三维层状场地中斜面均布荷载动力格林函数
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摘要
在作者三维层状场地精确动力刚度矩阵基础上,给出了三维层状场地内部斜面均布荷载动力格林函数。本文格林函数包含了场地的所有基本力学特性,可用于三维层状局部场地中波的散射及土-结构相互作用等问题的求解。文中对所得结果进行了精度检验,同时给出了一些数值结果,包括均匀半空间和基岩上单一土层中竖面或斜面荷载作用下的位移和应力格林函数。
Dynamic Green's functions for uniformly distributed loads acting on an inclined plane in 3-D layered site are presented in this paper based on the exact dynamic stiffness matrices of layered site.The Green's functions include all the essential mechanical properties of the medium,and can be used to resolve the problems of wave scattering and soil-structure interaction,etc.in 3-D layered site.The precision of the solutions are verified in the paper.Some numerical results are given which include the displacements and the stresses Green's functions due to dynamic uniformly distributed loads acting on a vertical plane or an inclined plane in homogeneous half-space and single layer over half-space.
Dynamic Green's functions for uniformly distributed loads acting on an inclined plane in 3-D layered site are presented in this paper based on the exact dynamic stiffness matrices of layered site.The Green's functions include all the essential mechanical properties of the medium,and can be used to resolve the problems of wave scattering and soil-structure interaction,etc.in 3-D layered site.The precision of the solutions are verified in the paper.Some numerical results are given which include the displacements and the stresses Green's functions due to dynamic uniformly distributed loads acting on a vertical plane or an inclined plane in homogeneous half-space and single layer over half-space.
引文
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[2]Banerjee P K,Mamoon S M.A fundamental solution due to a periodic point force in the interior of an elastic half-space[J].Earthq Eng StrucDyn,1990,19:91-105.
[3]林皋,李炳奇,申爱国.半无限弹性空间域内点加振格林函数的计算[J].力学学报,1994,26(5):583-592.
[4]Luco E,Apsel R J.On the Green’s functions for a layered half-space,Part I[J].Bull Seism Soc Am,1983,73:909-929.
[5]Pak R YS,Guzina B B.Three-dimensional Green’s functions for a multilayered half-space in displacement potentials[J].J Eng Mech,ASCE,2002,128:449-461.
[6]Kausel E,Peek R.Dynamic loads in the interior of a layered stratum:an explicit solution[J].Bull Seism Soc Am,1982,72:1459-1481.
[7]Wolf J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs:Prentice-Hall,1985
[8]Rajapakse R K ND,Wang Y.Green’s functions for transversely isotropic elastic half-space[J].J Eng Mech,ASCE,1993,119:1724-1746.
[9]Vostroukhov AV,Verichev S N,Kok AWM,et al.Steady-state response of a stratified half-space subjected to a horizontal arbitrary buried uni-form load applied at a circular area[J].Soil Dyn Earthq Eng,2004,24:449-459.
[10]梁建文,巴振宁.三维层状场地的精确动力刚度矩阵及格林函数[J].地震工程与工程振动,2007,27(5):7-17.
[2]Banerjee P K,Mamoon S M.A fundamental solution due to a periodic point force in the interior of an elastic half-space[J].Earthq Eng StrucDyn,1990,19:91-105.
[3]林皋,李炳奇,申爱国.半无限弹性空间域内点加振格林函数的计算[J].力学学报,1994,26(5):583-592.
[4]Luco E,Apsel R J.On the Green’s functions for a layered half-space,Part I[J].Bull Seism Soc Am,1983,73:909-929.
[5]Pak R YS,Guzina B B.Three-dimensional Green’s functions for a multilayered half-space in displacement potentials[J].J Eng Mech,ASCE,2002,128:449-461.
[6]Kausel E,Peek R.Dynamic loads in the interior of a layered stratum:an explicit solution[J].Bull Seism Soc Am,1982,72:1459-1481.
[7]Wolf J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs:Prentice-Hall,1985
[8]Rajapakse R K ND,Wang Y.Green’s functions for transversely isotropic elastic half-space[J].J Eng Mech,ASCE,1993,119:1724-1746.
[9]Vostroukhov AV,Verichev S N,Kok AWM,et al.Steady-state response of a stratified half-space subjected to a horizontal arbitrary buried uni-form load applied at a circular area[J].Soil Dyn Earthq Eng,2004,24:449-459.
[10]梁建文,巴振宁.三维层状场地的精确动力刚度矩阵及格林函数[J].地震工程与工程振动,2007,27(5):7-17.
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