A Hybrid Method for Analyzing the Dynamic Responses of Cavities or Shells Buried in an Elastic Half-Plane

Abstract

In this paper, based on a variational formalism which originally proposed by Mei [1] for infinite elastic medium and extended by Yeh, et al. [2,3] for elastic half-plane, a hybrid method which combines the finite element and series expansion method is implemented to solve the diffraction of plane waves by a cavity buried in an elastic half-plane. The finite domain which encloses all inhomogeneities including the cavity can be easily formulated by finite element methods. The unknown boundary data obtained by subtracting the known free fields from the total fields which include the boundary nodal displacements and tractions at the interface between the finite domain and the surrounding elastic half-plane are not independent of each other and can be correlated through a series representation. Due to the continuity condition at the interface, the same series representation is still valid for the exterior elastic half-plane to represents the scattered wave. The unknown coefficients of this series are treated as generalized coordinates and can be easily formulated by the same variational principle. The expansion function of the series is composed of basis function. Each basis function is constructed from the basis function for an infinite plane by superimposing an additional homogeneous reflective term to satisfy both traction free conditions at ground surface and radiation conditions at infinity. The numerical results are made against those obtained by boundary element methods, and good agreements are found.

SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method

“…Based on a variational formalism proposed by Mei (1980), a hybrid method combining the finite element and series‐expansion method was implemented to solve the scattering problems. Yeh et al (2000a,b, 2002, 2007) have extended the hybrid method to solve the problems of scattering wave by canyons, alluvial valleys or cavities (shells) buried in an elastic half‐plane, where the hybrid method was discussed in detail.…”

Scattering of Elastic Waves by a Buried Tunnel Under Obliquely Incident Waves Using T Matrix

“…Luco and de Barros [12] used the indirect boundary integral method to construct the scattering field and combined it with the Donell shell theory to study the responses of a cylindrical pipeline subjected to obliquely incident plane waves. Yeh et al [13] have recently proposed a hybrid method for analyzing the dynamics responses of shells buried in an elastic halfplane. Recently, Chen et al [14][15][16] used the boundary integral method with degenerate kernel of fundamental solutions to transform the improper boundary integrals to a series sum for study the exterior radiation and scattering problems with circular boundaries.…”