State Space Solution to 3D Multilayered Elastic Soils Based on Order Reduction Method
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摘要: 从以位移形式表达的三维弹性力学控制方程出发,经双重Fourier变换,并运用基于Cayley-Hamilton定理的降阶解法,推导出位移变量及其1阶导数的解,再利用物理方程求得单层地基的传递矩阵;结合边界条件和层间连续条件,进一步得到多层地基的状态空间解;编制相应程序进行数值分析,对多层地基中有软弱下卧层和坚硬下卧层时的沉降情况进行了比较和讨论.
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关键词:
- 状态空间解 /
- 多层弹性地基 /
- 双重Fourier变换 /
- 降阶解法
Abstract: Starting with the governing equations in terms of displacements of threedimensional elastic medium, the solutions of displacement components and their first derivatives were obtained by the application of a double Fourier transform and an order reduction method based on the CayleyHamilton theorem. Combining the solutions and the constitutive equations which connected the displacements and stresses, the transfer matrix of a single soil layer was acquired. And then the state space solution of multilayered elastic soils was further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. Numerical analysis based on the present theory was carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratum were compared and discussed. -
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