scholarly journals General solution of the two-dimensional intertwining relations for supercharges with hyperbolic (Lorentz) metrics

2013 ◽  
Vol 377 (3-4) ◽  
pp. 195-199 ◽  
Author(s):  
M.S. Bardavelidze ◽  
M.V. Ioffe ◽  
D.N. Nishnianidze
Keyword(s):  
General Solution ◽  
Two Dimensional ◽  
Lorentz Metrics

A general solution method for two-dimensional nonplanar oxidation

1983 ◽  
Vol 30 (9) ◽  
pp. 993-998 ◽  
Author(s):  
Daeje Chin ◽  
Soo-Young Oh ◽  
R.W. Dutton
Keyword(s):  
General Solution ◽  
Solution Method ◽  
Two Dimensional

The Stroh Formalism

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
General Solution ◽  
Elastic Body ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Stroh Formalism ◽  
Two Dimensional ◽  
Stroh's Formalism ◽  
Elasticity Problems ◽  
Anisotropic Elastic ◽  
Stroh’S Formalism

In this chapter we study Stroh's sextic formalism for two-dimensional deformations of an anisotropic elastic body. The Stroh formalism can be traced to the work of Eshelby, Read, and Shockley (1953). We therefore present the latter first. Not all results presented in this chapter are due to Stroh (1958, 1962). Nevertheless we name the sextic formalism after Stroh because he laid the foundations for researchers who followed him. The derivation of Stroh's formalism is rather simple and straightforward. The general solution resembles that obtained by the Lekhnitskii formalism. However, the resemblance between the two formalisms stops there. As we will see in the rest of the book, the Stroh formalism is indeed mathematically elegant and technically powerful in solving two-dimensional anisotropic elasticity problems. The possibility of extending the formalism to three-dimensional deformations is explored in Chapter 15.

Plane Electromechanical Fieldes in a Piezoelectric Material with a Crack

2006 ◽  
Vol 324-325 ◽  
pp. 247-250
Author(s):  
Shu Hong Liu ◽  
Meng Wu ◽  
Shu Min Duan ◽  
Hong Jun Wang
Keyword(s):  
Boundary Condition ◽  
General Solution ◽  
Piezoelectric Material ◽  
Mechanical Load ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Two Dimensional ◽  
Electric Boundary Condition ◽  
Boundary Collocation Method ◽  
Transversely Isotropic Piezoelectric Material

A two-dimensional electromechanical analysis is performed on a transversely isotropic piezoelectric material containing a crack based on the impermeable electric boundary condition. By introducing stress function, a general solution is provided in terms of triangle series. It is shown that the stress and electric displacement are all of 1/2 order singularity in front of the crack tip. In addition, the electromechanical fields in the vicinity of the crack when subjected to uniform tensile mechanical load are obtained using boundary collocation method.

Validation of a Thermal Spreading/Constriction Resistance Model for a Convectively Cooled Plate With an Applied Heat Flux

2008 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Heat Flux ◽  
General Solution ◽  
Neumann Boundary ◽  
Solution Technique ◽  
Two Dimensional ◽  
Experimental Heat ◽  
Experimental Heat Transfer ◽  
Present Solution ◽  
Resistance Model ◽  
Dimensional Boundary

A thermal resistance model of a two-dimensional boundary value problem (BVP) that is commonly found in engineering/experimental heat transfer is presented. The problem consists of two different convectively cooled sub-sections along one boundary, and a heat flux distribution imposed on a portion of another (opposite) boundary, coupled with adiabatic conditions (Neumann boundary conditions) along the remaining boundaries under steady-state conditions. In solving this BVP, the solution technique is highlighted. Consistent with theory, the solution to this problem depends on two Biot numbers, dimensionless heat flux and other dimensionless geometric parameters related to the problem. The present solution is an exact general solution to an existing two-dimensional problem found in literature, and as a special case, the general solution reduces exactly to the existing solution. Also, the present model is validated by comparing the present solution with measured data, and in terms of a temperature difference between two locations on the plate, the analytical solution is well within the experimental error of 0.03 K.

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