Figure 7 - uploaded by Yiannis Galidakis
Content may be subject to copyright.
Cases a) and b)

Cases a) and b)

Source publication
Research Proposal
Full-text available
Recently translated father's 1968 Ph.D. Thesis, appears to be related to Hilbert's Problem #21, in the context of Theory of Elasticity using Complex Variables. The Hilbert kernel is stressed on various points and a complete solution for its elastic profile is given up to compromise. The crack is described using analytic functions.

Contexts in source publication

Context 1
... z is a real variable such that 0 ≤ |z| ≤ R and ds = −dz because of cos(n, x) = 0 and cos(n, y) = 1. The components X n , Y n are found as follows for the three basic cases of charge: a) For continuous, uniformly distributed, normal charge on a section of the contour (Fig. ...
Context 2
... For continuous, uniformly distributed, tangential charge q on a section of the contour (Fig. 7b). X n = q, Y n = 0 for z between z ′ z ′′ . c) For given stresses σ ∞ x , σ ∞ y and τ ∞ xy where X n = Y n = 0. 4. Examining the structure of the functions Φ ′ 1 (z 1 ), Φ ′ 2 (z 2 ) in equations (17) we ...

Similar publications

Full-text available
Employing primarily analytic continuation, we derive analytical solutions to the anti-plane problem associated with a screw dislocation located anywhere inside an anisotropic tri-material composed of an intermediate anisotropic elastic layer of finite thickness sandwiched between two semi-infinite anisotropic elastic media. All three phases of the...


... Any such compression is (ultimately) characterized by the "crack" the compressive agent produces on the various elastic media it is applied upon. This, has been analyzed completely in [5] for the "generally" isotropic or anisotropic disk under tension 20 . The implosion type nuclear weapon on the other hand is another process which causes deformation and a "crack" (on a much larger scale). ...
... (6.10) 20 With the compressive agent being − → IA in the direction n, giving component stresses Xn and Yn on a linear element ∆s as in page 10, therein. This being the most general case, a model of any other case can be constructed with a subset of [5]. 21 As continuous however, it may not necessarily be linear. ...
... For example, under an appropriate coordinate transformation which takes the arguments ρ and φ onto a standard polar coordinate system ρ and θ, the curve can be seen to satisfy the polar form of the Cauchy-Riemann equations.5 The folia of Theorem 2.1 also bare similar p-polygonal symmetry to the symmetry of the orbit of the iterated exponential z z ··· on the Complex plane ([3]), with the exception of that when either m/ GCD(m, n) or n/ GCD(m, n) is divisible by 2, the period p is doubled. ...
Full-text available
The Spherical Harmonic Oscillator as a basis Model for the solution of various Classical or Relativistic IVP problems in Astrophysics and Mechanics