Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane

2015 ◽  
Vol 39 (16) ◽  
pp. 1821-1835 ◽  
Author(s):  
Qian Fang ◽  
Haoran Song ◽  
Dingli Zhang
Keyword(s):  
Stress Distribution ◽  
Half Plane ◽  
Complex Variable ◽  
Underwater Tunnel ◽  
Variable Analysis

Analysis of a Semi-Infinite Strip With Constant Stress Flanges Under Concentrated Loads

1966 ◽  
Vol 33 (3) ◽  
pp. 571-574 ◽  
Author(s):  
H. R. Meck
Keyword(s):  
Stress Distribution ◽  
Exact Solutions ◽  
Closed Form ◽  
Complex Variable ◽  
Constant Stress ◽  
Infinite Strip ◽  
Concentrated Loads ◽  
Simple Complex ◽  
Variable Analysis

An analysis is presented for a semi-infinite strip reinforced by flanges and subjected to concentrated in-plane loads at the ends of the flanges. The taper which results in constant flange stress is determined, and the stress distribution in the sheet is also found. A simple complex variable analysis is used which leads to exact solutions in closed form.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

On Bending of a Flat Slab Supported by Square-Shaped Columns and Clamped

1954 ◽  
Vol 21 (3) ◽  
pp. 263-270
Author(s):  
S. Woinowsky-Krieger
Keyword(s):  
Stress Distribution ◽  
Conformal Mapping ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Flat Slab ◽  
Flat Slabs ◽  
At Will

Abstract A solution is given in this paper for the problem of bending of an infinite flat slab loaded uniformly and rigidly clamped in square-shaped columns arranged to form the square panels of the slab. The complex variable method in connection with conformal mapping is used for this aim. Although not perfectly rigorous, the solution obtained is sufficiently accurate for practical purposes and, besides, it can be improved at will. Stress diagrams traced in a particular case of column dimensions do not wholly confirm the stress distribution, generally accepted in design of flat slabs.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

The Stresses in a Thick Cylinder Having a Square Hole Under Concentrated Loading

1958 ◽  
Vol 25 (4) ◽  
pp. 571-574
Author(s):  
Masaichiro Seika
Keyword(s):  
Stress Distribution ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Numerical Examples ◽  
Concentrated Loading ◽  
Thick Cylinder ◽  
Square Hole

Abstract This paper contains a solution for the stress distribution in a thick cylinder having a square hole with rounded corners under the condition of concentrated loading. The problem is investigated by the complex-variable method, associated with the name of N. I. Muskhelishvili. The unknown coefficients included in the solution are determined by the method of perturbation. Numerical examples of the solution are worked out and compared with the results available.

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.

scholarly journals Abelian theorems for Whittaker transforms

1987 ◽  
Vol 10 (3) ◽  
pp. 417-431 ◽  
Author(s):  
Richard D. Carmichael ◽  
R. S. Pathak
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Absolute Value ◽  
Final Value ◽  
The Right ◽  
Abelian Theorems

Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches0or∞in absolute value inside a wedge region in the right half plane.

Asymptotic behaviour of the H-transform in the complex domain

1987 ◽  
Vol 102 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Richard D. Carmichael ◽  
Ram S. Pathak
Keyword(s):  
Asymptotic Behaviour ◽  
Half Plane ◽  
Complex Variable ◽  
Structure Theorem ◽  
Generalized Functions ◽  
Complex Domain ◽  
The Right ◽  
Abelian Theorems

AbstractAbelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.

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