scholarly journals Stress concentration around irregular holes using complex variable method

Sadhana ◽  
1998 ◽  
Vol 23 (4) ◽  
pp. 393-412 ◽  
Author(s):  
K R Y Simha ◽  
S S Mohapatra
Keyword(s):  
Stress Concentration ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method

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.

scholarly journals Complex potentials in two-dimensional elasticity

1945 ◽  
Vol 184 (997) ◽  
pp. 129-179 ◽  
Keyword(s):  
Complex Variable ◽  
Body Force ◽  
Displacement Function ◽  
The Body ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Two Dimensional ◽  
Special Cases ◽  
Airy’S Stress Function

This paper gives an approach to two-dimensional isotropic elastic theory (plane strain and generalized plane stress) by means of the complex variable resulting in a very marked economy of effort in the investigation of such problems as contrasted with the usual method by means of Airy’s stress function and the allied displacement function. This is effected (i) by considering especially the transformation of two-dimensional stress; it emerges that the combinations xx + yy , xx — yy + 2 ixy are all-important in the treatment in terms of complex variables; (ii) by the introduction of two complex potentials Ω( z ), ω( z ) each a function of a single complex variable in terms of . which the displacements and stresses can be very simply expressed. Transformation of the cartesian combinations u + iv , xx + yy , xx — yy + 2 ixy to the orthogonal curvilinear combinations u ξ + iu n , ξξ + ηη, ξξ - ηη + 2iξη is simple and speedy. The nature of "the complex potentials is discussed, and the conditions that the solution for the displacements shall be physically admissible, i.e. single-valued or at most of the possible dislocational types, is found to relate the cyclic functions of the complex potentials. Formulae are found for the force and couple resultants at the origin z = 0 equivalent to the stresses round a closed circuit in the elastic material, and these also are found to relate the cyclic functions of the complex potentials. The body force has bhen supposed derivable from a particular body force potential which includes as special cases (i) the usual gravitational body force, (ii) the reversed mass accelerations or so-called ‘centrifugal’ body forces of steady rotation. The power of the complex variable method is exhibited by finding the appropriate complex potentials for a very wide variety of problems, and whilst the main object of the present paper has been to extend the wellknown usefulness of the complex variable method in non-viscous hydrodynamical theory to two-dimensional elasticity, solutions have been given to a number of new problems and corrections made to certain other previous solutions.

Bending of a circular plate with an eccentric circular patch symmetrically loaded with respect to its centre

1956 ◽  
Vol 52 (3) ◽  
pp. 584-598 ◽  
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Poisson’S Ratio ◽  
Complex Variable Method ◽  
Variable Method ◽  
Poisson's Ratio ◽  
General Boundary ◽  
General Boundary Condition ◽  
Circular Patch

ABSTRACTThe complex variable method is applied to obtain solutions for the deflexion of a supported circular plate with uniform line loading along an eccentric circle under a general boundary condition including the clamped boundary , a boundary with zero peripheral couple , a boundary with equal boundary cross-couples , a hinged boundary and a boundary for which , η being Poisson's ratio. These solutions are used to obtain the deflexion at any point of a circular plate having an eccentric circular patch symmetrically loaded with respect to its centre. Expressions for the slope and cross-couples over the boundary and the deflexions at the centres of the plate and the loaded patch are obtained.

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