scholarly journals On the regions of convergence of power-series which represent two-dimensional harmonic functions

1909 ◽  
Vol 10 (2) ◽  
pp. 271-271
Author(s):  
Maxime B{ôcher
Author(s):  
Victor Revenko ◽  
Andrian Revenko

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.


1973 ◽  
Vol 40 (3) ◽  
pp. 767-772 ◽  
Author(s):  
O. L. Bowie ◽  
C. E. Freese ◽  
D. M. Neal

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.


2018 ◽  
Vol 22 ◽  
pp. 01044
Author(s):  
Selahattin Gulsen ◽  
Mustafa Inc ◽  
Harivan R. Nabi

In this study, two-dimensional Burgers' and coupled Burgers' equations are examined by the residual power series method. This method provides series solutions which are rapidly convergent and their components are easily calculable by Mathematica. When the solution is polynomial, the method gives the exact solution using Taylor series expansion. The results display that the method is more efficient, applicable and accuracy and the graphical consequences clearly present the reliability of the method.


2011 ◽  
Vol 7 (2) ◽  
pp. 83-93 ◽  
Author(s):  
Md. Sarwar Alam ◽  
Md. Abdul Hakim Khan

The effect of external Magnetohydrodynamic (MHD) field on the steady two-dimensional nonlinear flow through Convergent-Divergent Channels of a viscous incompressible electrically conducting fluid is investigated. We compute the critical behaviour of the solution govern by the equation. Our approach uses the power series in order to observe the instability of the problem. The series is then summed by using various generalizations of the approximants. We find the critical values of various parameters and type of the principal singularity for different choice of MHD effect.DOI: 10.3329/jname.v7i2.5635


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