scholarly journals Conservation laws from any conformal transformations and the parameters for a sharp V-notch in plane elasticity

2013 ◽  
Vol 50 (9) ◽  
pp. 1394-1401 ◽  
Author(s):  
Weichen Shi ◽  
Lin Lu
Keyword(s):  
Conservation Laws ◽  
Plane Elasticity ◽  
Conformal Transformations

Problems of Plane Elasticity for Reinforced Boundaries

1955 ◽  
Vol 22 (2) ◽  
pp. 249-254
Author(s):  
J. R. M. Radok
Keyword(s):  
Plane Elasticity ◽  
Conformal Transformations ◽  
Thin Sheets ◽  
General Method

Abstract Based on N. I. Muskhelishvili’s approach to problems of plane elasticity, a general method has been deduced for the solution of problems of reinforced cutouts in infinitely thin sheets. As an illustration, the circular reinforced hole has been treated in detail and the results have been related to those obtained experimentally and theoretically by other authors. The solution for other shapes of cutouts will be greatly simplified, since full use may be made of the theory of conformal transformations.

Conservation Laws and Energy-Release Rates

1973 ◽  
Vol 40 (1) ◽  
pp. 201-203 ◽  
Author(s):  
B. Budiansky ◽  
J. R. Rice
Keyword(s):  
Conservation Laws ◽  
Energy Release ◽  
Complex Variable ◽  
Plane Elasticity ◽  
Special Point ◽  
Stress Distributions ◽  
Isotropic Plane ◽  
Release Rates ◽  
Energy Release Rates ◽  
Plastic Stress

New path-independent integrals recently discovered by Knowles and Sternberg are related to energy-release rates associated with cavity or crack rotation and expansion. Complex-variable forms are presented for the conservation laws in the cases of linear, isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly.

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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