Two-dimensional thermal elasticity problem for a body weakened by a system of thermally insulated cracks

1976 ◽  
Vol 16 (4) ◽  
pp. 626-633
Author(s):  
M. P. Savruk
Keyword(s):  
Elasticity Problem ◽  
Two Dimensional ◽  
Thermal Elasticity

A Generalized Method of Rotational Superposition for Problems With Elliptical Distribution of Boundary Values

1996 ◽  
Vol 63 (4) ◽  
pp. 911-918 ◽  
Author(s):  
Gwolong Lai ◽  
A. R. Robinson
Keyword(s):  
Elasticity Problem ◽  
New Technique ◽  
Two Dimensional ◽  
Elliptical Distribution ◽  
Boundary Values ◽  
Axially Symmetric ◽  
Circular Area ◽  
Static Elasticity ◽  
Circular Case ◽  
Elliptical Boundary

An extension of the usual rotational superposition is developed from geometrical considerations. This approach relates the solution of any dynamic or static elasticity problem which corresponds to boundary values on a circular area to the solution of the problem in which the same boundary values are “stretched” in one direction. From the two-dimensional problems that correspond by rotational superposition to the circular case, new two-dimensional problems are formulated which, when super-posed properly, result in the solution for the elliptical boundary distribution. This new technique is first presented for stretching the boundary values of axially symmetric problems, and then extended to others, including the elliptical shear dislocation problem.

A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media

1995 ◽  
Vol 450 (1939) ◽  
pp. 293-317 ◽  
Keyword(s):  
Composite Materials ◽  
Affine Transformation ◽  
Plane Elasticity ◽  
Elasticity Problem ◽  
Elastic Media ◽  
Two Dimensional ◽  
Dielectric Media ◽  
Elasticity Problems ◽  
Dielectric Tensors ◽  
Exact Relations

A correspondence between the two-dimensional complex dielectric equations and those of plane-strain elasticity is established. Specifically, homogeneous orthotropic dielectric media are shown to correspond to orthotropic elastic media, and by making an affine transformation of the elasticity problem, we obtain correspondences between orthotropic dielectric media and non-orthotropic elastic media. We also find a correspondence between the elasticity problem and a pair of dielectric problems in which the dielectric tensors are real. These correspondences are extended to certain classes of inhomogeneous media. Applied to composite materials, they imply exact relations between the effective tensors of associated dielectric and elasticity problems.

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