Complex potentials of a two-dimensional linearized problem in elasticity theory (compressible bodies)

1980 ◽  
Vol 16 (5) ◽  
pp. 417-425
Author(s):  
A. N. Guz'
Keyword(s):  
Elasticity Theory ◽  
Complex Potentials ◽  
Two Dimensional ◽  
Linearized Problem

Complex dynamical invariants for two-dimensional complex potentials

Pramana ◽  
2012 ◽  
Vol 79 (2) ◽  
pp. 173-183 ◽  
Author(s):  
J S VIRDI ◽  
F CHAND ◽  
C N KUMAR ◽  
S C MISHRA
Keyword(s):  
Complex Potentials ◽  
Two Dimensional ◽  
Dynamical Invariants

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

On complex potentials in elasticity theory

1988 ◽  
Vol 72 (1-2) ◽  
pp. 161-171 ◽  
Author(s):  
C. Constanda
Keyword(s):  
Elasticity Theory ◽  
Complex Potentials

scholarly journals Point defects in two-dimensional colloidal crystals: simulation vs. elasticity theory

Soft Matter ◽  
2009 ◽  
Vol 5 (3) ◽  
pp. 646-659 ◽  
Author(s):  
Wolfgang Lechner ◽  
Christoph Dellago
Keyword(s):  
Elasticity Theory ◽  
Point Defects ◽  
Colloidal Crystals ◽  
Two Dimensional

scholarly journals Complex potentials in two-dimensional elasticity

1945 ◽  
Vol 184 (997) ◽  
pp. 129-179 ◽  
Keyword(s):  
Complex Variable ◽  
Body Force ◽  
Displacement Function ◽  
The Body ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Two Dimensional ◽  
Special Cases ◽  
Airy’S Stress Function

This paper gives an approach to two-dimensional isotropic elastic theory (plane strain and generalized plane stress) by means of the complex variable resulting in a very marked economy of effort in the investigation of such problems as contrasted with the usual method by means of Airy’s stress function and the allied displacement function. This is effected (i) by considering especially the transformation of two-dimensional stress; it emerges that the combinations xx + yy , xx — yy + 2 ixy are all-important in the treatment in terms of complex variables; (ii) by the introduction of two complex potentials Ω( z ), ω( z ) each a function of a single complex variable in terms of . which the displacements and stresses can be very simply expressed. Transformation of the cartesian combinations u + iv , xx + yy , xx — yy + 2 ixy to the orthogonal curvilinear combinations u ξ + iu n , ξξ + ηη, ξξ - ηη + 2iξη is simple and speedy. The nature of "the complex potentials is discussed, and the conditions that the solution for the displacements shall be physically admissible, i.e. single-valued or at most of the possible dislocational types, is found to relate the cyclic functions of the complex potentials. Formulae are found for the force and couple resultants at the origin z = 0 equivalent to the stresses round a closed circuit in the elastic material, and these also are found to relate the cyclic functions of the complex potentials. The body force has bhen supposed derivable from a particular body force potential which includes as special cases (i) the usual gravitational body force, (ii) the reversed mass accelerations or so-called ‘centrifugal’ body forces of steady rotation. The power of the complex variable method is exhibited by finding the appropriate complex potentials for a very wide variety of problems, and whilst the main object of the present paper has been to extend the wellknown usefulness of the complex variable method in non-viscous hydrodynamical theory to two-dimensional elasticity, solutions have been given to a number of new problems and corrections made to certain other previous solutions.

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