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

Published online by Cambridge University Press:  05 May 2011

Chau-Shioung Yeh ,
Tsung-Jen Teng ,
Wen-Shinn Shyu  and
I-Chang Tsai
Chau-Shioung Yeh*
Affiliation:
Department of Civil Engineering, Institute of Applied Mechanics, National Taiwan University, Tainan, Taiwan 10617, R.O.C.
Tsung-Jen Teng*
Affiliation:
National Center for Research on Earthquake Engineering, Tainan, Taiwan 106, R.O.C.
Wen-Shinn Shyu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Tainan, Taiwan 10617, R.O.C.
I-Chang Tsai*
Affiliation:
Chung-Shan Institute of Science & Technology, Tao-Yuan, Taiwan 320, R.O.C.
*
* Professor
** Research Fellow
*** Graduate student
**** Senior Specialist
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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.

Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 2 , June 2002 , pp. 75 - 87
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

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References

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