非轴对称垂直荷载下双层弹性理论解及力学分析
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摘要
为更好地模拟车辆荷载对路基路面作用的荷载形式,以非轴对称层状弹性体系理论为基础,引入椭圆荷载形式,基于系数递推法,从连续体系层间结合条件出发,研究了表面层和路基荷载参数的理论解,给出了椭圆垂直荷载下双层连续弹性体系求解。根据理论解编写了C++程序,进而以椭圆垂直荷载下弹性半空间体理论解验证了程序的计算精度,并分析了圆形均布荷载与椭圆荷载下路面结构力学响应。分析结果表明,在椭圆荷载下,荷载圆中心的第一主应力、最大剪应力和竖向位移都比圆形均布荷载大,即在非轴对称荷载作用下,路面结构将产生更加剧烈的力学响应。
Numerous studies of on-ground pressure under tire showed that it is typical not a circular uniform loading.The ground loading distribution is related to the tire pressure and the loading.In order to simulate vehicle loading and pavement structure with a more accurate model,the expressions of loading based on the condition of double continuous interlayer combination was evaluated in this study.Also,the solution of double elastic system was obtained.The C++program was written according to the formula and the program was verified using the elastic half space program under asymmetric vertical loading.In addition,the distribution of pavement structure mechanical response under different loading was analyzed.The results showed that the first principal stress,the first principal strain,and the maximum shear stress of pavement structure under elliptic loading are larger than those under the cylindrical loading,which indicated that asymmetric load will aggravate the fracture and deformation of asphalt pavement.
Numerous studies of on-ground pressure under tire showed that it is typical not a circular uniform loading.The ground loading distribution is related to the tire pressure and the loading.In order to simulate vehicle loading and pavement structure with a more accurate model,the expressions of loading based on the condition of double continuous interlayer combination was evaluated in this study.Also,the solution of double elastic system was obtained.The C++program was written according to the formula and the program was verified using the elastic half space program under asymmetric vertical loading.In addition,the distribution of pavement structure mechanical response under different loading was analyzed.The results showed that the first principal stress,the first principal strain,and the maximum shear stress of pavement structure under elliptic loading are larger than those under the cylindrical loading,which indicated that asymmetric load will aggravate the fracture and deformation of asphalt pavement.
引文
[1]BURMISTER D M.The general theory of stresses and displacements in layered Systems.I[J].Journal of Applied Physics,1945,16(2):89-94.
[2]BURMISTER D M.The general theory of stresses and displacements in layered soil systems.III[J].Journal of Applied Physics,1945,16(5):296-302.
[3]HUANG Y H.Stresses and strains in viscoelastic multilayer systems subjected to moving loads[J].Highway Research Record 457,1973,22(4):60-71.
[4]郭大智,冯德成.层状弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001:163-195.GUO Dazhi,FENG Decheng.Mechanics of layered elastic system[M].Harbin:Harbin Institute of Technology Press,2001:162-195.(in Chinese)
[5]钟阳,陈静云,王龙,等.求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法[J].计算力学学报,2003,20(6):749-755.ZHONG Yang,CHEN Jingyun,WANG Long,et al.Exact stiffness matrix method for solving axisymmetric problems of multilayered viscoelastic half space under dynamic loading[J].Chinese Journal of Computational Mechanics,2003,20(6):749-755.(in Chinese)
[6]任瑞波,钟阳,张肖宁,等.多层粘弹性半空间轴对称问题的理论解[J].哈尔滨建筑大学学报,2000,33(6):124-128.REN Ruibo,ZHONG Yang,ZHANG Xiaoning,et al.Exact stiffness matrix method for solving axisymmetric problems of multilayered viscoelastic half space under dynamic loading[J].Journal of Harbin University of Civil Engineering and Architecture,2000,33(6):124-128.(in Chinese)
[7]董忠红,吕彭民.移动荷载下粘弹性层状沥青路面-动力响应模型[J].工程力学,2011,28(12):153-159.DONG Zhonghong,LPengmin.A model to study the dynamic response of visco-elastic layered system under moving load[J].Engineering Mechanics,2011,28(12):153-159.(in Chinese)
[8]李皓玉,杨绍普,刘进,等.移动分布荷载下层状粘弹性体系的动力响应分析[J].工程力学,2015,32(1):120-127.LI Haoyu,YANG Shaopu,LIU Jin,et al.Dynamic response in multilayered viscoelastic medium generated by moving distributed loads[J].Engineering Mechanics,2015,32(1):120-127.(in Chinese)
[9]史春娟,吕彭民.基于非线性模型的沥青路面动力响应研究[J].工程力学,2013,30(2):326-331.SHI Chunjuan,LPengmin.Study on the dynamic response of asphalt pavement based on the nonlinear viscoelastic model[J].Engineering Mechanics,2013,30(2):326-331.(in Chinese)
[10]ANGHELACHE G,MOISESCU R.Measurement of stress distributions in truck tyre contact patch in real rolling conditions[J].Vehicle System Dynamics,2012,50(12):1747-1760.
[11]WANG H,AL-QADI I L,STANCIULESCU I.Effect of surface friction on tire-pavement contact stresses during vehicle maneuvering[J].Journal of Engineering Mechanics,2013,140(4):04014001.
[12]陈松强,王东升,张瑞,等.非轴对称垂直荷载下弹性半空间体理论解及力学分析[J].中国科技论文,2017,12(7):806-811.CHEN Songqiang,WANG Dongsheng,ZHANG Rui,et al.The theoretical solution and mechanical analysis for elastic half-space under asymmetrical loading[J].China Sciencepaper,2017,12(7):806-811.(in Chinese)
[2]BURMISTER D M.The general theory of stresses and displacements in layered soil systems.III[J].Journal of Applied Physics,1945,16(5):296-302.
[3]HUANG Y H.Stresses and strains in viscoelastic multilayer systems subjected to moving loads[J].Highway Research Record 457,1973,22(4):60-71.
[4]郭大智,冯德成.层状弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001:163-195.GUO Dazhi,FENG Decheng.Mechanics of layered elastic system[M].Harbin:Harbin Institute of Technology Press,2001:162-195.(in Chinese)
[5]钟阳,陈静云,王龙,等.求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法[J].计算力学学报,2003,20(6):749-755.ZHONG Yang,CHEN Jingyun,WANG Long,et al.Exact stiffness matrix method for solving axisymmetric problems of multilayered viscoelastic half space under dynamic loading[J].Chinese Journal of Computational Mechanics,2003,20(6):749-755.(in Chinese)
[6]任瑞波,钟阳,张肖宁,等.多层粘弹性半空间轴对称问题的理论解[J].哈尔滨建筑大学学报,2000,33(6):124-128.REN Ruibo,ZHONG Yang,ZHANG Xiaoning,et al.Exact stiffness matrix method for solving axisymmetric problems of multilayered viscoelastic half space under dynamic loading[J].Journal of Harbin University of Civil Engineering and Architecture,2000,33(6):124-128.(in Chinese)
[7]董忠红,吕彭民.移动荷载下粘弹性层状沥青路面-动力响应模型[J].工程力学,2011,28(12):153-159.DONG Zhonghong,LPengmin.A model to study the dynamic response of visco-elastic layered system under moving load[J].Engineering Mechanics,2011,28(12):153-159.(in Chinese)
[8]李皓玉,杨绍普,刘进,等.移动分布荷载下层状粘弹性体系的动力响应分析[J].工程力学,2015,32(1):120-127.LI Haoyu,YANG Shaopu,LIU Jin,et al.Dynamic response in multilayered viscoelastic medium generated by moving distributed loads[J].Engineering Mechanics,2015,32(1):120-127.(in Chinese)
[9]史春娟,吕彭民.基于非线性模型的沥青路面动力响应研究[J].工程力学,2013,30(2):326-331.SHI Chunjuan,LPengmin.Study on the dynamic response of asphalt pavement based on the nonlinear viscoelastic model[J].Engineering Mechanics,2013,30(2):326-331.(in Chinese)
[10]ANGHELACHE G,MOISESCU R.Measurement of stress distributions in truck tyre contact patch in real rolling conditions[J].Vehicle System Dynamics,2012,50(12):1747-1760.
[11]WANG H,AL-QADI I L,STANCIULESCU I.Effect of surface friction on tire-pavement contact stresses during vehicle maneuvering[J].Journal of Engineering Mechanics,2013,140(4):04014001.
[12]陈松强,王东升,张瑞,等.非轴对称垂直荷载下弹性半空间体理论解及力学分析[J].中国科技论文,2017,12(7):806-811.CHEN Songqiang,WANG Dongsheng,ZHANG Rui,et al.The theoretical solution and mechanical analysis for elastic half-space under asymmetrical loading[J].China Sciencepaper,2017,12(7):806-811.(in Chinese)