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 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.

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.

Solution of Structural Mechanics Problems by the Differential Quadrature Finite Difference Method

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Partial Differential Operator ◽  
Structural Mechanics ◽  
Plane Elasticity ◽  
Differential Quadrature ◽  
Difference Operators ◽  
Elasticity Problems ◽  
Nonuniform Plate

Abstract The differential quadrature finite difference method (DQFDM) has been proposed by the author. The finite difference operators are derived by the differential quadrature (DQ). They can be obtained by using the weighting coefficients for DQ discretizations. The derivation is straight and easy. By using different orders or the same order but different grid DQ discretizations for the same derivative or partial derivative, various finite difference operators for the same differential or partial differential operator can be obtained. Finite difference operators for unequally spaced and irregular grids can also be generated through the use of generic differential quadrature (GDQ). The derivation of higher order finite difference operators is also easy. By adopting the same order of approximation to all mathematical terms existing in the problem to be solved, excellent convergence can be obtained due to the consistent approximation. The DQFDM is effective for solving structural mechanics problems. The numerical simulations for solving anisotropic nonuniform plate problems and two-dimensional plane elasticity problems are carried out. Numerical results are presented. They demonstrate the DQFDM.

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.

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