求解层状地基平面应变问题的解析层元法

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 English Version

（ 1. 同济大学地下建筑与工程系，上海 200092 ； 2. 岩土及地下工程教育部重点实验室，上海 200092 ）

基金项目: 国家自然科学基金项目（ 50578121 ）

详细信息

作者简介:
艾智勇 (1966 – ) ，男，江西余江人，博士，教授，主要从事岩土及地下工程方面的教学和研究工作。

中图分类号: TU443
计量
- 文章访问数: 1108
- HTML全文浏览量: 1
- PDF下载量: 419
出版历程
- 发布日期: 2011-11-14

Analytical layer element method for solving plane strain problem of multi-layered soils

(1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China; 2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China)

摘要

摘要: 提出了一个求解层状地基平面应变问题的解析层元法。从平面应变问题的基本控制方程出发，通过 Fourier 变换，并依据微分方程原理，推导出相应问题的解析解；基于该解析解，推导出平面应变问题的精确刚度矩阵，即解析层元；然后根据有限层法原理组合得到总刚度矩阵，通过求解总刚度矩阵形成的代数方程，得到层状地基平面应变问题在积分变换域内的解答；应用 Fourier 逆变换技术，得到物理域内的解。编制了相应的计算程序，讨论了土体的分层特性对地基沉降的影响。
- 解析层元 /
- 平面应变 /
- 层状地基 /
- Fourier 变换
Abstract: An analytical layer element method is proposed to solve the plane strain problem of multi-layered soils. Starting from the governing equations of the plane strain problem the analytical solution is obtained by introducing the Fourier transform and solving differential equations. And then, according to the analytical solution, an exact stiffness matrix for the multi-layered plane strain problem is established, which is called analytical layer element. The global stiffness matrix is established by using the principle of the finite layer method, and the solutions for the plane strain problem of multi-layered soils in the transform domain are obtained by solving the algebraic equations about the global stiffness matrix. The actual solutions in the physical domain are acquired by inverting the Fourier transform. Numerical analysis is carried out to discuss the influence of the layered characteristics on the vertical displacements of the soil.
- analytical layer element /
- plane strain /
- multi-layered soils /
- Fourier transform

HTML全文

参考文献(8)

[1]	Zienkkiewicz O C, Taylor K L. The finite element method[M]. 4th ed. New York: McGraw-Hill, 1987.
[2]	CHEUNG Y K. Finite strip method in structural mechanics[M]. New York: Pergamon Press, 1976.
[3]	张问清 , 赵锡宏 , 宰金珉 . 任意力系作用下的层状弹性半空间的有限层分析方法 [J]. 岩土工程学报 , 1982, 3 (2): 27 – 42. (ZHANG Wen-qing, ZHAO Xi-hong, ZAI Jin-min. Finite layer analysis for layered and elastic half-space under arbitrary force system[J]. Chinese Journal of Geotechnical Engineering, 1982, 3 (2): 27 – 42. (in Chinese))
[4]	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 Zhe-ren, GUO Da-zhi. The transfer matrix method for solving axisymetrical problems in multi-layered elastic half space [J]. China Civil Engineering Journal , 1992, 25 (6): 38 – 43. (in Chinese))
[5]	AI Z Y. YUE Z Q. THAM L G. YANG M. Extended Sneddon and Muki solutions for multilayered elastic materials[J]. International Journal of Engineering Science, 2002, 40 (13): 1453 – 1483.
[6]	SNEDDON I N. The use of integral transform[M]. New York: McGraw-Hill, 1972.
[7]	赵光恒 , 张子明 . 有限深弹性层上基础梁的计算 [J]. 华东水利学院学报 , 1984(2): 32 – 44. (ZHAO Guang-heng, ZHANG Zi-ming. Computation of foundation beams on elastic layers of finite depth[J]. Journal of Hehai University (Natural Sciences), 1984(2): 32 – 44. (in Chinese))
[8]	艾智勇 , 吴超 . 三维直角坐标系下分层地基的传递矩阵解 [J]. 重庆建筑大学学报 , 2008, 30 (2): 43 – 46. (AI Zhi-yong, WU Chao. Transfer matrix solutions of multi-layered soils in rectangular coordinate system[J]. Journal of Chongqing Jianzhu University, 2008, 30 (2): 43 – 46. (in Chinese))