Figure 7 - uploaded by Yiannis Galidakis

Content may be subject to copyright.

Source publication

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

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...

## Citations

... 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. ...

The Spherical Harmonic Oscillator as a basis Model for the solution of various Classical or Relativistic IVP problems in Astrophysics and Mechanics