligning stiffness decrease obviously with the addition of the longitudinal and lateral grooves, while the critical slip angle increases slightly.
In conclusion, only when the complex tread patterns are considered can the finite element analysis for the radial tire structure give more precise results.
引文
[1]李炜.2003.子午线轮胎结构有限元分析和设计原理的若干问题研究[D]:[博士].合肥:中国科学技术大学.
[2]庄继德.2001.现代汽车轮胎技术[M].北京:北京理工大学出版社.
[3]Robecchi E,Amici L.1973.Mechanics of the pneumatic tire.Part 1.The tire under inflation alone[J].Tire Science and Technology,1(3):290-345.
[4]Frank F,Hofferberth W.1967.Mechanics of the pneumatic tire[J].Rubber Chemistry and Technology,40(1):271-322.
[5]Walter J D.1978.Cord-rubber tire composites:theory and applications[J].Rubber Chemistry and Technology,51(3):524-576.
[6]束永平.2000.轮胎结构非线性分析的一般壳体精化理论[D]:[博士].上海:上海交通大学.
[7]Lacombe J.2000.Tire model for simulations of vehicle motion on high and low friction road surfaces[C/OL].Orlando,USA:Proceedings of the 2000 Winter Simulation Conference,[2008-03-15].Http://portal.acm.org/citation.cfm?coll=guide&dl=guide&id=510524.
[8]Akasaka T,Katok M,Nihei S,et al.1990.Two-dimensional contact pressure distribution of a radial tire[J].Tire Science and Technology,18(2):80-103.
[9]俞淇,周锋,丁剑平.1998.充气轮胎性能与结构[M].广州:华南理工大学出版社.
[I0]Yamagishi K,Togashi M,Furuya S.1987.A study on the contour of the radial tires:Rolling Contour Optimization Theory—RCOT[J].Tire Science and Technology,15(1):3-29.
[11]Ogawa H,Furuya S,Koseki H,et al.1990.A study on the contour of the truck and bus radial tire.Tire Science and Technology,18(4):236-261.
[12]梁守智,谢递志主编.1990.充气轮胎理论基础[M].化学工业部北京橡胶工业研究设计院,内部资料.
[13]洪宗跃,吴桂忠.2005.子午线轮胎有限元分析 第1讲 有限元在轮胎设计中的应用发展概况[J].轮胎工业,25(10):634-638.
[14]梁守智,钟延埙,张丹秋主编.1989.橡胶工业手册(第四分册)—轮胎[M].北京:化学工业出版社.
[15]俞淇,丁剑平,张安强,等.2006.子午线轮胎结构设计与制造技术[M].北京:化学工业出版社.
[16]Koehne S H,Matute B,Mundl R.2003.Evaluation of tire tread and body interactions in the contact patch[J].Tire Science and Technology,31(3):159-172.
[17]Patel H P,Zorowski C F.1978.Deformation of the pneumatic tire[J].Tire Science and Technology,6(4):233-247.
[18]Kennedy R H,Patel I P,Mcminn M S.1981.Radial truck tire inflation analysis:theory and experiment[J].Rubber Chemistry and Technology,54(3):751-766.
[19]Satyamurthy K,Hirschfelt L R.1987.An axisymmetric finite element and its use to examine the effects of construction variables on radial tires[J].Tire Science and Technology,15(2):97-122.
[20]Wu G Z,He X M.1992.Effects of aspect ratio on the stresses and deformations of radial passenger tires[J].Tire Science and Technology,20(2):74-82.
[21]李兵,李子然,夏源明,等.2007.扁平化对子午线轮胎力学性能影响的有限元分析[J].力学季刊,28(2):209-216.
[22]Kaga H,Okamoto K,Tozawa Y.1977.Stress analysis of a tire under vertical load by a finite element method[J].Tire Science and Technology,5(2):102-118.
[23]Eskinazi J D,Ishihara K.1990.Towards predicting relative belt edge endurance with the finite element method[J].Tire Science and Technology,18(4):216-235.
[24]Noor A K,Tanner J A.1985.Tire modeling and contact problems:advances and trends in the development of computational models for tires[J].Computers and Structures,20(3):517-533.
[25]Noor A K,Peters J M.1996.Reduction technique for tire contact problems[J].Computers and Structures,60(2):223-233.
[26]Danielson K T,Noor A K,Green J S.1996.Computational strategies for tire modeling and analysis[J].Computers and Structures,61(4):673-693.
[27]Danielson K T,Noor A K.1997.Finite elements developed in cylindrical coordinates for three-dimensional tire analysis[J].Tire Science and Technology,25(1):2-28.
[28]Ridha R A,Satyamurthy K,Hirschfelt L R.1985.Finite element modeling of a homogeneous pneumatic tire subjected to footprint loadings[J].Tire Science and Technology,13(2):95-110.
[29]Yan Xiangqiao.2001.Non-linear three-dimensional finite element modeling of radial tires[J].Mathematics and Computers in Simulation.58(1):51-70.
[30]Yan Xiangqiao,Wang Youshan,Feng Xijin.2002.Study for the endurance of radial truck tires with finite element modeling[J].Mathematics and Computers in Simulation,59(6):471-488.
[31]李炜,夏勇,夏源明.2002.载重子午线轮胎帘线受力的有限元分析[J].力学季刊,23(3):323-330.
[32]Sobhanie M.2003.Road load analysis[J].Tire Science and Technology,31(1):19-38.
[33]Rao K,Kumar R,Bohara P,et al.2003.Transient finite element analysis of tire dynamic behavior[J].Tire Science and Technology,31(2):104-127.
[34]Kao B G,Warholic T.2003.BAT model lateral parameters characterization using finite element model[J].Tire Science and Technology,31(4):225-247.
[35]Olatunbosun O A,Bolarinwa O.2004.FE simulation of the effect of tire design parameters on lateral forces and moments[J].Tire Science and Technology,32(3):146-163.
[36]Hall W,Mottram J T,Jones R P.2004.Tire modeling methodology with the explicit finite element code LS-DYNA[J].Tire Science and Technology,32(4):236-261.
[37]Guan Yanjin,Zhao Guoqun,Cheng Gang.2006.Influenqe of belt cord angle on radial tire under different rolling states[J].Journal of Reinforced Plastics and Composites,25(10):1059-1077.
[38]Ghoreishy M H R.2006.Finite element analysis of steady rolling tyre with slip angle:Effect of belt angle[J].Plastics,Rubber and Composites,35(2):83-90.
[39]Ghoreishy M H R.2007.A parametric study on the steady state rolling behaviour of a steel-belted radial tyre[J].Iranian Polymer Journal,16(8):539-548.
[40]Jeong K M,Kim K W,Beom H G.,et al.2007.Finite element analysis of nonuniformity of tires with imperfections[J].Tire Science and Technology,35(3):226-238.
[41]Goldstein A A.1996.Finite element analysis of a quasi-static rolling tire model for determination of truck tire forces and moments[J].Tire Science and Technology,24(4):278-293.
[42]Tonuk E,Unlusoy Y S.2001.Prediction of automobile tire cornering force characteristics by finite element modeling and analysis[J].Computers and Structures.79(13):1219-1232.
[43]王晓军,李炜,夏源明.2005.基于实验的数值反演的滚动轮胎稳态温度场的有限元分析[J].实验力学,20(1):1-9.
[44]吴福麒,李子然,李兵,等.2007.扁平化对子午线轮胎稳态温度场影响的有限元分析[J].中国科学技术大学学报,2007,37(10):1225-1230.
[45]张涛,李兵,夏源明.2005.FEM/BEM在轮胎振动和噪声特性分析中的应用[J].汽车技术,36(9):12-15.
[46]郝勇,李子然,李大应,等.2007.子午线轮胎驻波现象和临界速度的有限元分析[J].固体力学学报,28(3):303-307.
[47]Meschke G,Helnwein P.1994.Large-strain 3D-analysis of fibre-reinforced composite using rebar elements:hyperelastic formulations for cords[J].Computational Mechanics,13(4):241-254.
[48]Meschke G,Payer H J,Mang H A.1997.3D simulations of automobile tires:material modeling,mesh generation,and solution strategies[J].Tire Science and Technology,25(3):154-176.
[49]Sprenger W,Wagner W.On the formulation of geometrically nonlinear 3D-rebar-elements using the enhanced assumed strain method.Engineering Structures,21(1999):209-218.
[50]Ridha R A.1980.Computation of stresses,strains,and deformations of tires[J].Rubber Chemistry and Technology,53(4):849-902.
[51]Akasaka T,Kagami S,Yamazaki S.1993.Deformation analysis of a aadial tire loaded on a crossbar[J].Tire Science and Technology,21(1):40-63.
[52]Akasaka T,Kabe K,Koishi M,et al.1992.Analysis of the contact deformation of tread blocks[J].Tire Science and Technology,20(4):230-253.
[53]Peters J M.2001.Application of the lateral stress theory for groove wander prediction using finite element analysis[J].Tire Science and Technology,29(4):244-257.
[54]Khandhia Y A.1990.Finite element analysis of rubber problems[C].//Proceedings of the IOP short meeting of the stress analysis group of the Institute of Physics,24:11-31.
[55]Kim D M,Kwon Y C,Shin D Y.1997.A study on stress analysis of tire tread block[J].Journal of the Korean Society for Aeronautical and Space Science,25(5):55-61.
[56]Koehne S H,Mature B,Mundl R.2003.Evaluation of tire tread and body interactions in the contact patch[J].Tire Science and Technology,31(3):159-172.
[57]Hofstetter K,Grohs C,Eberhardsteiner J,et al.2006.Sliding behaviour of simplified tire tread patterns investigated by means of FEM[J].Computers and Structures,84(17-18):1151-1163.
[58]Tekkaya A E,Kavakli S.1995.3-D simulation of metal forming processes with automatic mesh generation[J].Steel Research,66(9):377-383.
[59]吕军,王忠金,王仲仁.2001.有限元六面体网格的典型生成方法及发展趋势[J].哈尔 滨:哈尔滨工业大学学报,33(4):485-490.
[60]Subramanian G,Prasanth A,Raveendra V.1996.Algorithm for two- and three-dimensional automatic structured mesh generation[J].Computer and Structure,61(3):471-477.
[61]Bowyer A.1981.Computing dirichlet tessellations[J].The Computer Journal,24(2):162-166.
[62]Watson D.1981.Computing the n-dimensional Delaunay tesselation with applications to Voronoi polytopes[J].The Computer Journal,24(2):167-172.
[63]陈晓霞主编.2004.ANSYS 7.0高级分析[M].北京:机械工业出版社.
[64]Taniguchi T,Goda T,Kasper H,et al.1996.Hexahedral mesh generation of complex composite domain[C].//Proceedingsofthe 5th International Conference on Grid Generation in Computational Field Simulations.Mississippi State University,699-707.
[65]左旭,卫原平,陈军等.1999.三维六面体有限元网格自动划分中的一种单元转换优化算法[J].计算力学学报,16(3):343-348.
[66]Gall R,Tabaddor F,Robbins D,et al.1995.Some notes on the finite element analysis of tires[J].Tire Science and Technology,23(3):175-188.
[67]佳通轮胎(中国)研发中心.2003.CHAMPIRO 55轮胎结构有限元分析[R].内部资料.
[68]Shiraishi M,Yoshinaga H,Miyori A,et al.2000.Simulation of a dynamically rolling tire[J].Tire Science and Technology,28(4):264-276.
[69]Cho J R,Kim K W,Yoo W S,et al.2004.Mesh generation considering detailed tread blocks for reliable 3-D tire analysis[J].Journal of Advances in Engineering Software,35(2):105-113.
[70]Cho J R,Kim K W,Jeo D H,et al.2005.Transient dynamic response analysis of 3-D patterned tire rolling over cleat[J].European Journal of Mechanics A/Solids,24(3):519-531.
[71]Cho J R,Choi J H,Yoo W S,et al.2006.Estimation of dry road braking distance considering frictional energy of patterned tires[J].Finite Elements in Analysis and Design,42(14-15):1248-1257.
[72]Cho J C,Jung B C.2007.Prediction of tread pattern wear by an explicit finite element model[J].Tire Science and Technology,35(4):276-299.
[73]Liu C H,Meschke G,Helnwein P,et al.1995.Tying algorithm for the linking of finite element meshes with different degrees of refinement[J].Computer Assisted Mechanics and Engineering Sciences,2(2):289-305.
[74]ABAQUS Inc..2006.ABAQUS Analysis User's Manual[M].Version 6.6.
[75]Seta E,Nakajima Y,Kamegawa T,et al.2000.Hydroplaning analysis by FEM and FVM:effect of tire rolling and tire pattern on hydroplaning[J].Tire Science and Technology,28(3):140-156.
[76]Oida S,Seta E,Heguri H,et al.2005.Soil/tire interaction analysis using FEM and FVM[J].Tire Science and Technology,33(1):38-62.
[77]Ghoreishy M H R.2006.Finite element analysis of the steel-belted radial tyre with tread pattern under contact load[J].Iranian Polymer Journal,15(8):667-674.
[78]Wu S R,Gu L,Chen H.1997.Airbag tire modeling by the explicit finite element method[J].Tire Science and Technology,25(4):288-300.
[79]Zhang Y,Hazard C.1999.The effects of tire properties and their interactions with the ground and suspension on vehicle dynamics behavior—a finite element approach[J].Tire Science and Technology,27(4):227-249.
[80]Liu H H.2003.Tread discontinuities as source of vibration/noise—transient dynamics of rolling tire[J].Tire Science and Technology,31(4):204-224.
[81]Mousseau R,Markale G..2003.Obstacle impact simulation of an ATV using an efficient tire model[J].Tire Science and Technology,31(4):248-269.
[82]Belytschko T,Liu W K,Moran B著.2002.连续体和结构的非线性有限元[M].庄茁译.北京:清华大学出版社.
[83]Schuring D J.1986.The rolling loss of pneumatic tires[J].Rubber Chemistry and Technology,53(4):601-727.
[84]Kim S J,Savkoor A R.1997.The contact problem of in-plane rolling of tires on a Flat road[J].Vehicle System Dynamics,27(1):189-206.
[85]管迪华,曾祥生,范成建.2006.轮胎动态模型的阻尼和对滚动阻力及动态响应影响的分析[J].汽车工程,28(7):643-646.
[86]Tielking J T,1983.A finite element tire model[J].Tire Science and Technology,11(1):50-63.
[87]Kennedy R H.1985.Three dimensional finite element methodology for steady state rotation with application to the tire[D]:[Ph.D.].Akron,USA:University of Akron.
[88]Kennedy R H,Padovan J.1987.Finite element analysis of a steady-state rotating tire subjected to point load or ground contact[J].Tire Science and Technology,15(4):243-260.
[89]Zheng D.2003.Prediction of tire tread wear with FEM steady state rolling contact simulation[J].Tire Science and Technology,31(3):189-202.
[90]ABAQUS Inc..2004.ABAQUS Analysis User's Manual[M].Version 6.5.
[91]ABAQUS Inc..2006.ABAQUS Release Notes[M].Version 6.6.
[92]陈理君,杨光大,董芹.1997.低噪声轮胎花纹设计原则[J].橡胶工业,44(3):150-155.
[93]Qi J,Herron J R,Sansalone K H,et al.2007.Validation of a steady-state transport analysis for rolling treaded tires[J].Tire Science and Technology,35(3):183-208.
[94]Xia Yong,Li Wei,Xia Yuanming.Test and characterization for the incompressible hyperelastic properties of conditioned rubbers under moderate finite deformation.Acta Mechanica Solida Sinica,2004,Vol.17,No.4,307-314.
[95]夏勇.2004.轮胎胶料在较大变形范围内准静态力学性能的研究——测试、表征以及细观数值本构模型[D]:[博士].合肥:中国科学技术大学,7-16.
[96]董毅.2006.轮胎胶料在较大变形范围内准静态力学性能温度相关性的测试与表征[D]:[硕士].合肥:中国科学技术大学,15-18.
[97]Yeoh O H.1993.Some forms of the strain energy function for rubber[J].Rubber Chemistry and Technology,66(5):754-771.
[98]李炜,夏勇,夏春光,等.2002.轮胎钢丝帘线拉伸力学性能的实验研究[J].实验力学,17(3):307-314.
[99]王晋平,夏根梯.1995.金属压缩试验的一种新方法[J].实验力学,10(3):218-221.
[100]杨苗苗.2004.减法试验在轮胎材料力学性能测试中的应用[D]:[本科].合肥:中国科学技术大学,20-29.
[101]庄继德.1996.汽车轮胎学[M].北京:北京理工大学出版社.
[102]Kennedy R H.2001.Prediction of tire shape change during post cure inflation[J].Tire Science and Technology,29(4):198-215.
[103]Chen B.2002.Influences of thermo-mechanical properties of polymeric cords on tires with and without post-cure inflation[J].Tire Science and Technology,30(3):156-179.
[104]李兵,李子然,夏源明.2007.有限元分析考评实例:子午线轮胎断面测试和轮胎有限元模型的修正[C].∥ABAQUS中国区用户大会2007用户论文集,262-266.
[105]严镇军.2001.复变函数[M].第2版.合肥:中国科学技术大学出版社,171-179.
[106]Staten M L,Canann S A,Owen S J.1998.BMSWEEP:Locating interior nodes during sweeping[C].//Proceedings of the 7th International Meshing Roundtable,Dearborn,USA.7-18.
[107]Lai M W,Benzley S E,Sjaardema G,et al.1998.Amultiple source and target sweeping method for generating all-hexahedral finite element meshes[C].//Proceedings of the 5th International Meshing Roundtable,Dearborn,USA.217-228
[108]翟建军,乔新宇,丁秋林.2007.基于扫掠法的六面体网格生成算法及实现[J].南京航空航天大学学报,39(1):71-74.
[109]庄茁,张帆,岑松,等.2005.ABAQUS非线性有限元分析与实例[M].北京:科学出版社,70-71,291-292.
[110]冯希金,王传铸,李伟,等.2003.用有限元法研究带束层角度对轿车轮胎性能的影响[J].轮胎工业,23(6):329-336.
[111]赵国群,程刚,管延锦,等.2004.带束层角度对子午胎结构性能影响的三维非线性有限元分析[J].弹性体,14(1):35-38.
[112]陈蔚,马改陵,崔文勇.2005.带束层角度对全钢子午线轮胎应力影响的有限元分析[J].北京化工大学学报,32(6):82-86.
[113]ABAQUS Inc.2006.Abaqus Example Problems Manual.Version 6.6.
[114]Belytschko T,Bindeman L P.1993.Assumed Strain Stabilization of the Eight Node Hexahedral Element[J].Computer Methods in Applied Mechanics and Engineering,105(2):225-260.
[115]International Organization for Standardization.1991.ISO 8855.Road vehicles-Vehicle dynamics and road-holding ability-Vocabulary[S].
[116]Society of Automotive Engineers.1978.SAE J670e.Vehicle Dynamics Terminology[S].
[117]喻凡,林逸.2005.汽车系统动力学[M].北京:机械工业出版社,30-67.
[118]Gent A N,Walter J D.2005.The Pneumatic Tire[M].Washington DC,USA:the National Highway Traffic Traffic Safety Adminisrtation,U.S.Department of Transportation.292-294.
[2]庄继德.2001.现代汽车轮胎技术[M].北京:北京理工大学出版社.
[3]Robecchi E,Amici L.1973.Mechanics of the pneumatic tire.Part 1.The tire under inflation alone[J].Tire Science and Technology,1(3):290-345.
[4]Frank F,Hofferberth W.1967.Mechanics of the pneumatic tire[J].Rubber Chemistry and Technology,40(1):271-322.
[5]Walter J D.1978.Cord-rubber tire composites:theory and applications[J].Rubber Chemistry and Technology,51(3):524-576.
[6]束永平.2000.轮胎结构非线性分析的一般壳体精化理论[D]:[博士].上海:上海交通大学.
[7]Lacombe J.2000.Tire model for simulations of vehicle motion on high and low friction road surfaces[C/OL].Orlando,USA:Proceedings of the 2000 Winter Simulation Conference,[2008-03-15].Http://portal.acm.org/citation.cfm?coll=guide&dl=guide&id=510524.
[8]Akasaka T,Katok M,Nihei S,et al.1990.Two-dimensional contact pressure distribution of a radial tire[J].Tire Science and Technology,18(2):80-103.
[9]俞淇,周锋,丁剑平.1998.充气轮胎性能与结构[M].广州:华南理工大学出版社.
[I0]Yamagishi K,Togashi M,Furuya S.1987.A study on the contour of the radial tires:Rolling Contour Optimization Theory—RCOT[J].Tire Science and Technology,15(1):3-29.
[11]Ogawa H,Furuya S,Koseki H,et al.1990.A study on the contour of the truck and bus radial tire.Tire Science and Technology,18(4):236-261.
[12]梁守智,谢递志主编.1990.充气轮胎理论基础[M].化学工业部北京橡胶工业研究设计院,内部资料.
[13]洪宗跃,吴桂忠.2005.子午线轮胎有限元分析 第1讲 有限元在轮胎设计中的应用发展概况[J].轮胎工业,25(10):634-638.
[14]梁守智,钟延埙,张丹秋主编.1989.橡胶工业手册(第四分册)—轮胎[M].北京:化学工业出版社.
[15]俞淇,丁剑平,张安强,等.2006.子午线轮胎结构设计与制造技术[M].北京:化学工业出版社.
[16]Koehne S H,Matute B,Mundl R.2003.Evaluation of tire tread and body interactions in the contact patch[J].Tire Science and Technology,31(3):159-172.
[17]Patel H P,Zorowski C F.1978.Deformation of the pneumatic tire[J].Tire Science and Technology,6(4):233-247.
[18]Kennedy R H,Patel I P,Mcminn M S.1981.Radial truck tire inflation analysis:theory and experiment[J].Rubber Chemistry and Technology,54(3):751-766.
[19]Satyamurthy K,Hirschfelt L R.1987.An axisymmetric finite element and its use to examine the effects of construction variables on radial tires[J].Tire Science and Technology,15(2):97-122.
[20]Wu G Z,He X M.1992.Effects of aspect ratio on the stresses and deformations of radial passenger tires[J].Tire Science and Technology,20(2):74-82.
[21]李兵,李子然,夏源明,等.2007.扁平化对子午线轮胎力学性能影响的有限元分析[J].力学季刊,28(2):209-216.
[22]Kaga H,Okamoto K,Tozawa Y.1977.Stress analysis of a tire under vertical load by a finite element method[J].Tire Science and Technology,5(2):102-118.
[23]Eskinazi J D,Ishihara K.1990.Towards predicting relative belt edge endurance with the finite element method[J].Tire Science and Technology,18(4):216-235.
[24]Noor A K,Tanner J A.1985.Tire modeling and contact problems:advances and trends in the development of computational models for tires[J].Computers and Structures,20(3):517-533.
[25]Noor A K,Peters J M.1996.Reduction technique for tire contact problems[J].Computers and Structures,60(2):223-233.
[26]Danielson K T,Noor A K,Green J S.1996.Computational strategies for tire modeling and analysis[J].Computers and Structures,61(4):673-693.
[27]Danielson K T,Noor A K.1997.Finite elements developed in cylindrical coordinates for three-dimensional tire analysis[J].Tire Science and Technology,25(1):2-28.
[28]Ridha R A,Satyamurthy K,Hirschfelt L R.1985.Finite element modeling of a homogeneous pneumatic tire subjected to footprint loadings[J].Tire Science and Technology,13(2):95-110.
[29]Yan Xiangqiao.2001.Non-linear three-dimensional finite element modeling of radial tires[J].Mathematics and Computers in Simulation.58(1):51-70.
[30]Yan Xiangqiao,Wang Youshan,Feng Xijin.2002.Study for the endurance of radial truck tires with finite element modeling[J].Mathematics and Computers in Simulation,59(6):471-488.
[31]李炜,夏勇,夏源明.2002.载重子午线轮胎帘线受力的有限元分析[J].力学季刊,23(3):323-330.
[32]Sobhanie M.2003.Road load analysis[J].Tire Science and Technology,31(1):19-38.
[33]Rao K,Kumar R,Bohara P,et al.2003.Transient finite element analysis of tire dynamic behavior[J].Tire Science and Technology,31(2):104-127.
[34]Kao B G,Warholic T.2003.BAT model lateral parameters characterization using finite element model[J].Tire Science and Technology,31(4):225-247.
[35]Olatunbosun O A,Bolarinwa O.2004.FE simulation of the effect of tire design parameters on lateral forces and moments[J].Tire Science and Technology,32(3):146-163.
[36]Hall W,Mottram J T,Jones R P.2004.Tire modeling methodology with the explicit finite element code LS-DYNA[J].Tire Science and Technology,32(4):236-261.
[37]Guan Yanjin,Zhao Guoqun,Cheng Gang.2006.Influenqe of belt cord angle on radial tire under different rolling states[J].Journal of Reinforced Plastics and Composites,25(10):1059-1077.
[38]Ghoreishy M H R.2006.Finite element analysis of steady rolling tyre with slip angle:Effect of belt angle[J].Plastics,Rubber and Composites,35(2):83-90.
[39]Ghoreishy M H R.2007.A parametric study on the steady state rolling behaviour of a steel-belted radial tyre[J].Iranian Polymer Journal,16(8):539-548.
[40]Jeong K M,Kim K W,Beom H G.,et al.2007.Finite element analysis of nonuniformity of tires with imperfections[J].Tire Science and Technology,35(3):226-238.
[41]Goldstein A A.1996.Finite element analysis of a quasi-static rolling tire model for determination of truck tire forces and moments[J].Tire Science and Technology,24(4):278-293.
[42]Tonuk E,Unlusoy Y S.2001.Prediction of automobile tire cornering force characteristics by finite element modeling and analysis[J].Computers and Structures.79(13):1219-1232.
[43]王晓军,李炜,夏源明.2005.基于实验的数值反演的滚动轮胎稳态温度场的有限元分析[J].实验力学,20(1):1-9.
[44]吴福麒,李子然,李兵,等.2007.扁平化对子午线轮胎稳态温度场影响的有限元分析[J].中国科学技术大学学报,2007,37(10):1225-1230.
[45]张涛,李兵,夏源明.2005.FEM/BEM在轮胎振动和噪声特性分析中的应用[J].汽车技术,36(9):12-15.
[46]郝勇,李子然,李大应,等.2007.子午线轮胎驻波现象和临界速度的有限元分析[J].固体力学学报,28(3):303-307.
[47]Meschke G,Helnwein P.1994.Large-strain 3D-analysis of fibre-reinforced composite using rebar elements:hyperelastic formulations for cords[J].Computational Mechanics,13(4):241-254.
[48]Meschke G,Payer H J,Mang H A.1997.3D simulations of automobile tires:material modeling,mesh generation,and solution strategies[J].Tire Science and Technology,25(3):154-176.
[49]Sprenger W,Wagner W.On the formulation of geometrically nonlinear 3D-rebar-elements using the enhanced assumed strain method.Engineering Structures,21(1999):209-218.
[50]Ridha R A.1980.Computation of stresses,strains,and deformations of tires[J].Rubber Chemistry and Technology,53(4):849-902.
[51]Akasaka T,Kagami S,Yamazaki S.1993.Deformation analysis of a aadial tire loaded on a crossbar[J].Tire Science and Technology,21(1):40-63.
[52]Akasaka T,Kabe K,Koishi M,et al.1992.Analysis of the contact deformation of tread blocks[J].Tire Science and Technology,20(4):230-253.
[53]Peters J M.2001.Application of the lateral stress theory for groove wander prediction using finite element analysis[J].Tire Science and Technology,29(4):244-257.
[54]Khandhia Y A.1990.Finite element analysis of rubber problems[C].//Proceedings of the IOP short meeting of the stress analysis group of the Institute of Physics,24:11-31.
[55]Kim D M,Kwon Y C,Shin D Y.1997.A study on stress analysis of tire tread block[J].Journal of the Korean Society for Aeronautical and Space Science,25(5):55-61.
[56]Koehne S H,Mature B,Mundl R.2003.Evaluation of tire tread and body interactions in the contact patch[J].Tire Science and Technology,31(3):159-172.
[57]Hofstetter K,Grohs C,Eberhardsteiner J,et al.2006.Sliding behaviour of simplified tire tread patterns investigated by means of FEM[J].Computers and Structures,84(17-18):1151-1163.
[58]Tekkaya A E,Kavakli S.1995.3-D simulation of metal forming processes with automatic mesh generation[J].Steel Research,66(9):377-383.
[59]吕军,王忠金,王仲仁.2001.有限元六面体网格的典型生成方法及发展趋势[J].哈尔 滨:哈尔滨工业大学学报,33(4):485-490.
[60]Subramanian G,Prasanth A,Raveendra V.1996.Algorithm for two- and three-dimensional automatic structured mesh generation[J].Computer and Structure,61(3):471-477.
[61]Bowyer A.1981.Computing dirichlet tessellations[J].The Computer Journal,24(2):162-166.
[62]Watson D.1981.Computing the n-dimensional Delaunay tesselation with applications to Voronoi polytopes[J].The Computer Journal,24(2):167-172.
[63]陈晓霞主编.2004.ANSYS 7.0高级分析[M].北京:机械工业出版社.
[64]Taniguchi T,Goda T,Kasper H,et al.1996.Hexahedral mesh generation of complex composite domain[C].//Proceedingsofthe 5th International Conference on Grid Generation in Computational Field Simulations.Mississippi State University,699-707.
[65]左旭,卫原平,陈军等.1999.三维六面体有限元网格自动划分中的一种单元转换优化算法[J].计算力学学报,16(3):343-348.
[66]Gall R,Tabaddor F,Robbins D,et al.1995.Some notes on the finite element analysis of tires[J].Tire Science and Technology,23(3):175-188.
[67]佳通轮胎(中国)研发中心.2003.CHAMPIRO 55轮胎结构有限元分析[R].内部资料.
[68]Shiraishi M,Yoshinaga H,Miyori A,et al.2000.Simulation of a dynamically rolling tire[J].Tire Science and Technology,28(4):264-276.
[69]Cho J R,Kim K W,Yoo W S,et al.2004.Mesh generation considering detailed tread blocks for reliable 3-D tire analysis[J].Journal of Advances in Engineering Software,35(2):105-113.
[70]Cho J R,Kim K W,Jeo D H,et al.2005.Transient dynamic response analysis of 3-D patterned tire rolling over cleat[J].European Journal of Mechanics A/Solids,24(3):519-531.
[71]Cho J R,Choi J H,Yoo W S,et al.2006.Estimation of dry road braking distance considering frictional energy of patterned tires[J].Finite Elements in Analysis and Design,42(14-15):1248-1257.
[72]Cho J C,Jung B C.2007.Prediction of tread pattern wear by an explicit finite element model[J].Tire Science and Technology,35(4):276-299.
[73]Liu C H,Meschke G,Helnwein P,et al.1995.Tying algorithm for the linking of finite element meshes with different degrees of refinement[J].Computer Assisted Mechanics and Engineering Sciences,2(2):289-305.
[74]ABAQUS Inc..2006.ABAQUS Analysis User's Manual[M].Version 6.6.
[75]Seta E,Nakajima Y,Kamegawa T,et al.2000.Hydroplaning analysis by FEM and FVM:effect of tire rolling and tire pattern on hydroplaning[J].Tire Science and Technology,28(3):140-156.
[76]Oida S,Seta E,Heguri H,et al.2005.Soil/tire interaction analysis using FEM and FVM[J].Tire Science and Technology,33(1):38-62.
[77]Ghoreishy M H R.2006.Finite element analysis of the steel-belted radial tyre with tread pattern under contact load[J].Iranian Polymer Journal,15(8):667-674.
[78]Wu S R,Gu L,Chen H.1997.Airbag tire modeling by the explicit finite element method[J].Tire Science and Technology,25(4):288-300.
[79]Zhang Y,Hazard C.1999.The effects of tire properties and their interactions with the ground and suspension on vehicle dynamics behavior—a finite element approach[J].Tire Science and Technology,27(4):227-249.
[80]Liu H H.2003.Tread discontinuities as source of vibration/noise—transient dynamics of rolling tire[J].Tire Science and Technology,31(4):204-224.
[81]Mousseau R,Markale G..2003.Obstacle impact simulation of an ATV using an efficient tire model[J].Tire Science and Technology,31(4):248-269.
[82]Belytschko T,Liu W K,Moran B著.2002.连续体和结构的非线性有限元[M].庄茁译.北京:清华大学出版社.
[83]Schuring D J.1986.The rolling loss of pneumatic tires[J].Rubber Chemistry and Technology,53(4):601-727.
[84]Kim S J,Savkoor A R.1997.The contact problem of in-plane rolling of tires on a Flat road[J].Vehicle System Dynamics,27(1):189-206.
[85]管迪华,曾祥生,范成建.2006.轮胎动态模型的阻尼和对滚动阻力及动态响应影响的分析[J].汽车工程,28(7):643-646.
[86]Tielking J T,1983.A finite element tire model[J].Tire Science and Technology,11(1):50-63.
[87]Kennedy R H.1985.Three dimensional finite element methodology for steady state rotation with application to the tire[D]:[Ph.D.].Akron,USA:University of Akron.
[88]Kennedy R H,Padovan J.1987.Finite element analysis of a steady-state rotating tire subjected to point load or ground contact[J].Tire Science and Technology,15(4):243-260.
[89]Zheng D.2003.Prediction of tire tread wear with FEM steady state rolling contact simulation[J].Tire Science and Technology,31(3):189-202.
[90]ABAQUS Inc..2004.ABAQUS Analysis User's Manual[M].Version 6.5.
[91]ABAQUS Inc..2006.ABAQUS Release Notes[M].Version 6.6.
[92]陈理君,杨光大,董芹.1997.低噪声轮胎花纹设计原则[J].橡胶工业,44(3):150-155.
[93]Qi J,Herron J R,Sansalone K H,et al.2007.Validation of a steady-state transport analysis for rolling treaded tires[J].Tire Science and Technology,35(3):183-208.
[94]Xia Yong,Li Wei,Xia Yuanming.Test and characterization for the incompressible hyperelastic properties of conditioned rubbers under moderate finite deformation.Acta Mechanica Solida Sinica,2004,Vol.17,No.4,307-314.
[95]夏勇.2004.轮胎胶料在较大变形范围内准静态力学性能的研究——测试、表征以及细观数值本构模型[D]:[博士].合肥:中国科学技术大学,7-16.
[96]董毅.2006.轮胎胶料在较大变形范围内准静态力学性能温度相关性的测试与表征[D]:[硕士].合肥:中国科学技术大学,15-18.
[97]Yeoh O H.1993.Some forms of the strain energy function for rubber[J].Rubber Chemistry and Technology,66(5):754-771.
[98]李炜,夏勇,夏春光,等.2002.轮胎钢丝帘线拉伸力学性能的实验研究[J].实验力学,17(3):307-314.
[99]王晋平,夏根梯.1995.金属压缩试验的一种新方法[J].实验力学,10(3):218-221.
[100]杨苗苗.2004.减法试验在轮胎材料力学性能测试中的应用[D]:[本科].合肥:中国科学技术大学,20-29.
[101]庄继德.1996.汽车轮胎学[M].北京:北京理工大学出版社.
[102]Kennedy R H.2001.Prediction of tire shape change during post cure inflation[J].Tire Science and Technology,29(4):198-215.
[103]Chen B.2002.Influences of thermo-mechanical properties of polymeric cords on tires with and without post-cure inflation[J].Tire Science and Technology,30(3):156-179.
[104]李兵,李子然,夏源明.2007.有限元分析考评实例:子午线轮胎断面测试和轮胎有限元模型的修正[C].∥ABAQUS中国区用户大会2007用户论文集,262-266.
[105]严镇军.2001.复变函数[M].第2版.合肥:中国科学技术大学出版社,171-179.
[106]Staten M L,Canann S A,Owen S J.1998.BMSWEEP:Locating interior nodes during sweeping[C].//Proceedings of the 7th International Meshing Roundtable,Dearborn,USA.7-18.
[107]Lai M W,Benzley S E,Sjaardema G,et al.1998.Amultiple source and target sweeping method for generating all-hexahedral finite element meshes[C].//Proceedings of the 5th International Meshing Roundtable,Dearborn,USA.217-228
[108]翟建军,乔新宇,丁秋林.2007.基于扫掠法的六面体网格生成算法及实现[J].南京航空航天大学学报,39(1):71-74.
[109]庄茁,张帆,岑松,等.2005.ABAQUS非线性有限元分析与实例[M].北京:科学出版社,70-71,291-292.
[110]冯希金,王传铸,李伟,等.2003.用有限元法研究带束层角度对轿车轮胎性能的影响[J].轮胎工业,23(6):329-336.
[111]赵国群,程刚,管延锦,等.2004.带束层角度对子午胎结构性能影响的三维非线性有限元分析[J].弹性体,14(1):35-38.
[112]陈蔚,马改陵,崔文勇.2005.带束层角度对全钢子午线轮胎应力影响的有限元分析[J].北京化工大学学报,32(6):82-86.
[113]ABAQUS Inc.2006.Abaqus Example Problems Manual.Version 6.6.
[114]Belytschko T,Bindeman L P.1993.Assumed Strain Stabilization of the Eight Node Hexahedral Element[J].Computer Methods in Applied Mechanics and Engineering,105(2):225-260.
[115]International Organization for Standardization.1991.ISO 8855.Road vehicles-Vehicle dynamics and road-holding ability-Vocabulary[S].
[116]Society of Automotive Engineers.1978.SAE J670e.Vehicle Dynamics Terminology[S].
[117]喻凡,林逸.2005.汽车系统动力学[M].北京:机械工业出版社,30-67.
[118]Gent A N,Walter J D.2005.The Pneumatic Tire[M].Washington DC,USA:the National Highway Traffic Traffic Safety Adminisrtation,U.S.Department of Transportation.292-294.