A finite-difference solution of boundary value problems for an equation of elliptic type

1972 ◽  
Vol 23 (2) ◽  
pp. 196-201
Author(s):  
I. M. Velikoivanenko ◽  
I. I. Lyashko ◽  
G. E. Mistetskii
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Type ◽  
Finite Difference Solution ◽  
Difference Solution

scholarly journals Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 420 ◽  
Author(s):  
Woncheol Jeong ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Residual Stresses ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Plastic Anisotropy ◽  
Strain Rates ◽  
Finite Difference Solution ◽  
Residual Stresses And Strains ◽  
Difference Solution

Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.

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