锚杆（索）的非局部摩擦效应及其抗拔力研究
|
摘要
在岩土工程问题的力学分析中,通常采用库仑摩擦定律分析摩擦问题,接触面上逐点采用的库仑摩擦定律是局部性质的,即接触面上摩擦域内某质点的摩擦效应只与该点的状态有关。实际上,接触界面是粗糙面之间的接触,某质点的摩擦效应不仅与该点的状态直接相关,还与该点有限大小邻域内的其它点的状态有关,这是一种非局部摩擦效应。
本文基于Oden等提出的非局部摩擦模型分析,建立适合岩土工程的分析模型,以锚杆(索)为研究对象,分析了锚杆(索)剪切应力的非局部摩擦效应,研究了非局部摩擦模型中的核函数对非局部效应的影响；根据梯度理论建立了梯度依赖的非局部摩擦模型并进行应用研究；应用非局部摩擦模型、非线性强度包络线以及考虑中间主应力影响的三剪强度准则分析锚索的极限承载力。主要内容有：
采用修正的非局部摩擦模型对预应力锚索锚固段进行受力分析。根据Kelvin问题的位移解导出预应力锚索锚固段的剪应力,得到了在非局部摩擦模型下的预应力锚索锚固段的剪应力解。对在非局部摩擦模型和局部摩擦模型(库仑模型)下的剪应力结果进行比较,并分析了影响剪应力的非局部效应的相关因素,验证了其有效性和合理性。
采用基于Oden等提出的非局部摩擦模型的修正式,对压力型锚索锚固段受力状态进行分析,采用非局部摩擦模型代替经典的库仑摩擦模型,建立其力的平衡方程,并利用摄动法对其进行求解。对非局部摩擦模型和局部摩擦模型(库仑模型)下剪应力和轴力结果进行了比较,并分析了反映非局部效应的相关因素。
利用Mindlin问题的位移解导出全长粘结式锚杆沿杆体表面所受的剪应力的弹性解,对全长粘结式锚杆进行非局部摩擦分析,得到了在修正后的非局部摩擦模型下的全长粘结式锚杆的侧剪应力。非局部摩擦模型下的全长粘结式锚杆的剪应力分布规律与试验得到的结果以及局部摩擦模型下的计算结果进行了对比。用四种不同的函数作为非局部摩擦模型中的核函数,进行非局部理论中的核函数选择探讨。通过与实验数据的对比,结果表明是合理有效的。
基于梯度理论建立了梯度依赖的非局部摩擦模型,并应用其对全长粘结式锚杆及预应力锚索进行了理论分析,全长粘结式锚杆与预应力锚索的受力特性相似,考虑非局部摩擦效应时,沿锚固体的剪应力峰值比不考虑要小。
采用梯度依赖的非局部摩擦模型和极限平衡原理研究了预应力锚索的极限抗拔力,分析非局部效应对其值的影响。为了分析中间主应力对极限抗拔力的影响,采用三剪屈服准则对其进行研究。同时,还分析了在非线性强度包络线(抛物线型、双曲线型)Mohr强度准则下锚索极限抗拔力,并对其计算结果进行了对比研究。
对岩土工程问题的非局部摩擦分析研究有助于更加深入地认识岩土工程问题中的摩擦机理,分析锚杆(索)的受力性能。采用不同的强度准则分析了锚索的极限抗拔力,这都为锚杆(索)的应用提供理论基础。
The Coulomb's friction model is widely used in geotechnical engineering. In this model, frictional stress at a point on contact surface depends only on the normal stress acting on the point. In order to analyze the effect of contact surface to friction, a nonlocal friction model is introduced to analyze the mechanical characteristics for geomaterial. Roughly speaking, the nonlocal friction model is given to describe that impending motion at a contact point between two deformable bodies will occur when the shear stress at the contact point reaches a value proportional to a weighted measure of the normal stress in a neighborhood of the point.
The nonlocal friction model proposed by Oden et al was modified in this dissertation. Anchor bolt (cable) are analyzed by using the modified nonlocal friction model. The influence of the kernel function in model is also studied. Based on gradient theory, the second-order gradient of stress is introduced into the nonlocal friction model. A gradient dependent nonlocal friction model is established and applied, the triple shear unified failure criterion which can reflect the intermediate principal stress effects on the yield characteristics and the nonlinear Mohr failure criterion are used to studied the ultimate pullout force of prestressed cable. The main content of the paper are summarized as follows:
The modified nonlocal friction model is used to analyze the anchorage mechanism of the interior bond section of the prestressed cables. Based on Kelvin s solution of displacement, a solution of shear stress in the anchorage is derived. The integral form of shear stress is obtained and solved. The nonlocal effect on the contact surface is shown and the solution of shear stress is given. The results are compared with those obtained by the nonlocal frication model and local frication model. Factors affecting the nonlocal friction are discussed.
Based on modified nonlocal friction model, the mechanical condition of the anchorage segment of the pressure-type cable is analyzed. The mechanical equilibrium equation is given and solved with the perturbation method. The nonlocal effect on the contact surface stress distribution is shown and the solution of shear stress and the axial force in a cable is given. The results are compared with those obtained by the nonlocal frication model and local frication model. The results also show that nonlocal effect changes with nonlocal effect size.
The modified nonlocal frication model was used to analyze the wholly grouted anchor. Based on Mindlin s solution of displacement, an elastic solution of shear stress on bolt surface for wholly grouted anchor is derived. Wholly grouted anchor was analyzed by the modified nonlocal frication models which have different kernel functions, the nonlocal effect on the contact surface stress distribution was shown here and the solution of shear stress on bolt surface was given. The results were compared with those obtained by the modified nonlocal frication model which has different kernel functions and local frication model and experimental results in references. It is found that the results obtained by modified nonlocal frication model coincides reasonably well with experimental results, and coincides better than the local frication model. The result shows that nonlocal friction law is more practicable. The nonlocal friction effect is also discussed along with different kernel functions.
Based on the gradient theory, a gradient dependent nonlocal friction model is established and used to analyze the wholly grouted bolt and the pressure-type cable. The mechanical characters of the wholly grouted bolt and the pressure-type cable are similar. When the nonlocal friction effects are considered, the shear stress peak value at the anchorage zone is smaller than those obtained by using the model not accunting for nonlocal effects.
Based on the gradient dependent nonlocal friction model and the ultimate equilibrium principle, the ultimate pullout force of prestressed cable is studied. In order to consider the influence of the intermediate principal stress, the triple shear unified failure criterion was used to analyze the prestressed cable.The nonlinear Mohr failure criterion, such as the hyperbolic Mohr farlure criterion and two-parameter parabolic failure envelope, are used to analyze the ultimate pullout force. A comparative study was made of the results of different strength criterion.
The study is helpful for understanding the friction mechanism in geotechnical problems. Meanwhile, the mechanics characteristics of the anchor bolt (cable) are studied. Based on different failure criterion, the ultimate pullout force of prestressed cable is studied.It can serves as good theoretical bases for the application and development of the anchorage techniques.
本文基于Oden等提出的非局部摩擦模型分析,建立适合岩土工程的分析模型,以锚杆(索)为研究对象,分析了锚杆(索)剪切应力的非局部摩擦效应,研究了非局部摩擦模型中的核函数对非局部效应的影响；根据梯度理论建立了梯度依赖的非局部摩擦模型并进行应用研究；应用非局部摩擦模型、非线性强度包络线以及考虑中间主应力影响的三剪强度准则分析锚索的极限承载力。主要内容有：
采用修正的非局部摩擦模型对预应力锚索锚固段进行受力分析。根据Kelvin问题的位移解导出预应力锚索锚固段的剪应力,得到了在非局部摩擦模型下的预应力锚索锚固段的剪应力解。对在非局部摩擦模型和局部摩擦模型(库仑模型)下的剪应力结果进行比较,并分析了影响剪应力的非局部效应的相关因素,验证了其有效性和合理性。
采用基于Oden等提出的非局部摩擦模型的修正式,对压力型锚索锚固段受力状态进行分析,采用非局部摩擦模型代替经典的库仑摩擦模型,建立其力的平衡方程,并利用摄动法对其进行求解。对非局部摩擦模型和局部摩擦模型(库仑模型)下剪应力和轴力结果进行了比较,并分析了反映非局部效应的相关因素。
利用Mindlin问题的位移解导出全长粘结式锚杆沿杆体表面所受的剪应力的弹性解,对全长粘结式锚杆进行非局部摩擦分析,得到了在修正后的非局部摩擦模型下的全长粘结式锚杆的侧剪应力。非局部摩擦模型下的全长粘结式锚杆的剪应力分布规律与试验得到的结果以及局部摩擦模型下的计算结果进行了对比。用四种不同的函数作为非局部摩擦模型中的核函数,进行非局部理论中的核函数选择探讨。通过与实验数据的对比,结果表明是合理有效的。
基于梯度理论建立了梯度依赖的非局部摩擦模型,并应用其对全长粘结式锚杆及预应力锚索进行了理论分析,全长粘结式锚杆与预应力锚索的受力特性相似,考虑非局部摩擦效应时,沿锚固体的剪应力峰值比不考虑要小。
采用梯度依赖的非局部摩擦模型和极限平衡原理研究了预应力锚索的极限抗拔力,分析非局部效应对其值的影响。为了分析中间主应力对极限抗拔力的影响,采用三剪屈服准则对其进行研究。同时,还分析了在非线性强度包络线(抛物线型、双曲线型)Mohr强度准则下锚索极限抗拔力,并对其计算结果进行了对比研究。
对岩土工程问题的非局部摩擦分析研究有助于更加深入地认识岩土工程问题中的摩擦机理,分析锚杆(索)的受力性能。采用不同的强度准则分析了锚索的极限抗拔力,这都为锚杆(索)的应用提供理论基础。
The Coulomb's friction model is widely used in geotechnical engineering. In this model, frictional stress at a point on contact surface depends only on the normal stress acting on the point. In order to analyze the effect of contact surface to friction, a nonlocal friction model is introduced to analyze the mechanical characteristics for geomaterial. Roughly speaking, the nonlocal friction model is given to describe that impending motion at a contact point between two deformable bodies will occur when the shear stress at the contact point reaches a value proportional to a weighted measure of the normal stress in a neighborhood of the point.
The nonlocal friction model proposed by Oden et al was modified in this dissertation. Anchor bolt (cable) are analyzed by using the modified nonlocal friction model. The influence of the kernel function in model is also studied. Based on gradient theory, the second-order gradient of stress is introduced into the nonlocal friction model. A gradient dependent nonlocal friction model is established and applied, the triple shear unified failure criterion which can reflect the intermediate principal stress effects on the yield characteristics and the nonlinear Mohr failure criterion are used to studied the ultimate pullout force of prestressed cable. The main content of the paper are summarized as follows:
The modified nonlocal friction model is used to analyze the anchorage mechanism of the interior bond section of the prestressed cables. Based on Kelvin s solution of displacement, a solution of shear stress in the anchorage is derived. The integral form of shear stress is obtained and solved. The nonlocal effect on the contact surface is shown and the solution of shear stress is given. The results are compared with those obtained by the nonlocal frication model and local frication model. Factors affecting the nonlocal friction are discussed.
Based on modified nonlocal friction model, the mechanical condition of the anchorage segment of the pressure-type cable is analyzed. The mechanical equilibrium equation is given and solved with the perturbation method. The nonlocal effect on the contact surface stress distribution is shown and the solution of shear stress and the axial force in a cable is given. The results are compared with those obtained by the nonlocal frication model and local frication model. The results also show that nonlocal effect changes with nonlocal effect size.
The modified nonlocal frication model was used to analyze the wholly grouted anchor. Based on Mindlin s solution of displacement, an elastic solution of shear stress on bolt surface for wholly grouted anchor is derived. Wholly grouted anchor was analyzed by the modified nonlocal frication models which have different kernel functions, the nonlocal effect on the contact surface stress distribution was shown here and the solution of shear stress on bolt surface was given. The results were compared with those obtained by the modified nonlocal frication model which has different kernel functions and local frication model and experimental results in references. It is found that the results obtained by modified nonlocal frication model coincides reasonably well with experimental results, and coincides better than the local frication model. The result shows that nonlocal friction law is more practicable. The nonlocal friction effect is also discussed along with different kernel functions.
Based on the gradient theory, a gradient dependent nonlocal friction model is established and used to analyze the wholly grouted bolt and the pressure-type cable. The mechanical characters of the wholly grouted bolt and the pressure-type cable are similar. When the nonlocal friction effects are considered, the shear stress peak value at the anchorage zone is smaller than those obtained by using the model not accunting for nonlocal effects.
Based on the gradient dependent nonlocal friction model and the ultimate equilibrium principle, the ultimate pullout force of prestressed cable is studied. In order to consider the influence of the intermediate principal stress, the triple shear unified failure criterion was used to analyze the prestressed cable.The nonlinear Mohr failure criterion, such as the hyperbolic Mohr farlure criterion and two-parameter parabolic failure envelope, are used to analyze the ultimate pullout force. A comparative study was made of the results of different strength criterion.
The study is helpful for understanding the friction mechanism in geotechnical problems. Meanwhile, the mechanics characteristics of the anchor bolt (cable) are studied. Based on different failure criterion, the ultimate pullout force of prestressed cable is studied.It can serves as good theoretical bases for the application and development of the anchorage techniques.
引文
[1]James.k,Mitchell. Fundamental of soil behavior[M].1976.
[2]陈刚,潘一山.单轴压缩下岩石应变局部化的应变梯度塑性解[J].岩十力学,25(5)：694-699.
[3]Hansor N.W. Influence of surface roughness of prestressing strand on band performance[J]. Journal of Prestressed Conerete Institute,1969,14(1):32-45.
[4]Goto Y., Cracks formed in concrete around deformed tension bars[J]. Journal of Ameriean Conerete Institute,1971,68:(4):244-251.
[5]孔宪宾,任青文,汪洪武.土层锚杆技术的发展及研究动态[J].水利水电科技进展,1999,19(6)： 12-16.
[6]张乐文,汪稔.岩土锚固理论研究之现状[J].岩土力学,2002,23(5)：627-631.
[7]程良奎.岩土锚固的现状与发展[J].土木工程学报,2001,34(3)：7-12.
[8]张乐文,李术才.岩土锚固的现状与发展[J].岩石力学与工程学报,2003,22(增1)2214-2221.
[9]Phillips SHE. Factors affecting the design of anchorages in rock[R]. London:cementation Research Ltd.,1970
[10]蒋忠信.拉力型锚索锚固固段剪应力分布的高斯曲线模式[J].岩土工程学报,2001,23(6)696-699.
[11]何思明,王成华.预应力锚索破坏特性及极限抗拔力研究[J].岩石力学与工程学报2004,23(17)：2966～2971.
[12]尤春安,战玉宝.预应力锚索锚固段的应力分布规律及分析[J].岩力学与工程学报,2005,24(6)：925-928.
[13]尤春安,高明,张利民等.锚固体应力分布的试验研究[J].岩十力学,2004,25(增刊)：63-66.
[14]尤春安.全长粘结式锚杆的受力分析[J].岩石力学与工程学报,2000,19(3)：339-341.
[15]尤春安.压力型锚索锚固固段的受力分析[J].岩土工程学报,2004,26(6)：828-831.
[16]战玉宝,毕宣可,尤春安.预应力锚索锚固段应力分布影响因素分析[J].土木工程学报,2007,40(6)：49-53.
[17]王建宁按共同变形原理计算地锚工程中黏结型锚头内力[A].岩土锚固固工程新技术[M].北京：人民交通出版社,1998,52-63.
[18]杨庆,朱训国,栾茂田.全长注浆岩石锚杆双曲线模型的建立及锚固效应的参数分析[J].岩石力学与工：程学报,2007.26(4)：692-698.
[19]徐景茂,顾雷雨.锚索内锚固段注浆体与孔壁之间峰值抗剪强度试验研究[J].岩石力学与工程学报,2004,23(22)：3765-3769.
[20]Serrano A, Olalla C. Tensile resistance of rock anchors[J].International Journal of Rock Mechanics and Mining Sciences,1999.36(10):449-474.
[21]Serrano A, etal. Ultimate bearing capacity at the tip of a pile in rock-part application[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39(7):847-866.
[22]Brincker R, Ulfrajaer JP, Adamsen P, Languad L, Toft R. Analytical model for hook anchor pullout. In:Widmann, editor. Anchors in theory and practice. Rotterdam:Balkema,1995.p.3-18.
[23]Wijk.GA. Theoretical remark on the field round prestressed rock bolts[J]. Int J Rock Mech Min Sci,1978,6:289-294.
[24]Yue Caia, Tetsuro Esakia, Yujing Jiang. Arock bolt and rock mass interaction model[J]. International Journal of Rock Mechanics& Mining Sciences,2004,41:1055-1067.
[25]Yue Cai a, Tetsuro Esaki, Yujing Jiang.An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling[J]. Tunnelling and Underground Space Technology,2004, 19:607-618.
[26]M. Moosavi, R. Grayeli. A model for cable bolt-rock mass interaction:Integration with discontinuous deformation analysis (DDA) algorithm[J].International Journal of Rock Mechanics & Mining Sciences,2006,43:661-670.
[27]Nak-Kyung Kim, Jong-Sik Park, Sung-Kyu Kim. Numerical simulation of ground anchors[J]. Computers and Geotechnics,2007.34:498-507.
[28]L.P.Yap, A.A.Rodeger. A study of the behavior of vertical rock anchors using the finite element method[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.1984,21:47-61.
[29]Ana Ivanovic, Andy Starkey, Richard D. Neilson, Albert A. Rodger. The influence of load on the frequency response of rock bolt anchorage[J]. Advances in Engineering Software,2003,34: 697-705.
[30]Ana Ivanovic, Richard D. Neilson. Influence of geometry and material properties on the axial vibration of a rock bolt[J]. International Journal of Rock Mechanics& Mining Sciences,2008, 45:941-951.
[31]Brhim Benmokrane, Haixue Xu. ERIC Bellavance. Bond Strength of Cement Grouted Glass Fibre Reinforced Plastic (GFRP) Anchor Bolts[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr. Vol.33, No.5, pp.455-465,1996
[32]A. Kihc, E. Yasar, A.G. Celik. Effect of grout properties on the pull-out load capacity of fully grouted rock bolt[J]. Tunnelling and Underground Space Technology,2002,17:355-362.
[33]邹志晖,汪志林.锚杆在不同岩体中的工作机理[J].岩土工程学报.1993,16(5)：71-78.
[34]Jarred D J, Haberfield C M. Tendon grout interface performance in grouted anchored anchors[A]. Proc. Grond Anchorages and Anchored Structure[C]. London:Thomas Telford,1997.
[35]B.Benmokrance, A. Chennouf. Laboratoty evaluation of cement-based grouts and grouted rock anchors[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1995,32(7):633-642.
[36]S. Yazict, P.K.Kaiser. Bond strength of grouted cable bolts[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1992(29):293-306.
[37]P.K.Kaiser. Effect of stress change on the bond strength of fully-grouted rock bolts[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1992(29):279-292.
[38]S.S. Sakla a, A.F. Ashour, Prediction of tensile capacity of single adhesive anchorsusing neural networks[J], Computers and Structures,2005,83:1792-1803.
[39]M.A. Alqedra a, A.F. Ashouro rediction of shear capacity of single anchors located near concrete edge using neural networks[J]. Computers and Structures 83 (2005) 2495-2502.
[40]范宇洁,郑七振,魏林.预应力锚索锚固体的破坏机理和极限承载能力研究[J].岩石力学与工程学报,2005,24(15)：2765-2769.
[41]许明,张永兴,阴可.锚杆极限承载力的人工神经网络预测[J].岩石力学与工程学报,2002,21(5)：755-758.
[42]魏新江,张世民,危伟.全长粘结式锚杆抗拔力计算公式的探讨[J].岩土工程学报,2006,28(7)：902-905.
[43]何思明,王成华.预应力锚索破坏特性及极限抗拔力研究[J].岩石力学与工程学报,2004,23(17)：2966-2971.
[44]邹金锋,李亮,杨小礼,邓宗伟.基于非线性Mohr-Coulomb强度准则下锚索极限抗拔力研究[J].岩土工程学报,2007,29(1)：107-111.
[45]邓宗伟,冷伍时,李志勇等.基于统一强度准则的预应力锚索极限承载力计算[J].岩石力学与工程学报,2007,26(6)：1138-1144.
[46]黄克智,黄永刚.固体本构关系[M].北京,清华大学出版社,1999.
[47]杨德品,扶名福.连续介质力学[M].南昌：江西高教出版社,1991.
[48]Eringen A C. Nonlocal continuum field theories[M]. New York:Springer,2002.
[49]Eringen A C.非局部场论[J].戴天民译,南京,江苏科学技术出版社,1982.
[50]Eringen A.C.,etal. On nonlocal elasticity[J]. Int. J. Engng Sci,1972,10:233-248.
[51]Eringen A.C.etal.Theories of nonlocal plasticity[J]. Int.J.Engng Sci,1983,10:741-751.
[52]扶名福,丁成辉,吴洪飞.非局部塑性内时本构理论[J].南昌大学学报,1998,20(3)：1-10.
[53]A.C.Eringen.etal. A lubrication theory for fluids with microstructure. int.J.Engen.Sci. 1995,33:2297-2308.
[54]扶名福等.非局部流体力学的互易定律和变分原理[J].浙江大学学报,1991,25(1)：349-357.
[55]黄再兴.关于非局部场论的两点注记[J].固体力学学报,1997.18(2)：158-162.
[56]姚寅,黄再兴.非局部核与应变局部化问题解的相关性[J].南京航空航天大学学报,2008,40(6)：768-773.
[57]王小平,孟国涛.非局部化弹塑性理论及其应用[J].岩石力学与工程学报,2007,26(增1)：2964-2967.
[58]沈新普,沈国晓,陈立新,杨璐.梯度增强的弹塑性损伤非局部本构模型研究[J].应用数学和力学,2005.26(2)：201-214.
[591 Bazant Z P, Pijaudier Cabot. Nonlocal continuum damage, localization instability and convergence[J]. ASME, J Appl Mech,1988,55:287-293
[60]Cosserat E, Cosserat F. Theorie des CorPs Deformables[M]. Paris:Herman et fils.1909.
[61]Aifantis E C. On the role of gradients in the localization of deformation and fracture [J]. Int J EngSci,1992,30:1279-1299.
[62]Aifantis E C. Strain gradient interpretation of size effect [J].Int J.Fract,1999,95:299.
[63]顾晓鲁,钱鸿缙,刘惠珊,汀时敏.地基与基础[M].北京：中国建筑工业出版社,1993.
[64]李录贤,沈亚鹏,叶天麒.摩擦接触问题的数学规划解法[J].应用力学学报,1998,15(2)： 49-55.
[65]冯登泰.接触力学的发展概况[J].力学进展.1987,17(4)：431-446.
[66]Duvaut,G.LOI DE FROTTEMENT NON LOCALE. Journal de Mecanique Theorique et Appliquee Jun23-281980 p73-780750-7240.
[67]Mahrenholtz. O.; Appeltauer, J.; Bontcheva. N.; Brzozowski. M. Nonlocal friction-application to rolling with spread. Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM. Applied Mathematics and Mechanics 76 Suppl 41996 p 603.
[68]Mahrenholtz O., N. Bontcheva, R. lankov, M. Datcheva. Investigation of the infuence of surface roughness on metal forming processes[J]. Mechanics Research Communications, Vol.27, No.4,393-402,2000.
[69]Mahrenholtz. O, N. Bontcheva, R. lankov, M. Datcheva, Influence of asperities on friction during metal forming processes[J], Proc. ECCM'99, Munich,31 August-3 Sept.1999.
[70]Mahrenholtz O., N. Bontcheva, Application of the non-linear non-local friction law to metal forming processes[J], In:Umformung 2000 Plus, Ed. M. Geiger, Meisenbach-Verlag Bamberg, 1999,207-214.
[71]Mahrenholtz O., N. Bontcheva, R. lankov. Nonlocal friction during metal forming processes[J]. ZAMM.2001.81. Suppl.2,353-354.
[72]J T Oden, E B Pires. Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problem s in Elasticity[J], J of App Mech of A SM E,1983,50:67-76.
[73]Demkowicz L and Oden J T. On some existence and uniqueness results in contact problem with nonlocal friction[J], Nonlinear Anal.1982,6,1075-1093.
[74]Touzaline Arezki,Mignot Alain,Existence of solutions for quasistatic problems of unilateral contact with nonlocal friction for nonlinear elastic materials[J], Electronic Journal of Differential Equations,2005, No.99, pp.1-13.
[75]J.A.C. Martins and J.T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal friction and interface laws[J], Nonlinear Analysis, Theory. Meth.Applic.1987,11:407-428.
[76]Marius Cocou, Existence of solutions of a dynamic Signorini's problem with nonlocal friction in viscoelasticity[J], Z. angew. Math. Phys.2002,53:1099-1109.
[77]L.Consiglieri, Steady-state thermal viscous incompressible flows with convective-radiative effects and a nonlocal Coulomb friction law[J], Comm. Appl. Analysis 2006,10 (4):491-502.
[78]L.Consiglieri,, Existence for a class of non-Newtonian fluids with a nonlocal friction boundary condition[J], Acta Mathematica Sinica (Engl. Ser.),2006,22 (2):523-534.
[79]L. Consiglieri, A nonlocal friction problem for a class of non-Newtonian flows[J], Portugaliae Mathematica 2003,60 (2):237-252.
[80]L. Consiglieri, Stationary solutions for a Bingham flow with nonlocal friction, published in Mathematical topics in fluid mechanics (Lisbon,1991),237-243, Ed. J.F.Rodrigues and A.Sequeira, Pitman Res. Notes in Math. Ser.274, Longman Sci. Tech., Harlow,1992.
[81]扶名福,郭良.通过圆弧模具库仑摩擦下下下的平面拉拔数值滑移线场求解[J].塑性工程学报,2001,8(4)：67-71.
[82]扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用[J].力学季刊,2001,22(1)：112-116.
[83]扶名福,郭良.圆柱体镦粗非局部摩擦问题及近似求解[J].固体力学的现代进展(杨桂通教授七十寿辰贺文集). 徐秉业,张善元主编. 北京：万国学术出版社,2000.
[84]扶名福,郭良.采用非局部摩擦定律处理平面镦粗问题及其近似解[J].塑性工程学报,2001,8(1)：59-61.
[85]扶名福,刘伟平.非局部摩擦在工程中的应用.第十二届全国结构工程(2003、10)会议大会邀请报告.
[86]郭良,扶名福.楔形模宽条料拉拔非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2001,23(1)：1-4.
[87]郭良,扶名福.非局部摩擦问题在平面镦粗中的应用及其近似解[J].塑性工程学报,2001,8(1)：59-61
[88]郭良.非局部摩擦及滑移线场优化法在塑性成形中的应用研究[D].南昌大学博士学位论文,2001,6.
[89]罗海宝,扶名福,非局部摩擦在变薄翻边成形工序中的应用[J].塑性工程学报,2003,10(6)： 26-29。
[90]罗海宝,扶名福,采用非局部摩擦模型处理半圆形砧拔长问题时的近似解[J].南昌大学学报(理科版),2003,27(专辑)：88-91.
[91]罗海宝,扶名福,平辊轧制非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2003,25(4)：1-4.
[92]闫小青,罗海宝,扶名福,非局部摩擦模型下轧制单位力分析[J].南昌大学学报(理科版),2004,28(1)：43-45.
[93]闫小青,扶名福,锥形模圆柱挤压非局部摩擦问题[J].南昌大学学报(工科版),2003,25(3)：10-12。
[94]闫小青,闫小青,罗海宝,扶名福等.非局部摩擦在几种塑性成形工艺中的应用[J].应用数学与力学,2005,26(11)：1287-1292。
[95]闫小青.塑性成形中非局部摩擦的数值分析与实验[D],南昌大学博十学位论文,2008,11)
[96]李茂林,扶名福,闫小青.锥形模圆柱体超塑性挤压非局部摩擦分析[J],南昌大学学报(理科版),2007,31(6)：586-589；
[97]李茂林,扶名福.非局部摩擦模型下圆板的超塑性锻压[J].南昌大学学报(理科版),2008,32(6)：554-556.
[98]李茂林,扶名福,闫小青.楔形模宽条料超塑性拉拔非局部摩擦分析[J].锻压技术, 2008,33(6)：125-127.
[99]蔡改贫,翁海珊,姜志宏等.振动拉拔的非非局部摩擦问题的近似求解及表面效应初探[J].机械工程学报,2006,42(8)：190-194.
[100]蔡改贫,张晖,刘峥.金属脉冲振动拉拔成形一维表面效应机理分析[J].锻压技术,2009,34(1)：130-134.
[101]刘伟平,扶名福、曾宪坤,彭强生.深长摩擦桩的非局部摩擦分析[J].地质与勘探,2005,41(4)：102-105.
[102]杨海清,周小平,张永兴.管缝式锚杆在拉拔荷载作用下受力分析模型[J].岩土力学,2007.28(增)：236-240.
[103]何思明,李新坡.预应力锚杆作用机制研究[J].岩石力学与工程学报。2006,25(9)：1876-1880.
[104]汪海滨,高波.预应力锚索荷载分布机理原位试验研究[J].岩石力学与工程学报,2005,24(12)：2113-2118.
[105]中国工：程建设标准化协会标准.岩十锚杆(索)技术规程(CECS22：2005)[S].北京：中国计划出版社出版,2005.
[106]程良全,范景伦,韩军,许建平.岩十锚固[M].2003.中国建筑工业出版社.
[107]吉卫东.预应力锚固机理分析[J].土工基础,2009,23(4)：59-62.
[108]建设部,国家质量监督检验检疫总局,GB50330-2002,建筑边工程技术规范[S].北京：中国建筑工业出版社,2002.
[109]张端良,董燕军,唐乐人,胡毅夫.预应力锚索锚固段周边剪应力分布特性的弹性理论分析[J].岩石力学与工程学报,2004,23(增2)：4735-4738.
[110]尤春安,战玉宝.预应力锚索锚固固段界面滑移的细观力学分析[J].岩石力学与工程学报,2009,28(J0)：1976-1985.
[111]KILIC A, YASAR E, CELIK A G. Effect of grout properties on the pull-out load capacity of fully grouted rock bolt[J]. Tunnelling and Underground Space Technology,2002,17(4): 355-362.
[112]张永兴,饶枭宇,唐树名等.预应力锚索注浆体与岩石结界面抗剪强度试验[J].中国公路学报,2008,21(6)：1-6.
[113]伍国军,陈卫忠,贾善坡,杨建平.岩石锚固界面剪切流变试验及模型研究[J].岩石力学与工程学报,2010,29(3)：520-527.
[114]肖世国,周德培.非全长粘结型锚索锚固段长度的一种确定方法[J].岩石力学与工程学报,2004.23(9)：1530-1534.
[115]丁秀丽,盛谦,韩军,程良奎,白世伟.预应力锚索锚固机理的数值模拟试验研究[J].岩石学与工程学报,2202,21(7)：980-988.
[116]杜庆华,余寿文,姚振汉.弹性理论[M].北京科学出版社,1986.
[117]J.T.Oden and E.B.Pires. Numerical analysis of certain contact problems with non-classical friction laws[J]. Comput.& Struct, Vol.16, No.1-4, p 481-485,1983.
[118]张端良,董燕军,唐乐人,胡毅夫.预应力锚索锚固段周边剪应力分布特性的弹性理论分析[J].岩石力学与工程学报,2004,23(增2)：4735-4738.
[119]王艳芬,王元汉,盛谦.拉力型锚索锚固段周边岩体的应力分布[J].岩土力学,2006,27 (增)：948-951.
[120]程良奎,胡建林.土层锚杆的几个力学问题[J].见：中国岩土锚固工程协会主编.岩十工程中的锚固技术.北京：人民交通出版社,1996.
[121]章青,陈爱玖,李珍,卓家寿,孙学毅.基于界面元法的改进压力集中型锚索作用分析[J].工程力学,2008,25(4)：45-49.
[122]夏元友,范卫琴,芮瑞.王艳丽压力分散型锚索作用效果的数值模拟分析[J].岩土力学2008.29(11)：3144-3148.
[123]刑占清,杨健,杨晓东.压力分散型无粘结预应力锚索作用机理及内锚固段长度研究[J].中国水利水电科学研究院学报,2006,(6)：88-92.
[124]杨庆,朱训国,栾茂田.压力型锚索锚固段应力分布及影响参数分析[J].岩石力学与工程学报,2006,25(增2)：4065-4070.
[125]A.H.奈弗著.摄动方法[J].王辅俊等译,上海：上海科技出版社,1984.
[126]王忠昶,栾茂田,杨庆.基于不同权函数的非局部理论对比分析[J].西安交通大学学报2006,40(11)：1348-1356.
[127]卡姆克.E.常微分方程手册[M].北京：科学出版社,1977.
[128]邹振祝,陈建.无单元法在孔洞应力集中问题中的应用[J].石家庄铁道学院学报,2000,13(2)：1-5.
[129]刘天祥,刘更,朱均,虞烈.无网格法的研究进展[J].机械工程和学报,2002,38(5)：7-12.
[130]刘振华,刘建新,庞承宗.静电场无网格方法中权函数的研究[J].华北电力大学学报,2003.30(1)：18-21.
[131]Kroner E. Elasticity theory of material with long range cohesive forces[J]. Int J Solids Struct,1967,3:732-742.
[132]Eringen A C. Nonlocal polar elastic continua[J]. Int. J Solids Struct.,1972,10:223-248.
[133]赵启林,孙宝俊.非局部损伤模型的客观性研究[J].工程力学,2003,20(5)：185-189.
[134]Xikui Li, S Cescotto. A mixed element method in gradient plasticity for pressure dependent material and modelling of strain localization[J]. Computer Methods Appl Mechanics Engng,1997,144:287-305.
[135]Aifantis EC. On the role of gradients in the localization of deformation and fracture[J]. International Journal of Engineering Science 1992,30:1279-1299.
[136]Rene de Borst, J.Pamin, MareG, D.Geers, On coupled gradient-dependent plasticity and damage theories with a view to localization analysis[J].Eur.J.Mech.A Solids 1999,18(3):939-962
[137]王学滨,潘一山,宋维源.岩石试件尺寸效应的塑性剪切应变梯度模型[J].岩土工程学报,2001,23(6)：701-703.
[138]赵冰,李宁.盛国刚软化岩土介质的应变局部化研究进展——意义.现状.应变梯度[J].岩土力学2005,26(3)：494-499.
[139]赵彭年.松散介质力学[M].北京：地震出版社,1995.
[140]YANG Xiao-li, LI Liang, YIN Jian-hua. Stability analysis of rock slopes with a modified Hoek-Brown failure criterion[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(2):181-190.
[141]YANG Xiao-li,LI Liang,YIN Jian-hua.Seismic and static stability analysis for rock slopes by a kinematical approach[J].Geotechnique,2004,54(8):543-549.
[142]Mogi K. Effect of intermediate principal stress on rockfailure[J]. J Geophys Res,1967,72: 51175131.
[143]Michelis P. Polyaxial yielding of granular rock[J]. J EngMech ASCE,1985,111(18):1049 1066.
[144]许东俊,耿乃光.岩石强度随中间主应力的变化规律[J].固体力学学报,1985,6(1)：72-80.
[145]俞茂宏,杨松岩,刘春阳等.统一平面应变滑移线场理论[J].土木工程学报.199730(2)：14-26.
[146]俞茂宏.双剪理论及其应用[M].北京：科学出版社,1998.
[147]胡小荣,俞茂宏.岩土类介质强度准则新探[J].岩石力学与工：程学报,2004,23(18)：3037-3043.
[148]胡小荣,林太清.三剪屈服准则及其在极限内压计算中的应用[J].中国有色金属学报,2007,17(2)：207-215.
[149]胡小荣.基于三剪屈服准则的空间轴对特征线场理论及其应用[J].中国有色金属学报,2007,17(9)：1447-1452.
[150]赵彭年.二次抛物线型极限曲线的巷道围岩应力及位移[J].有色金属,1979,(1)：41-44.
[151]李春光,郑宏,葛修润,王水林.双参数抛物型Mohr强度准则及其材料破坏规律研究[J].岩石力学与工程学报,2005,24(24)：4428-4433.
[152]佘成学,刘 杰.基于Mohr强度理论的双参数抛物线型屈服准则[J].武汉大学学报(工学版),2008,41(1)：31—34.
[153]李顺群,焦学英,王芳.Mohr包线的二次曲线形式[J].辽宁工程技术大学学报,2005,24(6)：853-855.
[154]周火明,熊诗湖,刘小红等.三峡船闸边坡岩体拉剪试验及强度准则研究[J].岩石力学与工程学报,2005,24(24)：4418-4421.
[155]谭学术,鲜学福,郑道访等.复合岩体力学理论及其应用[M].北京：煤炭工业出版社,1994.
[156]李云安,葛修润,糜崇蓉,张鸿昌.岩-土-混凝土破坏准则及其强度参数估算[J].岩石力学与工程学报,2004,23(5)：770-776.
[157]蔡美峰,何满潮,刘东燕.岩石力学与工程[M].科·学出版社,2002.
[158]刘佑荣,唐辉明.岩体力学[M].武汉：中国地质大学出版社,1999.
[159]李春光,郑宏,葛修润,王水林.双参数抛物型Mohr强度准则及其材料破坏规律研究[J],岩石力学与工程学报,2005,24(24)：4428-4433.
[160]蔡中民,徐文令,张建文.非线性Mohr-Coulomb体边坡的极限荷载[J].固体力学学报,1995,16(3)：254-258.
[2]陈刚,潘一山.单轴压缩下岩石应变局部化的应变梯度塑性解[J].岩十力学,25(5)：694-699.
[3]Hansor N.W. Influence of surface roughness of prestressing strand on band performance[J]. Journal of Prestressed Conerete Institute,1969,14(1):32-45.
[4]Goto Y., Cracks formed in concrete around deformed tension bars[J]. Journal of Ameriean Conerete Institute,1971,68:(4):244-251.
[5]孔宪宾,任青文,汪洪武.土层锚杆技术的发展及研究动态[J].水利水电科技进展,1999,19(6)： 12-16.
[6]张乐文,汪稔.岩土锚固理论研究之现状[J].岩土力学,2002,23(5)：627-631.
[7]程良奎.岩土锚固的现状与发展[J].土木工程学报,2001,34(3)：7-12.
[8]张乐文,李术才.岩土锚固的现状与发展[J].岩石力学与工程学报,2003,22(增1)2214-2221.
[9]Phillips SHE. Factors affecting the design of anchorages in rock[R]. London:cementation Research Ltd.,1970
[10]蒋忠信.拉力型锚索锚固固段剪应力分布的高斯曲线模式[J].岩土工程学报,2001,23(6)696-699.
[11]何思明,王成华.预应力锚索破坏特性及极限抗拔力研究[J].岩石力学与工程学报2004,23(17)：2966～2971.
[12]尤春安,战玉宝.预应力锚索锚固段的应力分布规律及分析[J].岩力学与工程学报,2005,24(6)：925-928.
[13]尤春安,高明,张利民等.锚固体应力分布的试验研究[J].岩十力学,2004,25(增刊)：63-66.
[14]尤春安.全长粘结式锚杆的受力分析[J].岩石力学与工程学报,2000,19(3)：339-341.
[15]尤春安.压力型锚索锚固固段的受力分析[J].岩土工程学报,2004,26(6)：828-831.
[16]战玉宝,毕宣可,尤春安.预应力锚索锚固段应力分布影响因素分析[J].土木工程学报,2007,40(6)：49-53.
[17]王建宁按共同变形原理计算地锚工程中黏结型锚头内力[A].岩土锚固固工程新技术[M].北京：人民交通出版社,1998,52-63.
[18]杨庆,朱训国,栾茂田.全长注浆岩石锚杆双曲线模型的建立及锚固效应的参数分析[J].岩石力学与工：程学报,2007.26(4)：692-698.
[19]徐景茂,顾雷雨.锚索内锚固段注浆体与孔壁之间峰值抗剪强度试验研究[J].岩石力学与工程学报,2004,23(22)：3765-3769.
[20]Serrano A, Olalla C. Tensile resistance of rock anchors[J].International Journal of Rock Mechanics and Mining Sciences,1999.36(10):449-474.
[21]Serrano A, etal. Ultimate bearing capacity at the tip of a pile in rock-part application[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39(7):847-866.
[22]Brincker R, Ulfrajaer JP, Adamsen P, Languad L, Toft R. Analytical model for hook anchor pullout. In:Widmann, editor. Anchors in theory and practice. Rotterdam:Balkema,1995.p.3-18.
[23]Wijk.GA. Theoretical remark on the field round prestressed rock bolts[J]. Int J Rock Mech Min Sci,1978,6:289-294.
[24]Yue Caia, Tetsuro Esakia, Yujing Jiang. Arock bolt and rock mass interaction model[J]. International Journal of Rock Mechanics& Mining Sciences,2004,41:1055-1067.
[25]Yue Cai a, Tetsuro Esaki, Yujing Jiang.An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling[J]. Tunnelling and Underground Space Technology,2004, 19:607-618.
[26]M. Moosavi, R. Grayeli. A model for cable bolt-rock mass interaction:Integration with discontinuous deformation analysis (DDA) algorithm[J].International Journal of Rock Mechanics & Mining Sciences,2006,43:661-670.
[27]Nak-Kyung Kim, Jong-Sik Park, Sung-Kyu Kim. Numerical simulation of ground anchors[J]. Computers and Geotechnics,2007.34:498-507.
[28]L.P.Yap, A.A.Rodeger. A study of the behavior of vertical rock anchors using the finite element method[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr.1984,21:47-61.
[29]Ana Ivanovic, Andy Starkey, Richard D. Neilson, Albert A. Rodger. The influence of load on the frequency response of rock bolt anchorage[J]. Advances in Engineering Software,2003,34: 697-705.
[30]Ana Ivanovic, Richard D. Neilson. Influence of geometry and material properties on the axial vibration of a rock bolt[J]. International Journal of Rock Mechanics& Mining Sciences,2008, 45:941-951.
[31]Brhim Benmokrane, Haixue Xu. ERIC Bellavance. Bond Strength of Cement Grouted Glass Fibre Reinforced Plastic (GFRP) Anchor Bolts[J]. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr. Vol.33, No.5, pp.455-465,1996
[32]A. Kihc, E. Yasar, A.G. Celik. Effect of grout properties on the pull-out load capacity of fully grouted rock bolt[J]. Tunnelling and Underground Space Technology,2002,17:355-362.
[33]邹志晖,汪志林.锚杆在不同岩体中的工作机理[J].岩土工程学报.1993,16(5)：71-78.
[34]Jarred D J, Haberfield C M. Tendon grout interface performance in grouted anchored anchors[A]. Proc. Grond Anchorages and Anchored Structure[C]. London:Thomas Telford,1997.
[35]B.Benmokrance, A. Chennouf. Laboratoty evaluation of cement-based grouts and grouted rock anchors[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1995,32(7):633-642.
[36]S. Yazict, P.K.Kaiser. Bond strength of grouted cable bolts[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1992(29):293-306.
[37]P.K.Kaiser. Effect of stress change on the bond strength of fully-grouted rock bolts[J]. Int. J. Rock Mech.Min. Sci.& Geomech. Abstr.1992(29):279-292.
[38]S.S. Sakla a, A.F. Ashour, Prediction of tensile capacity of single adhesive anchorsusing neural networks[J], Computers and Structures,2005,83:1792-1803.
[39]M.A. Alqedra a, A.F. Ashouro rediction of shear capacity of single anchors located near concrete edge using neural networks[J]. Computers and Structures 83 (2005) 2495-2502.
[40]范宇洁,郑七振,魏林.预应力锚索锚固体的破坏机理和极限承载能力研究[J].岩石力学与工程学报,2005,24(15)：2765-2769.
[41]许明,张永兴,阴可.锚杆极限承载力的人工神经网络预测[J].岩石力学与工程学报,2002,21(5)：755-758.
[42]魏新江,张世民,危伟.全长粘结式锚杆抗拔力计算公式的探讨[J].岩土工程学报,2006,28(7)：902-905.
[43]何思明,王成华.预应力锚索破坏特性及极限抗拔力研究[J].岩石力学与工程学报,2004,23(17)：2966-2971.
[44]邹金锋,李亮,杨小礼,邓宗伟.基于非线性Mohr-Coulomb强度准则下锚索极限抗拔力研究[J].岩土工程学报,2007,29(1)：107-111.
[45]邓宗伟,冷伍时,李志勇等.基于统一强度准则的预应力锚索极限承载力计算[J].岩石力学与工程学报,2007,26(6)：1138-1144.
[46]黄克智,黄永刚.固体本构关系[M].北京,清华大学出版社,1999.
[47]杨德品,扶名福.连续介质力学[M].南昌：江西高教出版社,1991.
[48]Eringen A C. Nonlocal continuum field theories[M]. New York:Springer,2002.
[49]Eringen A C.非局部场论[J].戴天民译,南京,江苏科学技术出版社,1982.
[50]Eringen A.C.,etal. On nonlocal elasticity[J]. Int. J. Engng Sci,1972,10:233-248.
[51]Eringen A.C.etal.Theories of nonlocal plasticity[J]. Int.J.Engng Sci,1983,10:741-751.
[52]扶名福,丁成辉,吴洪飞.非局部塑性内时本构理论[J].南昌大学学报,1998,20(3)：1-10.
[53]A.C.Eringen.etal. A lubrication theory for fluids with microstructure. int.J.Engen.Sci. 1995,33:2297-2308.
[54]扶名福等.非局部流体力学的互易定律和变分原理[J].浙江大学学报,1991,25(1)：349-357.
[55]黄再兴.关于非局部场论的两点注记[J].固体力学学报,1997.18(2)：158-162.
[56]姚寅,黄再兴.非局部核与应变局部化问题解的相关性[J].南京航空航天大学学报,2008,40(6)：768-773.
[57]王小平,孟国涛.非局部化弹塑性理论及其应用[J].岩石力学与工程学报,2007,26(增1)：2964-2967.
[58]沈新普,沈国晓,陈立新,杨璐.梯度增强的弹塑性损伤非局部本构模型研究[J].应用数学和力学,2005.26(2)：201-214.
[591 Bazant Z P, Pijaudier Cabot. Nonlocal continuum damage, localization instability and convergence[J]. ASME, J Appl Mech,1988,55:287-293
[60]Cosserat E, Cosserat F. Theorie des CorPs Deformables[M]. Paris:Herman et fils.1909.
[61]Aifantis E C. On the role of gradients in the localization of deformation and fracture [J]. Int J EngSci,1992,30:1279-1299.
[62]Aifantis E C. Strain gradient interpretation of size effect [J].Int J.Fract,1999,95:299.
[63]顾晓鲁,钱鸿缙,刘惠珊,汀时敏.地基与基础[M].北京：中国建筑工业出版社,1993.
[64]李录贤,沈亚鹏,叶天麒.摩擦接触问题的数学规划解法[J].应用力学学报,1998,15(2)： 49-55.
[65]冯登泰.接触力学的发展概况[J].力学进展.1987,17(4)：431-446.
[66]Duvaut,G.LOI DE FROTTEMENT NON LOCALE. Journal de Mecanique Theorique et Appliquee Jun23-281980 p73-780750-7240.
[67]Mahrenholtz. O.; Appeltauer, J.; Bontcheva. N.; Brzozowski. M. Nonlocal friction-application to rolling with spread. Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM. Applied Mathematics and Mechanics 76 Suppl 41996 p 603.
[68]Mahrenholtz O., N. Bontcheva, R. lankov, M. Datcheva. Investigation of the infuence of surface roughness on metal forming processes[J]. Mechanics Research Communications, Vol.27, No.4,393-402,2000.
[69]Mahrenholtz. O, N. Bontcheva, R. lankov, M. Datcheva, Influence of asperities on friction during metal forming processes[J], Proc. ECCM'99, Munich,31 August-3 Sept.1999.
[70]Mahrenholtz O., N. Bontcheva, Application of the non-linear non-local friction law to metal forming processes[J], In:Umformung 2000 Plus, Ed. M. Geiger, Meisenbach-Verlag Bamberg, 1999,207-214.
[71]Mahrenholtz O., N. Bontcheva, R. lankov. Nonlocal friction during metal forming processes[J]. ZAMM.2001.81. Suppl.2,353-354.
[72]J T Oden, E B Pires. Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problem s in Elasticity[J], J of App Mech of A SM E,1983,50:67-76.
[73]Demkowicz L and Oden J T. On some existence and uniqueness results in contact problem with nonlocal friction[J], Nonlinear Anal.1982,6,1075-1093.
[74]Touzaline Arezki,Mignot Alain,Existence of solutions for quasistatic problems of unilateral contact with nonlocal friction for nonlinear elastic materials[J], Electronic Journal of Differential Equations,2005, No.99, pp.1-13.
[75]J.A.C. Martins and J.T. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal friction and interface laws[J], Nonlinear Analysis, Theory. Meth.Applic.1987,11:407-428.
[76]Marius Cocou, Existence of solutions of a dynamic Signorini's problem with nonlocal friction in viscoelasticity[J], Z. angew. Math. Phys.2002,53:1099-1109.
[77]L.Consiglieri, Steady-state thermal viscous incompressible flows with convective-radiative effects and a nonlocal Coulomb friction law[J], Comm. Appl. Analysis 2006,10 (4):491-502.
[78]L.Consiglieri,, Existence for a class of non-Newtonian fluids with a nonlocal friction boundary condition[J], Acta Mathematica Sinica (Engl. Ser.),2006,22 (2):523-534.
[79]L. Consiglieri, A nonlocal friction problem for a class of non-Newtonian flows[J], Portugaliae Mathematica 2003,60 (2):237-252.
[80]L. Consiglieri, Stationary solutions for a Bingham flow with nonlocal friction, published in Mathematical topics in fluid mechanics (Lisbon,1991),237-243, Ed. J.F.Rodrigues and A.Sequeira, Pitman Res. Notes in Math. Ser.274, Longman Sci. Tech., Harlow,1992.
[81]扶名福,郭良.通过圆弧模具库仑摩擦下下下的平面拉拔数值滑移线场求解[J].塑性工程学报,2001,8(4)：67-71.
[82]扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用[J].力学季刊,2001,22(1)：112-116.
[83]扶名福,郭良.圆柱体镦粗非局部摩擦问题及近似求解[J].固体力学的现代进展(杨桂通教授七十寿辰贺文集). 徐秉业,张善元主编. 北京：万国学术出版社,2000.
[84]扶名福,郭良.采用非局部摩擦定律处理平面镦粗问题及其近似解[J].塑性工程学报,2001,8(1)：59-61.
[85]扶名福,刘伟平.非局部摩擦在工程中的应用.第十二届全国结构工程(2003、10)会议大会邀请报告.
[86]郭良,扶名福.楔形模宽条料拉拔非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2001,23(1)：1-4.
[87]郭良,扶名福.非局部摩擦问题在平面镦粗中的应用及其近似解[J].塑性工程学报,2001,8(1)：59-61
[88]郭良.非局部摩擦及滑移线场优化法在塑性成形中的应用研究[D].南昌大学博士学位论文,2001,6.
[89]罗海宝,扶名福,非局部摩擦在变薄翻边成形工序中的应用[J].塑性工程学报,2003,10(6)： 26-29。
[90]罗海宝,扶名福,采用非局部摩擦模型处理半圆形砧拔长问题时的近似解[J].南昌大学学报(理科版),2003,27(专辑)：88-91.
[91]罗海宝,扶名福,平辊轧制非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2003,25(4)：1-4.
[92]闫小青,罗海宝,扶名福,非局部摩擦模型下轧制单位力分析[J].南昌大学学报(理科版),2004,28(1)：43-45.
[93]闫小青,扶名福,锥形模圆柱挤压非局部摩擦问题[J].南昌大学学报(工科版),2003,25(3)：10-12。
[94]闫小青,闫小青,罗海宝,扶名福等.非局部摩擦在几种塑性成形工艺中的应用[J].应用数学与力学,2005,26(11)：1287-1292。
[95]闫小青.塑性成形中非局部摩擦的数值分析与实验[D],南昌大学博十学位论文,2008,11)
[96]李茂林,扶名福,闫小青.锥形模圆柱体超塑性挤压非局部摩擦分析[J],南昌大学学报(理科版),2007,31(6)：586-589；
[97]李茂林,扶名福.非局部摩擦模型下圆板的超塑性锻压[J].南昌大学学报(理科版),2008,32(6)：554-556.
[98]李茂林,扶名福,闫小青.楔形模宽条料超塑性拉拔非局部摩擦分析[J].锻压技术, 2008,33(6)：125-127.
[99]蔡改贫,翁海珊,姜志宏等.振动拉拔的非非局部摩擦问题的近似求解及表面效应初探[J].机械工程学报,2006,42(8)：190-194.
[100]蔡改贫,张晖,刘峥.金属脉冲振动拉拔成形一维表面效应机理分析[J].锻压技术,2009,34(1)：130-134.
[101]刘伟平,扶名福、曾宪坤,彭强生.深长摩擦桩的非局部摩擦分析[J].地质与勘探,2005,41(4)：102-105.
[102]杨海清,周小平,张永兴.管缝式锚杆在拉拔荷载作用下受力分析模型[J].岩土力学,2007.28(增)：236-240.
[103]何思明,李新坡.预应力锚杆作用机制研究[J].岩石力学与工程学报。2006,25(9)：1876-1880.
[104]汪海滨,高波.预应力锚索荷载分布机理原位试验研究[J].岩石力学与工程学报,2005,24(12)：2113-2118.
[105]中国工：程建设标准化协会标准.岩十锚杆(索)技术规程(CECS22：2005)[S].北京：中国计划出版社出版,2005.
[106]程良全,范景伦,韩军,许建平.岩十锚固[M].2003.中国建筑工业出版社.
[107]吉卫东.预应力锚固机理分析[J].土工基础,2009,23(4)：59-62.
[108]建设部,国家质量监督检验检疫总局,GB50330-2002,建筑边工程技术规范[S].北京：中国建筑工业出版社,2002.
[109]张端良,董燕军,唐乐人,胡毅夫.预应力锚索锚固段周边剪应力分布特性的弹性理论分析[J].岩石力学与工程学报,2004,23(增2)：4735-4738.
[110]尤春安,战玉宝.预应力锚索锚固固段界面滑移的细观力学分析[J].岩石力学与工程学报,2009,28(J0)：1976-1985.
[111]KILIC A, YASAR E, CELIK A G. Effect of grout properties on the pull-out load capacity of fully grouted rock bolt[J]. Tunnelling and Underground Space Technology,2002,17(4): 355-362.
[112]张永兴,饶枭宇,唐树名等.预应力锚索注浆体与岩石结界面抗剪强度试验[J].中国公路学报,2008,21(6)：1-6.
[113]伍国军,陈卫忠,贾善坡,杨建平.岩石锚固界面剪切流变试验及模型研究[J].岩石力学与工程学报,2010,29(3)：520-527.
[114]肖世国,周德培.非全长粘结型锚索锚固段长度的一种确定方法[J].岩石力学与工程学报,2004.23(9)：1530-1534.
[115]丁秀丽,盛谦,韩军,程良奎,白世伟.预应力锚索锚固机理的数值模拟试验研究[J].岩石学与工程学报,2202,21(7)：980-988.
[116]杜庆华,余寿文,姚振汉.弹性理论[M].北京科学出版社,1986.
[117]J.T.Oden and E.B.Pires. Numerical analysis of certain contact problems with non-classical friction laws[J]. Comput.& Struct, Vol.16, No.1-4, p 481-485,1983.
[118]张端良,董燕军,唐乐人,胡毅夫.预应力锚索锚固段周边剪应力分布特性的弹性理论分析[J].岩石力学与工程学报,2004,23(增2)：4735-4738.
[119]王艳芬,王元汉,盛谦.拉力型锚索锚固段周边岩体的应力分布[J].岩土力学,2006,27 (增)：948-951.
[120]程良奎,胡建林.土层锚杆的几个力学问题[J].见：中国岩土锚固工程协会主编.岩十工程中的锚固技术.北京：人民交通出版社,1996.
[121]章青,陈爱玖,李珍,卓家寿,孙学毅.基于界面元法的改进压力集中型锚索作用分析[J].工程力学,2008,25(4)：45-49.
[122]夏元友,范卫琴,芮瑞.王艳丽压力分散型锚索作用效果的数值模拟分析[J].岩土力学2008.29(11)：3144-3148.
[123]刑占清,杨健,杨晓东.压力分散型无粘结预应力锚索作用机理及内锚固段长度研究[J].中国水利水电科学研究院学报,2006,(6)：88-92.
[124]杨庆,朱训国,栾茂田.压力型锚索锚固段应力分布及影响参数分析[J].岩石力学与工程学报,2006,25(增2)：4065-4070.
[125]A.H.奈弗著.摄动方法[J].王辅俊等译,上海：上海科技出版社,1984.
[126]王忠昶,栾茂田,杨庆.基于不同权函数的非局部理论对比分析[J].西安交通大学学报2006,40(11)：1348-1356.
[127]卡姆克.E.常微分方程手册[M].北京：科学出版社,1977.
[128]邹振祝,陈建.无单元法在孔洞应力集中问题中的应用[J].石家庄铁道学院学报,2000,13(2)：1-5.
[129]刘天祥,刘更,朱均,虞烈.无网格法的研究进展[J].机械工程和学报,2002,38(5)：7-12.
[130]刘振华,刘建新,庞承宗.静电场无网格方法中权函数的研究[J].华北电力大学学报,2003.30(1)：18-21.
[131]Kroner E. Elasticity theory of material with long range cohesive forces[J]. Int J Solids Struct,1967,3:732-742.
[132]Eringen A C. Nonlocal polar elastic continua[J]. Int. J Solids Struct.,1972,10:223-248.
[133]赵启林,孙宝俊.非局部损伤模型的客观性研究[J].工程力学,2003,20(5)：185-189.
[134]Xikui Li, S Cescotto. A mixed element method in gradient plasticity for pressure dependent material and modelling of strain localization[J]. Computer Methods Appl Mechanics Engng,1997,144:287-305.
[135]Aifantis EC. On the role of gradients in the localization of deformation and fracture[J]. International Journal of Engineering Science 1992,30:1279-1299.
[136]Rene de Borst, J.Pamin, MareG, D.Geers, On coupled gradient-dependent plasticity and damage theories with a view to localization analysis[J].Eur.J.Mech.A Solids 1999,18(3):939-962
[137]王学滨,潘一山,宋维源.岩石试件尺寸效应的塑性剪切应变梯度模型[J].岩土工程学报,2001,23(6)：701-703.
[138]赵冰,李宁.盛国刚软化岩土介质的应变局部化研究进展——意义.现状.应变梯度[J].岩土力学2005,26(3)：494-499.
[139]赵彭年.松散介质力学[M].北京：地震出版社,1995.
[140]YANG Xiao-li, LI Liang, YIN Jian-hua. Stability analysis of rock slopes with a modified Hoek-Brown failure criterion[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(2):181-190.
[141]YANG Xiao-li,LI Liang,YIN Jian-hua.Seismic and static stability analysis for rock slopes by a kinematical approach[J].Geotechnique,2004,54(8):543-549.
[142]Mogi K. Effect of intermediate principal stress on rockfailure[J]. J Geophys Res,1967,72: 51175131.
[143]Michelis P. Polyaxial yielding of granular rock[J]. J EngMech ASCE,1985,111(18):1049 1066.
[144]许东俊,耿乃光.岩石强度随中间主应力的变化规律[J].固体力学学报,1985,6(1)：72-80.
[145]俞茂宏,杨松岩,刘春阳等.统一平面应变滑移线场理论[J].土木工程学报.199730(2)：14-26.
[146]俞茂宏.双剪理论及其应用[M].北京：科学出版社,1998.
[147]胡小荣,俞茂宏.岩土类介质强度准则新探[J].岩石力学与工：程学报,2004,23(18)：3037-3043.
[148]胡小荣,林太清.三剪屈服准则及其在极限内压计算中的应用[J].中国有色金属学报,2007,17(2)：207-215.
[149]胡小荣.基于三剪屈服准则的空间轴对特征线场理论及其应用[J].中国有色金属学报,2007,17(9)：1447-1452.
[150]赵彭年.二次抛物线型极限曲线的巷道围岩应力及位移[J].有色金属,1979,(1)：41-44.
[151]李春光,郑宏,葛修润,王水林.双参数抛物型Mohr强度准则及其材料破坏规律研究[J].岩石力学与工程学报,2005,24(24)：4428-4433.
[152]佘成学,刘 杰.基于Mohr强度理论的双参数抛物线型屈服准则[J].武汉大学学报(工学版),2008,41(1)：31—34.
[153]李顺群,焦学英,王芳.Mohr包线的二次曲线形式[J].辽宁工程技术大学学报,2005,24(6)：853-855.
[154]周火明,熊诗湖,刘小红等.三峡船闸边坡岩体拉剪试验及强度准则研究[J].岩石力学与工程学报,2005,24(24)：4418-4421.
[155]谭学术,鲜学福,郑道访等.复合岩体力学理论及其应用[M].北京：煤炭工业出版社,1994.
[156]李云安,葛修润,糜崇蓉,张鸿昌.岩-土-混凝土破坏准则及其强度参数估算[J].岩石力学与工程学报,2004,23(5)：770-776.
[157]蔡美峰,何满潮,刘东燕.岩石力学与工程[M].科·学出版社,2002.
[158]刘佑荣,唐辉明.岩体力学[M].武汉：中国地质大学出版社,1999.
[159]李春光,郑宏,葛修润,王水林.双参数抛物型Mohr强度准则及其材料破坏规律研究[J],岩石力学与工程学报,2005,24(24)：4428-4433.
[160]蔡中民,徐文令,张建文.非线性Mohr-Coulomb体边坡的极限荷载[J].固体力学学报,1995,16(3)：254-258.