Impedance functions for three-dimensional foundations supported on an infinitely-long canyon of uniform cross-section in a homogeneous half-space

1991 ◽  
Vol 20 (11) ◽  
pp. 1011-1027 ◽  
Author(s):  
Liping Zhang ◽  
Anil K. Chopra
Keyword(s):  
Half Space ◽  
Cross Section ◽  
Three Dimensional ◽  
Homogeneous Half Space ◽  
Uniform Cross Section ◽  
Impedance Functions

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 THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS

2012 ◽  
Vol 24 (07) ◽  
pp. 1250018 ◽  
Author(s):  
DAVID KREJČIŘÍK ◽  
HELENA ŠEDIVÁKOVÁ
Keyword(s):  
Cross Section ◽  
Parallel Transport ◽  
Three Dimensional ◽  
Reference Curve ◽  
Dirichlet Laplacian ◽  
Resolvent Convergence ◽  
Uniform Cross Section ◽  
Reference Curves ◽  
Twisting Angle ◽  
Quantum Waveguides

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrödinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuring the asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a parallel transport along the curve and a refined smoothing of the curvature via the Steklov approximation.

scholarly journals The problem of a rigid punch moving on a viscoelastic half-plane with inertial effects approximately included

1979 ◽  
Vol 21 (2) ◽  
pp. 198-229 ◽  
Author(s):  
J. M. Golden
Keyword(s):  
Half Space ◽  
Cross Section ◽  
Hilbert Transform ◽  
Constant Velocity ◽  
Inertial Effects ◽  
Rigid Punch ◽  
Viscoelastic Effects ◽  
Uniform Cross Section ◽  
Special Case ◽  
Quantities Of Interest

AbstractThe problem of an infinitely long rigid punch of uniform cross-section moving across a viscoelastic half-space at constant velocity, large enough so that inertial effects cannot be neglected, is examined and solved in various approximations. Frictional shear is assumed to exist between the punch and the half-space. The method, which is an extension of that developed in previous papers [6, 7], is applicable for any form of viscoelastic behaviour in the half-space. For the special case of discrete spectrum behaviour the method is described in detail. For the case where the punch is cylindrical and viscoelastic effects are small compared with elastic effects, explicit expressions are given for all quantities of interest, in particular the coefficient of hysteretic friction. A general Hilbert transform formula is derived in the appendix.

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.

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.

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