二维粘弹性波数值模拟方法及北川县城震害分析
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摘要
提出一种研究复杂地形二维粘弹性介质中波动问题的数值模拟方法。利用标准线性固体(SLS)微分型本构方程给出计算当前应力的公式,基于三角形网格给出控制体的动力平衡方程,在时间域上逐步递推计算给出各节点的加速度、速度、位移和各格子的应力。与解析解的对比结果验证了方法的正确性。该方法自动满足复杂地形的自由表面条件。研究了地震作用下北川县城区域的剪应力、加速度场的动态集中现象,分析了震害原因。
A numerical method is presented for simulating wave propagation in a viscoelastic media with an irregular boundary.The standard linear solid (SLS) mechanism is used to characterize the viscoelastic media.The stress formulae for recursive calculation are derived from SLS constitutive relations.The dynamic equilibrium equations of controlled volumes are established by using the mesh of triangular grid.By applying the dynamic equilibrium equations of controlled volumes and the stress formulae alternately,the nodal accelerations,velocities,displacements,and the stresses in each grid can be obtained in time domain.The result comparing with the analytical solution shows that the numerical algorithm presented is an effective method.The free boundary condition of arbitrary irregularity is satisfied naturally.The dynamic concentration phenomena of shear stress and accelerations are investigated for the area of Beichuan county town with a topography surface.The seismic disaster reasons of the Beichuan county town are analyzed.
A numerical method is presented for simulating wave propagation in a viscoelastic media with an irregular boundary.The standard linear solid (SLS) mechanism is used to characterize the viscoelastic media.The stress formulae for recursive calculation are derived from SLS constitutive relations.The dynamic equilibrium equations of controlled volumes are established by using the mesh of triangular grid.By applying the dynamic equilibrium equations of controlled volumes and the stress formulae alternately,the nodal accelerations,velocities,displacements,and the stresses in each grid can be obtained in time domain.The result comparing with the analytical solution shows that the numerical algorithm presented is an effective method.The free boundary condition of arbitrary irregularity is satisfied naturally.The dynamic concentration phenomena of shear stress and accelerations are investigated for the area of Beichuan county town with a topography surface.The seismic disaster reasons of the Beichuan county town are analyzed.
引文
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[5]Jousset P,Neuberg J,Jolly A.Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography[J].Geophysical Journal International,2004,159(2):776―802.
[6]Hestholm S,Ruud B.2D finite-difference viscoelastic wave modeling including surface topography[J].Geophysical Prospecting,2000,48(2):341―373.
[7]Hestholm S.Tree-dimensional finite difference viscoelastic wave modeling including surface topography[J].Geophysical Journal International,1999,139(3):852―878.
[8]Alshaikh I A,Turhan D,Mengi Y.Two-dimensional transient wave propagation in viscoelastic layered media[J].Journal of Sound and Vibration,2001,244(5):837―858.
[9]Liu Tielin,Liu Kaishin,Zhang Jinxiang.Unstructured gird method for stress wave propagation in elastic media[J].Computer Methods in Applied Mechanics and Engineering,2004,193(23-26):2427―2452.
[10]Liu T,Liu K,Zhang J.Triangular grid method for stress-wave propagation in2-D orthotropic materials[J].Archive of Applied Mechanics,2005,74(7):477―488.
[11]王礼立.应力波基础[M].北京:国防工业出版社,2005.Wang Lili.Foundation of stress waves[M].Beijing:National Defense Industry Press,2005.(in Chinese)
[2]Carcione J M,Kosloff D,Kosloff R.Viscoacoustic wave propagation simulation in the earth[J].Geophysics,1988,53(6):769―777.
[3]Spathis A T.Evidence of rock microstructure from seismic wave propagation[J].Engineering Fracture Mechanics,1990,35(1-3):377―384.
[4]Jiang L,Haddow J B.A finite element solution of plane wave propagation in inhomogeneous linear viscoelastic solids[J].Journal of Sound and Vibration,1995,184(3):429―438.
[5]Jousset P,Neuberg J,Jolly A.Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography[J].Geophysical Journal International,2004,159(2):776―802.
[6]Hestholm S,Ruud B.2D finite-difference viscoelastic wave modeling including surface topography[J].Geophysical Prospecting,2000,48(2):341―373.
[7]Hestholm S.Tree-dimensional finite difference viscoelastic wave modeling including surface topography[J].Geophysical Journal International,1999,139(3):852―878.
[8]Alshaikh I A,Turhan D,Mengi Y.Two-dimensional transient wave propagation in viscoelastic layered media[J].Journal of Sound and Vibration,2001,244(5):837―858.
[9]Liu Tielin,Liu Kaishin,Zhang Jinxiang.Unstructured gird method for stress wave propagation in elastic media[J].Computer Methods in Applied Mechanics and Engineering,2004,193(23-26):2427―2452.
[10]Liu T,Liu K,Zhang J.Triangular grid method for stress-wave propagation in2-D orthotropic materials[J].Archive of Applied Mechanics,2005,74(7):477―488.
[11]王礼立.应力波基础[M].北京:国防工业出版社,2005.Wang Lili.Foundation of stress waves[M].Beijing:National Defense Industry Press,2005.(in Chinese)
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