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Analytical Solution for Partial Slip Behavior of Multiple Elastic Contacts of Similar Materials

Ghanati, Parisa | 2013

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45091 (45)
  4. University: Sharif University of Technology
  5. Department: Engineering Department
  6. Advisor(s): Adibnazari, Saeed
  7. Abstract:
  8. In the present study, an analytical procedure has been presented to analyze a generic two-dimensional frictional multiple contact problem between two isotropic, homogeneous and elastically similar half planes, under the constant normal (including applied moments) and oscillatory tangential loading, with partial slip behavior. This procedure is based on the classical singular integral equations approach. By applying boundary conditions at nonsingular end points, new side conditions have been derived and titled “the consistency conditions” for multiple contacts. These conditions are necessary for determining the position of nonsingular end points, when the number of them exceeds the number of the contact zones. Subsequently, in order to have access to the gradient of the relative surface displacement functions, a direct approach has been utilized. Moreover, a new relation has been proposed to determine the Muskhelishvili potential function by utilizing the gradient of the relative surface displacement functions at out of the contact area. This approach has been applied to some contact problems, which have an exact closed form solution. Furthermore, access to analytical solutions of contact problems has been investigated and two symmetric double contact problems with nonsingular end points, which do not have a closed form solution, have been analyzed. The results show that for the weak normal loading, the approximated extent of the contact zones in a multiple contact problem with nonsingular end points may be estimated conveniently by assuming that the extent of the contact zones is the same as the overlapped extent in the free interpenetration figure. However, for a given value of the normal force, the error, which is caused by this assumption, increases remarkably with decreasing the distance between the contact zones. Finally, a new approach has been presented to obtain an approximate closed form solution for symmetric double contacts with smooth contact zones. This method is a highly accurate and low computational complexity approach
  9. Keywords:
  10. Analytical Method ; Singular Integral Equations ; Muskhelishvili Potential Function ; Two Dimensional Multiple Contacts ; Portial Slip Behavior

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