Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

2008 ◽  
Vol 51 (7) ◽  
pp. 773-780 ◽  
Author(s):  
LianHe Li ◽  
TianYou Fan
Keyword(s):  
Complex Variable ◽  
Plane Elasticity ◽  
Complex Variable Method ◽  
Variable Method ◽  
Icosahedral Quasicrystals

COMPLEX VARIABLE METHOD FOR THE PLANE ELASTICITY OF QUASICRYSTALS WITH POINT GROUP 10

2008 ◽  
Vol 22 (29) ◽  
pp. 5145-5153
Author(s):  
LIAN-HE LI ◽  
TIAN-YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Plane Elasticity ◽  
Complex Variable Method ◽  
Variable Method ◽  
Real Form ◽  
General Complex ◽  
Elasticity Problems ◽  
Group 10 ◽  
Special Case

General complex variable method for solving plane elasticity problems of quasicrystals with point group 10 has been proposed. The stress and displacement components of phonon and phason fields are expressed by four arbitrary analytic functions. Explicit real-form displacement expressions for the dislocation problem of the quasicrystal is obtained through the use of this method.The interaction between two parallel dislocations is also discussed in detail. All the present results can be reduced to the exact solutions for the quasicrystals with point group 10 mm in the special case.

Application of Numerical Mapping to the Muskhelishvili Method in Plane Elasticity

1963 ◽  
Vol 30 (3) ◽  
pp. 410-414 ◽  
Author(s):  
V. L. Pisacane ◽  
L. E. Malvern
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Complex Variable ◽  
Digital Computer ◽  
Plane Elasticity ◽  
Complex Variable Method ◽  
Variable Method ◽  
Elasticity Problems ◽  
Finite Difference Solution ◽  
Simply Connected

A procedure for treating plane-elasticity problems in simply connected regions, consisting of use of numerical mapping methods in order to apply the Muskhelishvili complex variable method, is demonstrated. This approach now makes the whole complex variable method susceptible to automatic solution on a digital computer. An example is considered for which the exact solution was known; a comparison to the finite-difference solution for this example is also made.

Complex Variable Method for Eigensolution Sensitivity Analysis

AIAA Journal ◽  
2006 ◽  
Vol 44 (12) ◽  
pp. 2958-2961 ◽  
Author(s):  
B. P. Wang ◽  
A. P. Apte
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method

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.

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.

scholarly journals Complex Variable Solutions for Forces and Displacements of Circular Lined Tunnels

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingbo Han ◽  
Yongxu Xia ◽  
Xing Wang ◽  
Lunlei Chai
Keyword(s):  
Rock Mass ◽  
Complex Variable ◽  
Earth Pressure ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Lateral Earth Pressure ◽  
Series Expression ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complex variable method for solving the forces and displacements of circular lined tunnels is presented. Complex potentials for the stresses and displacements are expressed in the term of series expression. The undetermined coefficients of the complex potentials are obtained according to the stress boundary conditions along the lining inner surface and the displacement and surface traction boundary condition along the lining and rock-mass interface. Solutions for the stresses and displacements of the tunnel lining and rock-mass are then established by applying Muskhekishvili’s complex variable method. In addition, forces solutions for linings are presented based on the tangential stress at the two boundaries. Examples are finally established to reveal the applicability and accuracy of the proposed method. The effects of the degrees from the tunnel crown to the invert, coefficient of the lateral earth pressure, and distance from the rock-mass to the interface on the regulations of the lining forces and rock-mass stresses are also thoroughly investigated.

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