Three-dimensional analytical model for the dynamic interaction of twin tunnels in a homogeneous half-space

2019 ◽  
Vol 230 (3) ◽  
pp. 1159-1179 ◽  
Author(s):  
Chao He ◽  
Shunhua Zhou ◽  
Peijun Guo ◽  
Quanmei Gong
Keyword(s):  
Half Space ◽  
Analytical Model ◽  
Three Dimensional ◽  
Dynamic Interaction ◽  
Homogeneous Half Space ◽  
Twin Tunnels

Transient Response of Multiple Rigid Foundations on an Elastic, Homogeneous Half-Space

1994 ◽  
Vol 61 (3) ◽  
pp. 656-663 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Boundary Element ◽  
Half Space ◽  
Transient Response ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Nonlinear Problems ◽  
Fundamental Solutions ◽  
Dynamic Interaction ◽  
Homogeneous Half Space ◽  
Element Approach

Three-dimensional transient response of both massless and massive multiple, rigid foundations, bonded to an elastic, homogeneous half-space, is investigated to study the effect of dynamic interaction through-soil. The numerical procedure is formulated in terms of the boundary element approach by means of the transient fundamental solutions developed by the authors (1994). This procedure works efficiently for the problem addressed here since the separated foundations are analyzed without discretizing the surface of the half-space outside the contact areas between the half-space and the foundations. It also provides the possibility to study nonlinear problems involved with semi-infinite soils.

Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1754-1759 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Hankel Transform ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Homogeneous Half Space ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
The Many

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).

scholarly journals Ruga-formation instabilities of a graded stiffness boundary layer in a neo-Hookean solid

2014 ◽  
Vol 470 (2168) ◽  
pp. 20140218 ◽  
Author(s):  
Mazen Diab ◽  
Kyung-Suk Kim
Keyword(s):  
Boundary Layer ◽  
Half Space ◽  
Compressive Strain ◽  
Three Dimensional ◽  
Decay Length ◽  
Element Analysis ◽  
Dimensional Parameter ◽  
First Order ◽  
Homogeneous Half Space ◽  
Lateral Plane

We present an analysis of ruga-formation instabilities arising in a graded stiffness boundary layer of a neo-Hookean half space, caused by lateral plane-strain compression. In this study, we represent the boundary layer by a stiffness distribution exponentially decaying from a surface value Q 0 to a bulk value Q B with a decay length of 1/ a . Then, the normalized perturbation wavenumber, k ¯ = k / a , and the compressive strain, ε , control formation of a wrinkle pattern and its evolution towards crease or fold patterns for every stiffness ratio η = Q B / Q 0 . Our first-order instability analysis reveals that the boundary layer exhibits self-selectivity of the critical wavenumber for nearly the entire range of 0< η <1, except for the slab ( η =0) and homogeneous half-space ( η =1) limits. Our second-order analysis supplemented by finite-element analysis further uncovers various instability-order-dependent bifurcations, from stable wrinkling of the first order to creasing of the infinite-order cascade instability, which construct diverse ruga phases in the three-dimensional parameter space of ( ε , k ¯ , η ) . Competition among film-buckling, local film-crease and global substrate-crease modes of energy release produces diverse ruga-phase domains. Our analysis also reveals the subcritical crease states of the homogeneous half space. Our results are, then, compared with the behaviour of equivalent bilayer systems for thin-film applications.

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