Interaction of Multiple Cylindrical Cavities and Fixed Surface in Elastic Semi-Space

In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. Sometimes the surface of the structure is fixed, and it could be seen as a rigid line. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities and the fixed surface, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with fixed surface and multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the displacement boundary condition of the fixed surface, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space with fixed surface can be investigated further.

Response of Non-Homogeneous Saturated Soils and Free-Field to Incident Plane SH Wave

Based on the Biot’s Theory, the dynamic response of non-homogeneous saturated soil has been studied using Helmholtz vector decomposition principle and Exact Dynamic Stiffness Method (EDSM). Reflection and transmission of SH wave in non-homogeneous saturated soil have also been analyzed in considering the continuous variation of physical and mechanical properties of saturated foundation along the thickness. The general calculation formula about the reflection and transmission coefficients of bedrock and free field on both surfaces was achieved. Assuming that the material properties have an exponential law distribution and gradient variation along the thickness-coordinate, the dynamic response of non-homogeneous saturated soils under incident plane SH wave was discussed by numerical examples. The results show that the incident angle, the thickness and heterogeneity index of saturated soil have significant influences on the ratio of the ground displacement and bedrock displacement.

Scattering of Anti-Plane SH-Wave by Multiple Cylindrical Inclusions in Elastic Semi-Space

Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction. The scattering field produced by multiple circular inclusions determines the dynamic stress concentration factor around the circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated, because there are many factors influenced. Researchers solved these problems by analysis and numerical methods. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions. Based on this solution, the problem of interaction of multiple cylindrical inclusions and a linear crack in semi-space can be investigated further.