On the Regions of Convergence of Power-Series which Represent Two-Dimensional Harmonic Functions

1909 ◽  
Vol 10 (2) ◽  
pp. 271 ◽  
Author(s):  
Maxime Bocher
Keyword(s):  
Power Series ◽  
Harmonic Functions ◽  
Two Dimensional

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

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.

Solution of Plane Problems of Elasticity Utilizing Partitioning Concepts

1973 ◽  
Vol 40 (3) ◽  
pp. 767-772 ◽  
Author(s):  
O. L. Bowie ◽  
C. E. Freese ◽  
D. M. Neal
Keyword(s):  
Analytic Function ◽  
Power Series ◽  
Collocation Method ◽  
Stress Function ◽  
Function Theory ◽  
Series Expansions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Power Series Expansions

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.

scholarly journals Approximate Solutions of Two-Dimensional Burgers' and Coupled Burgers' Equations by Residual Power Series Method

2018 ◽  
Vol 22 ◽  
pp. 01044
Author(s):  
Selahattin Gulsen ◽  
Mustafa Inc ◽  
Harivan R. Nabi
Keyword(s):  
Power Series ◽  
Taylor Series Expansion ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Series Method ◽  
Power Series Method ◽  
Burgers Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power

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.

scholarly journals Critical behaviour of the MHD flow in convergent-divergent channels

2011 ◽  
Vol 7 (2) ◽  
pp. 83-93 ◽  
Author(s):  
Md. Sarwar Alam ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Power Series ◽  
Mhd Flow ◽  
Conducting Fluid ◽  
Critical Behaviour ◽  
Nonlinear Flow ◽  
Two Dimensional ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Flow Through ◽  
Principal Singularity

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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