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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.
引用本文: 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 Zhi-yong, SU Hui, CHENG Yi-chong. Analytical layer element method for solving plane strain problem of multi-layered soils[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(11): 1797-1800.
Citation: AI Zhi-yong, SU Hui, CHENG Yi-chong. Analytical layer element method for solving plane strain problem of multi-layered soils[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(11): 1797-1800.

求解层状地基平面应变问题的解析层元法

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

  • 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。

     

    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.

     

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