直角坐标系下黏弹性层状地基动力响应分析

寇磊; 徐建国; 王博

doi:10.21656/1000-0887.380155

直角坐标系下黏弹性层状地基动力响应分析

doi: 10.21656/1000-0887.380155

郑州大学水利与环境学院, 郑州450002

基金项目: 国家自然科学基金(51708512;51579226);河南省高等学校重点科研项目(17A560031);郑州大学青年专项科研启动基金（F0000881）

详细信息

作者简介:
寇磊（1983—），男，讲师，博士(通讯作者. E-mail: klyhe@163.com).

中图分类号: TU433
计量
- 文章访问数: 1194
- HTML全文浏览量: 178
- PDF下载量: 503
- 被引次数: 0
出版历程
- 收稿日期: 2017-05-26
- 修回日期: 2017-07-30
- 刊出日期: 2018-05-15

Dynamic Response Analysis of Viscoelastic Multilayered Foundation in the Cartesian Coordinate System

School of Water Conservancy & Environment Engineering, Zhengzhou University, Zhengzhou 450002, P.R.China

Funds: The National Natural Science Foundation of China(51708512; 51579226)

摘要

摘要: 基于直角坐标系下黏弹性力学的基本控制方程，运用Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论，推导轴对称动荷载及非轴对称动荷载作用时黏弹性地基三维空间问题积分变换域内的解析单元刚度矩阵；根据边界条件和层间连续条件集成总刚度矩阵；求解含有总刚度矩阵方程的代数方程，得到积分变换域内相应问题的解；利用Fourier-Laplace积分逆变换得到真实物理域内的解.编制相应程序计算黏弹性层状地基动力响应与已有解答进行对比，验证了提出方法的正确性.
- 直角坐标系 /
- 轴对称动荷载 /
- 黏弹性层状地基 /
- 解析刚度矩阵 /
- 动力响应
Abstract: Based on the governing viscoelastic equations in the Cartesian coordinate system, the analytical element stiffness matrices in the integral transform domain of 3D problems of viscoelastic foundation under axisymmetric and non-axisymmetric dynamic loads were derived with the Fourier-Laplace transform, the decoupling transformation, the differential equations theory and the matrix theory. The global stiffness matrix was assembled in view of the boundary conditions and the continuity between adjacent layers, the solution in the integral transform domain was obtained from the algebraic equations involving the global stiffness matrix, and the solution in the physical domain was acquired through the inverse Fourier-Laplace transform. Through a corresponding computer program, comparison of the dynamic responses of viscoelastic multilayered foundation between the proposed algorithm and the existing method proves the validity of the former.
- Cartesian coordinate system /
- axisymmetric dynamic loading /
- viscoelastic layered foundation /
- analytical stiffness matrix /
- dynamic response

HTML全文

参考文献(16)

[1]	SMALL J C, BOOKER J R. Finite layer analysis of layered elastic materials using a flexibility approach, part 1: strip loadings[J]. International Journal for Numerical Methods in Engineering,1984,20(6): 1025-1037.
[2]	SMALL J C, BOOKER J R. Finite layer analysis of layered elastic materials using a flexibility approach, part 2: circular and rectangular loadings[J]. International Journal for Numerical Methods in Engineering,1986,23(5): 959-978.
[3]	钟阳, 王哲人, 郭大智. 求解多层弹性半空间轴对称问题的传递矩阵法[J]. 土木工程学报, 1992,25(6): 38-43.(ZHONG Yang, WANG Zheren, GUO Dazhi. The transfer matrix method for solving axisymmetric problems in muti-layered elastic half space[J]. China Civil Engineering Journal,1992,25(6): 38-43.(in Chinese))
[4]	艾智勇, 成怡冲. 三维横观各向同性成层地基的传递矩阵解[J]. 岩土力学, 2010,31(S2): 25-29.(AI Zhiyong, CHENG Yichong. Transfer matrix solutions of three-dimensional transversely isotropic multilayered soils[J]. Rock and Soil Mechanics,2010,31(S2): 25-29.(in Chinese))
[5]	钟阳, 耿立涛. 多层弹性平面问题解的精确刚度矩阵法[J]. 岩土力学, 2008,29(10): 2829-2832.(ZHONG Yang, GENG Litao. Explicit solution of multiplayer elastic plane by exact stiffness matrix method[J]. Rock and Soil Mechanics,2008,29(10): 2829-2832.(in Chinese))
[6]	钟阳. 多层弹性半空间问题解的精确刚度矩阵法[J]. 应用力学学报, 2008,25(2): 316-319.(ZHONG Yang. Explicit solution of multilayered elastic half space by exact stiffness matrix method[J]. Chinese Journal of Applied Mechanics,2008,25(2): 316-319.(in Chinese))
[7]	艾智勇, 苏辉, 成怡冲. 求解层状地基平面应变问题的解析层元法[J]. 岩土工程学报, 2011,33(11): 1797-1800.(AI Zhiyong, SU Hui, CHENG Yichong. Analytical layer element method for solving plane strain problem of multi-layered soils[J]. Chinese Journal of Geotechnical Engineering,2011,33(11): 1797-1800.(in Chinese))
[8]	艾智勇, 曾凯, 曾文泽. 层状地基三维问题的解析层元解[J]. 岩土工程学报, 2012,34(6): 1154-1158.(AI Zhiyong, ZENG Kai, ZENG Wenze. Analytical layer-element solution for three-dimensional problem of multilayered foundation[J].Chinese Journal of Geotechnical Engineering,2012,34(6): 1154-1158.(in Chinese))
[9]	韩泽军, 林皋, 周小文. 三维横观各向同性层状地基任意点格林函数求解[J]. 岩土工程学报, 2016,38(12): 2218-2225.(HAN Zejun, LIN Gao, ZHOU Xiaowen. Solution to Green’s functions for arbitrary points in 3D cross-anisotropic multi-layered soil[J]. Chinese Journal of Geotechnical Engineering,2016,38(12): 2218-2225.(in Chinese))
[10]	韩泽军, 林皋, 李建波. 二维层状地基格林函数的求解[J]. 土木工程学报, 2015,48(10): 99-107.(HAN Zejun, LIN Gao, LI Jianbo. The solution of Green’s functions for two-dimensional layered ground[J]. China Civil Engineering Journal,2015,48(10): 99-107.(in Chinese))
[11]	寇磊, 白云. 直角坐标系黏弹性层状地基荷载作用下的解析刚度矩阵解[J]. 中南大学学报(自然科学版), 2014,45(7): 2346-2352.(KOU Lei, BAI Yun. Analytical stiffness matrix of viscoelastic layered foundation under loading in Cartesian coordinate system[J]. Journal of Central South University(Science and Technology),2014,45(7): 2346-2352.(in Chinese))
[12]	寇磊, 白云. 直角坐标系下层状黏弹性地基Biot固结解析刚度矩阵解[J]. 应用数学和力学, 2016,37(1): 84-96.(KOU Lei, BAI Yun. Analytical stiffness matrixes for Biot consolidation of multilayered viscoelastic foundations in the Cartesian coordinate system[J]. Applied Mathematics and Mechanics,2016,37(1): 84-96.(in Chinese))
[13]	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. Explicit solution for dynamic response of asymmetrical problems in multilayered viscoelastic half space by exact stiffness matrix method[J]. Chinese Journal of Computational Mechanics,2003,20(6):749-755.(in Chinese))
[14]	严国政. 常微分方程[M]. 北京: 科学出版社, 2012: 32-36.(YAN Guozheng.Ordinary Differential Equations[M]. Beijing: Science Press, 2012: 32-36.(in Chinese))
[15]	WANG J C, BOOKER J R. A Fourier-Laplace transform finite element method for the analysis of contaminant transport in porous media[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1996,23(14): 1763-1796.
[16]	TAKBOT A. The accurate numerical inversion of Laplace transforms[J]. IMA Journal of Applied Mathematics,1979,23(1): 97-120.