【摘要】 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。更多还原

【Abstract】 Starting from the basic equations of elasticity for three-dimensional problem,the analytical solution in the integral transform domain is obtained by use of the decoupled transform technique and the Fourier transform method.Based on the analytical solution,the exact stiffness matrix which is called analytical layer-element for the three-dimensional problem of multilayered elastic foundation is derived.The global stiffness matrix is assembled by means of the principle of finite layer method,and the solutions for the three-dimensional problem of multilayered foundation in the transform domain are obtained by solving the algebraic equations of the global stiffness matrix.Finaly,the solutions in the physical domain are acquired by inverting the Fourier transform.The validity of the proposed theory and numerical method is examined by comparing the results in this study with those of Boussinesq solution and the finite element soft ABAQUS,and numerical calculation shows that the influence of stratification on the displacement of foundation is remarkable.更多还原