Analytical layer-element method fornon-axisymmetric loading problem of multi-layered soils
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摘要: 从弹性层状地基非轴对称问题的解析解出发,推导出Hankel积分变换域内单层地基的解析层元,即对称的精确刚度矩阵;然后根据有限层法原理组合相邻层元得到总刚度矩阵,并结合边界条件,求解总刚度矩阵形成的代数方程,得到层状地基非轴对称问题在Hankel积分变换域内的解答;最后应用Hankel逆变换技术,得到物理域内的解。编制了相应的计算程序,分析了非轴对称荷载作用下多层地基沿径向的地表水平位移性状。Abstract: Starting from the analytical solution for the non-axisymmetric elastic problem of multi-layered soils, the analytical layer element of a single soil layer, namely a symmetric exact stiffness matrix, is acquired in the Hankel transform domain. The global stiffness matrix is obtained by assembling the interrelated layer-elements based on the principles of finite layer method. By solving algebraic equations of the global stiffness matrix which satisfy the boundary conditions, we can get the solution to the non-axisymmetric loading problem for multi-layered soils in the Hankel transform domain. Eventually the actual solutions in the physical domain can be acquired by inverting the Hankel transform. Numerical calculation and analysis are carried out by means of the corresponding computer program, and the surface horizontal displacement of multi-layered soils along the radial direction under non-axisymmetric loading is discussed.
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