Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary eleme...Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary element method to simulate the solution of an elastic solid with a curved free surface under impact loading. This problem is considered difficult for numerical methods. Lamb’s problem is calculated first to verify the method. Then the method is applied on the problems with different surface curvatures. The method simulates the phenomenon of Rayleigh’s wave propagating on a curved surface very well. The results are shown in figures.展开更多
Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axis...Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axisymmetric governing dynamic equation in the Biot’s theory of two-phase medium is solved. Integral solutions with the soil skeleton displacements and pore pressure as the main unknown quantity are obtained. On the basis of this solution, a systematic study on Lamb’ s problems for saturated soils is performed. Considering the case of drained surface and the case of undrained surface, the integral solutions for surface radial, vertical and circumferential direction displacements under the vertical surface force and horizontal surface force are obtained, which would be reduced to the solutions of the classical Lamb’s problem. So, the correctness of the solutions would be verified. The numerical example indicates that the two-dimensional (2-D) model cannot be applied to 3-D problem accurately.展开更多
文摘Impulsive line load in a half-space (Lamb’s problem) can be solved with a closed form solution. This solution is helpful for understanding the phenomenon of Rayleigh’s waves. In this article, we use a boundary element method to simulate the solution of an elastic solid with a curved free surface under impact loading. This problem is considered difficult for numerical methods. Lamb’s problem is calculated first to verify the method. Then the method is applied on the problems with different surface curvatures. The method simulates the phenomenon of Rayleigh’s wave propagating on a curved surface very well. The results are shown in figures.
文摘Based on the integral transformation method with which the combinatory integral transform of the displacements and the combinatory integral transform of the stresses are presented, the three-dimensional (3-D) non-axisymmetric governing dynamic equation in the Biot’s theory of two-phase medium is solved. Integral solutions with the soil skeleton displacements and pore pressure as the main unknown quantity are obtained. On the basis of this solution, a systematic study on Lamb’ s problems for saturated soils is performed. Considering the case of drained surface and the case of undrained surface, the integral solutions for surface radial, vertical and circumferential direction displacements under the vertical surface force and horizontal surface force are obtained, which would be reduced to the solutions of the classical Lamb’s problem. So, the correctness of the solutions would be verified. The numerical example indicates that the two-dimensional (2-D) model cannot be applied to 3-D problem accurately.
