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Elastic Fields of a Confocal Elliptic Ring at the States of Plane Strain and Plane Stress

Esmaeili, Mahmoud | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45971 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. In this thesis an analytical solution is introduced for finding the elastic fields of stress and strain in a confocal elliptic ring at the state of general plane problem. A confocal elliptic ring is a doubly connected region which its external and internal boundaries are ellipses with the same focal points. We used the method of complex variables, the functions of Kolosov-Muskhelishvili potentials, Laurent series expansion for analytical functions, the method of the analytic continuation of Milne-Thomson, elliptic hyperbolic coordinates, and two dimensional conformal mapping to do this study. the importance of this analysis is because we can simulate some problems of the elasticity by changing the geometrical parameters of such a ring, most importantly, the stress analysis in the crack occurred in a circular or elliptical or infinite plane. The complexity of this problem is due to the duplication of the section connectedness. The results achieved in this thesis are applicable in the analysis of the elastic fields of the stress and strain in the thin-walled and thick-walled cylinders. Some different examples of such problems with their practical applications are introduced in this thesis
  9. Keywords:
  10. Conformal Mapping ; Elastic Fields ; Elliptic-Hyperbolic Equation ; Kolosov-Muskhelishivili Potentials ; Milne-Thamson Analytic Continuation

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