Iterative solution to the self-consistent problem of an electron gun with an arbitrarily shaped cathode based on combined finite difference: an integral equation approach

2000 ◽  
Author(s):  
Mikhail A. Monastyrski ◽  
A. G. Murav'ev ◽  
Victor A. Tarasov
Keyword(s):  
Integral Equation ◽  
Finite Difference ◽  
Iterative Solution ◽  
The Self ◽  
Electron Gun ◽  
Equation Approach ◽  
Self Consistent ◽  
Integral Equation Approach ◽  
Consistent Problem

An Integral Equation Approach to the Inclusion Problem of Elastoplasticity

1982 ◽  
Vol 49 (2) ◽  
pp. 312-318 ◽  
Author(s):  
W. C. Johnson ◽  
J. K. Lee
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Yield Condition ◽  
Transformation Strain ◽  
Iterative Solution ◽  
Inclusion Problem ◽  
Flow Rule ◽  
Equation Approach ◽  
Coherent Precipitate ◽  
Integral Equation Approach

An integral equation approach is derived for the calculation of the elastoplastic strain field associated with a transformed inclusion of constant stress-free transformation strain and for an inhomogeneity when the far stress field remains elastic. The assumptions of a coherent precipitate and the deformation theory of plasticity are employed although any yield condition and flow rule can be chosen. The complexity of the integral equation is such that an iterative solution scheme is necessary. The technique is applied to a spherical precipitate in a uniform elastic stress field where associated stress and strain fields and plastic zone are calculated. The nature of the plastic relaxation process compares qualitatively with two-dimensional plane stress behavior. Extension of this technique to the nonaxisymmetric problem is also examined.

AN INTEGRAL EQUATION APPROACH TO PHASE TRANSITIONS IN FERROFLUIDS

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1847-C8-1848
Author(s):  
G. A. R. Martin ◽  
A. Bradbury ◽  
R. W. Chantrell
Keyword(s):  
Integral Equation ◽  
Phase Transitions ◽  
Equation Approach ◽  
Integral Equation Approach
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