传递矩阵法求解弹性半空间单一覆盖层轴对称动力问题的误差分析
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摘要
为解决弹性半空间单一覆盖层轴对称动力问题中传递矩阵病态的问题,提出了误差分析方法。分3种情况讨论了采用传递矩阵法计算弹性半空间单一覆盖层轴对称动力问题中被积函数处理方法,进而对逆Hankel变换和逆Laplace变换的处理方法进行了简要说明,据此提出了减小误差的方法。通过退化模型对所提出的方法进行了验证,结果表明该方法可有效减小误差,为利用传递矩阵法求解层状半空间动力问题中传递矩阵病态的问题提供了思路。
In order to solve the problem that transfer matrix in axisymmetric dynamic problem of single soil layer overlaid on elastic half-space is ill-conditioned,the error analysis method is presented.The disposal method for integrand is discussed in three conditions;then the disposal method for the inverse-Hankel transformation and the inverse-Laplace transformation is briefly introduced.Based on these,the method how to decrease the error is presented.The analysis result is verified through the degenerating model.The result indicates that the method presented can effectively decrease error.All this work can provide idea for solve the problem that transfer matrix in axisymmetric dynamic problem of layered elastic half space.
In order to solve the problem that transfer matrix in axisymmetric dynamic problem of single soil layer overlaid on elastic half-space is ill-conditioned,the error analysis method is presented.The disposal method for integrand is discussed in three conditions;then the disposal method for the inverse-Hankel transformation and the inverse-Laplace transformation is briefly introduced.Based on these,the method how to decrease the error is presented.The analysis result is verified through the degenerating model.The result indicates that the method presented can effectively decrease error.All this work can provide idea for solve the problem that transfer matrix in axisymmetric dynamic problem of layered elastic half space.
引文
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[5]尹一平,王元汉.传递矩阵法的Zn误差分析[J].岩土力学,2001,22(4):440-442.YIN Yi-ping,WANG Yuan-han.Analysis of error caused by Zn in transferring matrix method[J].Rock and Soil Mechanics,2001,22(4):440-442.
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[7]尹一平,王元汉.传递矩阵法的ξ误差分析[J].岩土力学,2002,23(5):608-611.YIN Yi-ping,WANG Yuan-han.Analysis of error caused byξin transferring matrix method[J].Rock and Soil Mechanics,2002,23(5):608-611.
[8]邓学钧,黄卫,黄晓明.路面结构计算和设计电算方法[M].南京:东南大学出版社,1997:117-118.
[9]ZENG S P,LIANG R.A fundamental solution of a multilayered half-space due to an impulsive ring source[J].Soil Dynamics and Engineering,2002,(22):541-550.
[10]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988.
[11]刘凯欣,刘广裕.垂直点源问题的一个精确解[J].科学通报,2004,49(5):419-423.LIU Kai-xin,LIU Guang-yu.An exact solution of vertical point source problem[J].Chinese Science Bulletin,2004,49(5):419-423.
[12]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.
[2]孟凡顺,郭海燕,叶天麒.用传递矩阵法求解多层层状弹性半空间轴对称动力问题的奇异解[J].地震工程与工程振动,1995,15(2):44-51.MENG Fan-shun,GUO Hai-yan,YE Tian-qi.The singular solutions of axisymmetric elastodynamic problem for multilayered halfspace by means of transfer matrix[J].Earthquake Engineering and Engineering Vibration,1995,15(2):44-51.
[3]黄菊花,何成宏,杨国泰.任意激励下层状黏弹性地基地面振动的解析解[J].塑性工程学报,1999,6(1):74-80.HUANG Ju-hua,HE Cheng-hong,YANG Guo-tai.Analytical solution of the ground displacement by arbitrary shape load exciting on layered viscoelastic media[J].Journal of Plasticity Engineering,1999,6(1):74-80.
[4]郑鑫,陶夏新.竖向激励下弹性半空间单一覆盖层的表面位移[J].扬州大学学报(自然科学版),2010,13(2):70-74.ZHENG Xin,TAO Xia-xin.Displacement field subjected to pulse simulate on single soil layer overlaid on elastic half-space[J].Journal of Yangzhou University(Natural Science Edition),2010,13(2):70-74.
[5]尹一平,王元汉.传递矩阵法的Zn误差分析[J].岩土力学,2001,22(4):440-442.YIN Yi-ping,WANG Yuan-han.Analysis of error caused by Zn in transferring matrix method[J].Rock and Soil Mechanics,2001,22(4):440-442.
[6]DURBIN F.Numerical inversion of Laplace transforms:An efficient improvement to Dubner and Abate’s method[J].The Computer Journal,1974,17(6):371-376.
[7]尹一平,王元汉.传递矩阵法的ξ误差分析[J].岩土力学,2002,23(5):608-611.YIN Yi-ping,WANG Yuan-han.Analysis of error caused byξin transferring matrix method[J].Rock and Soil Mechanics,2002,23(5):608-611.
[8]邓学钧,黄卫,黄晓明.路面结构计算和设计电算方法[M].南京:东南大学出版社,1997:117-118.
[9]ZENG S P,LIANG R.A fundamental solution of a multilayered half-space due to an impulsive ring source[J].Soil Dynamics and Engineering,2002,(22):541-550.
[10]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988.
[11]刘凯欣,刘广裕.垂直点源问题的一个精确解[J].科学通报,2004,49(5):419-423.LIU Kai-xin,LIU Guang-yu.An exact solution of vertical point source problem[J].Chinese Science Bulletin,2004,49(5):419-423.
[12]廖振鹏.工程波动理论导论(第二版)[M].北京:科学出版社,2002.
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