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从弹性力学三维问题的基本控制方程出发,通过双重Fourier变换及解耦变换技术,推导出相应问题在积分变换域的解析解;根据该解析解,进而推导出三维弹性地基问题的精确刚度矩阵,即解析层元;然后根据有限层法原理,组装得到总体刚度矩阵;通过求解总体刚度矩阵形成的代数方程,得到三维层状地基问题在变换域内的解答;最后应用Fourier逆变换技术,得到其物理域内的解。与经典Bounsinesq解及有限元软件ABAQUS的结果进行比较,验证了本文理论及数值计算方法的正确性;计算分析结果还表明:土体的分层特性对地基沉降具有较显著的影响。
Based on the basic governing equations of the three-dimensional elastic mechanics problem, the analytic solution of the corresponding problem in the integral transform domain is deduced through the double Fourier transform and the decoupling transform technique. Based on the analytical solution, the exact stiffness matrix of the three-dimensional elastic foundation problem is deduced. Then the total stiffness matrix is assembled according to the principle of finite layer method. By solving the algebraic equation formed by the global stiffness matrix, the solution of the three-dimensional layered ground problem in the transform domain is obtained. Finally, Fourier transform is applied to obtain the physical Solutions in the domain. Compared with the classical Bounsinesq solution and the finite element software ABAQUS, the correctness of the theoretical and numerical methods in this paper is validated. The calculation and analysis results also show that the stratification of soil has a significant influence on the settlement of foundation.