scholarly journals The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functions

1983 ◽  
Vol 5 (1) ◽  
pp. 14-21 ◽  
Author(s):  
A. E. Heins ◽  
E. Mmeister
Keyword(s):  
Plane Problem ◽  
Half Plane ◽  
Analytic Functions

Transient analysis of conducting half-plane problem with noncausal scattering image

1994 ◽  
Vol 7 (1) ◽  
pp. 31-35 ◽  
Author(s):  
K. I. Nikoskinen ◽  
I. V. Lindell ◽  
M. E. Ermutlu
Keyword(s):  
Plane Problem ◽  
Half Plane ◽  
Transient Analysis ◽  
Scattering Image

Analytic stress solution for a circular tunnel in half plane with a concentrated force

2019 ◽  
Vol 24 (12) ◽  
pp. 3862-3879
Author(s):  
Hui Cai ◽  
Ai-zhong Lu ◽  
Yao-cai Ma
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
Half Plane ◽  
Analytic Functions ◽  
Surrounding Rock ◽  
Circular Tunnel ◽  
Concentrated Force ◽  
Stress Solution ◽  
Stress Boundary Condition ◽  
Stress Boundary

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

Flux integrals for Sommerfeld's half-plane problem

1981 ◽  
Vol 24 (2) ◽  
pp. 793-800 ◽  
Author(s):  
Sergio Servadio
Keyword(s):  
Plane Problem ◽  
Half Plane

Mixed boundary value problems of the type of Sommerfeld's half-plane problem

1986 ◽  
Vol 104 (3-4) ◽  
pp. 261-277 ◽  
Author(s):  
F.-O. Speck
Keyword(s):  
Partial Differential Equations ◽  
Plane Problem ◽  
Half Plane ◽  
Mixed Boundary ◽  
Diffraction Theory ◽  
Elliptic Partial Differential Equations ◽  
Common Boundary ◽  
Physical Problems ◽  
The Common ◽  
Theory Lead

SynopsisVarious physical problems in diffraction theory lead us to study modifications of the Sommerfeld half-plane problem governed by two proper elliptic partial differential equations in complementary ℝ3 half-spaces Ω± and we allow different boundary or transmission conditions on two half-planes, which together form the common boundary of Ω±.

The V-notched elastic half-plane problem

1979 ◽  
Vol 32 (1-3) ◽  
pp. 125-140 ◽  
Author(s):  
P. S. Theocaris ◽  
N. I. Ioakimidis
Keyword(s):  
Plane Problem ◽  
Half Plane
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