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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。
A analytical layer element method is proposed to solve the plane strain problem in layered soils. Based on the basic control equations of plane strain problem, the analytic solution of the corresponding problem is deduced by Fourier transform and according to the principle of differential equation. Based on the analytical solution, the exact stiffness matrix of plane strain problem is derived, that is, the analytic layer element. Then, The finite element method is used to obtain the total stiffness matrix. By solving the algebraic equations formed by the total stiffness matrix, the solution of the plane strain problem in the layered ground in the integral transform domain is obtained. The inverse Fourier transform technique is used to obtain the solution in the physical domain. The corresponding calculation program is compiled and the effect of soil layering on settlement of foundation is discussed.