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Preliminary report

UDC: 539.42:519.61/.65

DOI: 10.7251/afts.2014.0611.059L

COBISS.RS-ID 4572952

 

DEFINITION OF CRACKS FOR THE ULTIMATEDEGENERATION PROCESS OF REVOLVING ELLIPSOIDS

 

Lukić Dragan1, Zlatanović Elefterija2
2University of Niš, Faculty of Civil Engineering and Architecture of Niš

 

 ABSTRACT  Full text (pdf)

The state of stress around cavities of the revolving ellipsoidal shape (prolate or oblate) in the extreme cases of their degeneration is a very complex problem. Namely, the shape of cavities is defined by an appropriate curvilinear coordinate system, which contains hyperbolic and trigonometric functions. In this paper, the treatment of revolving ellipsoid coordinates has been presented, along with transformations of ellipsoids for corresponding limiting values of their coordinates. Various forms of cracking can be defined through the ellipsoid degeneration process. In addition, the paper is dealing with a definition of the stress state for the limiting cases of degeneration.

 

Keywords: revolving ellipsoid, ultimate degeneration process, crack, state of stress

 

REFERENCES

[1]
Lukic, D. (1998). Contribution to methods of stress state determination around cavity of rotational ellipsoid   shape, by use of elliptic coordinates, PhD thesis, University of  Belgrade.
[2]
Hobson, E.W. (1931). Spherical and ellipsoidal harmonics, Cambridge
[3]
Sneddon, N., Lowengrub, M. (1969). Crack Problems in the Classical theory of Elasticity, New York.
[4]
Neuber, H. (1958). Kerbspannungslehre, Springer-Verlag, Berlin.
[5]
Edwards, R.H. (1951). Stress Concentrations Around Spheroidal Inclusions and Cavities, J. Appl.Mechanics, Vol.18, pp 19-30.
[6]
Lukić, D., Prokić, A., Anagnosti, P. (2009).  Stress-strain field around elliptic cavities in elastic continuum, European Journal of Mechanics - A/Solids, Vol. 28, No. 1, pp. 86- 93.
[7]
Lukić, D., Prokić, A., Brčić, S. (2011). Stress state around cylinrical cavities in isotropic medium, Archives for Technical Sciences, Technical Institute of Bijeljina, No 5, pp. 40-47.

 

 

 

 

  

  

  

  

  

  

 

   

 
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