弹性半空间二维出平面自由波场的一维化时域算法
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摘要
提出了一种计算出平面SH波斜入射时弹性半空间自由波场时域计算的一维化有限元方法。首先利用Snell定律确定平面波沿水平方向的传播规律,在用有限元法对弹性半空间进行离散化时,竖向单元尺寸根据波动有限元模拟精度要求确定,而水平向有限元网格尺寸根据水平向波的传播规律和采用的离散时间步长确定,使得有限元离散模型中任意节点的运动可以用水平向相邻节点的运动表示,从而将二维有限元节点运动方程组化为一维的形式。求解此一维方程组,可得到弹性半空间中一列节点的运动,再根据行波的传播规律,可确定全空间自由波场。理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性。
A 1D finite element method in time domain is developed,where the wave motion of free field in elastic half-space by SH wave oblique incidence is simulated.The horizontal propagation characteristic of plane wave is revealed on the basis of Snell law,when the elastic half-space is discreted by finite element,the vertical element size is determined according to the demand of simulation accuracy,and the horizontal element size is determined by the propagation characteristic and the discrete time step.Therefore,the displacement of any node in finite element model can be represented by that of the adjacent node in horizontal direction to reduce the wave motion equations in 2D finite element model to 1D scheme.Solving the 1D equations,the displacement of nodes in one vertical line is obtained,and the wave motion in half space is sought based on the propagation characteristic of traveling wave.Both the theoretical analysis and the numerical results demonstrate the satisfied accuracy and stability.
A 1D finite element method in time domain is developed,where the wave motion of free field in elastic half-space by SH wave oblique incidence is simulated.The horizontal propagation characteristic of plane wave is revealed on the basis of Snell law,when the elastic half-space is discreted by finite element,the vertical element size is determined according to the demand of simulation accuracy,and the horizontal element size is determined by the propagation characteristic and the discrete time step.Therefore,the displacement of any node in finite element model can be represented by that of the adjacent node in horizontal direction to reduce the wave motion equations in 2D finite element model to 1D scheme.Solving the 1D equations,the displacement of nodes in one vertical line is obtained,and the wave motion in half space is sought based on the propagation characteristic of traveling wave.Both the theoretical analysis and the numerical results demonstrate the satisfied accuracy and stability.
引文
[1]沈聚敏,周锡元,高小旺,等.抗震工程学[M].北京:中国建筑工业出版社,2000.
[2]廖振鹏.工程波动理论导论[M].第二版,北京:科学出版社,2002.
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[4]Bardet J P,Ichii K,Lin C H.ERRA:A computer programfor equivalent-linear earthquake site response analysis of lay-ered soil deposits[R].Los Angels:University of Southern Cal-ifornia,CA,2000.
[5]李山有,廖振鹏,周正华.大型结构地震反应数值模拟中的波动输入[J].地震工程与工程振动,2001,6(2):1-5.
[6]刘晶波,廖振鹏.有限元离散模型中的出平面波动[J].力学学报,1992,3(2):207-215.
[2]廖振鹏.工程波动理论导论[M].第二版,北京:科学出版社,2002.
[3]Idriss I M,Sun J I.SHAKE91:A computer program for con-ducting equivalent linear seismic response analysis of horizon-tally layered soil deposits[R].Davis,University of California,1992.
[4]Bardet J P,Ichii K,Lin C H.ERRA:A computer programfor equivalent-linear earthquake site response analysis of lay-ered soil deposits[R].Los Angels:University of Southern Cal-ifornia,CA,2000.
[5]李山有,廖振鹏,周正华.大型结构地震反应数值模拟中的波动输入[J].地震工程与工程振动,2001,6(2):1-5.
[6]刘晶波,廖振鹏.有限元离散模型中的出平面波动[J].力学学报,1992,3(2):207-215.
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