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Year 2016, Volume 3, Issue 2, 61 - 72, 31.12.2016
https://doi.org/10.17350/HJSE19030000033

Abstract

References

  • 1. Baroumes L, Bouillon E, Christin F. An improved long life duration ceramic matrix composite material for jet aircraft engine applications. 24th International Congress of the Aeronautical Sciences (2004).
  • 2. Esfandiar H, Daneshmand S, Mondali M. Analysis of elastic-plastic behavior of fiber metal laminates subjected to in-plane tensile loading. Int. J. Advanced Design and Manufacturing Technology 5(1), (2011).
  • 3. Itou S. Thermal stress intensity factors of an infinite orthotropic layer with a crack. International Journal of Fracture 103(3), (2000) 279-291.
  • 4. Thompson W. (Lord Kelvin), Note on the integration of the equations of equilibrium of an elastic solid. Cambridge and Dublin Math. J 3, (1848) 87–89.
  • 5. Green G. An essay on the application of mathematical analysis to the theories of electricity and magnetism, Nottingham, England, T. Wheelhouse, (1828) 10-12.
  • 6. Lamé G. Leçons sur la théorie mathématique de l’élasticité des corps solides, (1852).
  • 7. Boussinesq J. Application des potentiels a l’e´tude de l’e´quilibre et du mouvement des solides e´lastiques, Gauthier-Villars, (1885).
  • 8. Hertz H. Vber die beruhrung fester elastischer korper (On the contact of elastic solids). J. Reine Angew. Math. 92, (1882) 156–171 (in German).
  • 9. Cerruti V. A Treatise on the mathematical theory of elasticity in: A.E.H. Love (ed.), Fourth edition, Dover Publications, New York, (1882) 16.
  • 10 Southwell RV. On the concentration of stress in the neighborhood of a small spherical flow. Phil. Mag., Ser. 7,1, (1926) 71.
  • 11. Mindlin RD. Force at a point in the interior of a semi-infinite half space, Journal of Applied Physics 79, (1936) 195–202.
  • 12. Barber JR, Ciavarella M. Contact mechanics in research trends in solid mechanics, (ed. G. Dvorak), International Journal of Solids and Structures, 37, (2000) 29-43.
  • 13. Muskhelishvili NL. Singular integral equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1953. (based on the second Russian edition published in 1946).
  • 14. England AH. Complex variable methods in elasticity, Wiley Interscience, London, 1971.
  • 15. Johnson KL. Contact Mechanics, Cambridge University Press, 1987.
  • 16. Erdogan F. Mixed boundary value problems in mechanics. in: Nemat-Nasser, S. (ed.), Mechanics Today 4, Pergamon Press, (1978) 1–86.
  • 17. Erdogan F. Approximate solutions of systems of singular integral equations, SIAM J. Appl. Math. 17 (1969) 1041–59.
  • 18. Stroh A. Dislocations and cracks in anisotropic elasticity, Philos. Mag. 3(30) (1958) 625–646.
  • 19. Stroh A. Steady state problems in anisotropic elasticity, J. Math. Phys., 41(2) (1962) 77–103.
  • 20. Lekhnitskii SG. Theory of elasticity of an anisotropic elastic body, Holden-Day, San Francisco 1963.
  • 21. Sveklo VA. Boussinesq type problems for the anisotropic half-space, J. Appl. Math. Mech. 28 (1964) 1099–1105.
  • 22. Willis JR. Hertzian contact of anisotropic bodies, J. Mech. Phys. Solids 14 (1966) 163–176.
  • 23. Shi AA, Lin Y, Ovaert TC. Indentation of an orthotropic halfspace by a rigid ellipsoidal indenter, J. Tribol. 125 (2003) 223–231.
  • 24. Kahya V, Birinci A, Erdol R. Frictionless contact problem between two orthotropic elastic layer, International Journal of Computational and Mathematical Sciences 1 (2007) 121– 127.
  • 25. Batra R, Jian W, Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer, Int. J. Solids Struct 45(22) (2008) 5814–5830.
  • 26. Bagault C, Nelias D, Baietto MC, Contact analyses for anisotropic half space: effect of the anisotropy on the pressure distribution and contact area. Journal of Tribology 134 (3) (2012).
  • 27. Ashrafi H, Mahzoon M, Shariyat M. A new mathematical modeling of contact treatment between an orthotropic material and a rigid indenter, Iranian Journal of Materials Science and Engineering 9(1) (2012) 29-41.
  • 28. Dong X-Q, Zhou Y-T, Wang L-M, Ding S-H, Park J-B. Stress state of two collinear stamps over the surface of orthotropic materials, Arch Appl. Mech (2014)
  • 29. Ramirez G, Heyliger P. Frictionless contact in a layered piezoelectric half-space, Smart Mater. Struct 12 (2003) 612–625.
  • 30. Ramirez G. Frictionless contact in a layered piezoelectric medium characterized by complex eigenvalues, Journal of Smart Materials and Structures, 15(5) (2006) 1287-1295.
  • 31. Zhou YT , Lee, KY. Exact solutions of a new, 2D frictionless contact model for orthotropic piezoelectric materials indented by a rigid sliding punch, Philosophical Magazine 92(15) (2012) 1937–1965.
  • 32. Zhou YT, Lee KY, Frictional contact of anisotropic piezoelectric materials indented by flat and semi-parabolic stamps, Arch Appl. Mech. 83 (2013) 73–95.
  • 33. Krenk S. On the elastic constants of plane orthotropic elasticity, Journal of Composite Materials 13 (1979) 108- 116.
  • 34. Cinar A, Erdogan F. The crack and wedging problem for an orthotropic strip, International Journal of Fracture (1982) 83–102.
  • 35. Ozturk M, Erdogan F. Mode I crack problem in an inhomogeneous orthotropic medium, International Journal of Engineering, Sci. 35(9) (1997) 869-883.
  • 36. Ozturk M, Erdogan F. The mixed mode crack problem in an inhomogeneous orthotropic medium, International Journal of Fracture 98, (1999) 243–261.
  • 37. Guler MA. Contact stresses in an orthotropic medium: a closed-form solution, International Journal of Mechanical Sciences 87 (2014) 72–88
  • 38. Guler MA, Erdogan F. Contact mechanics of graded coatings, International Journal of Solids and Structures 41, (2004) 3865–3889.
  • 39. Guler MA, Erdogan F. Contact mechanics of two deformable elastic solids with graded coatings, Mechanics of Materials, 38(2006) 633–647.
  • 40. Guler MA, Erdogan F. The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings, International Journal of Mechanical Sciences49(2) (2007) 161–182.
  • 41. Kucuksucu A, Guler MA, Avci A. Closed-form solution of a frictional sliding contact problem for an orthotropic elastic half-plane indented by a wedge-shaped punch, Key Engineering Materials 618 (2014) 203-225.
  • 42. Bakırta I. The contact problem of an orthotropic nonhomogeneous elastic half space, International Journal of Engineering Science, 22 (1984) 347-359.
  • 43. Erdogan F. Fracture materials and contact problems in materials involving graded coatings and interfacial zones, Final Technical Reports, Lehigh University, (2001).
  • 44 Chou YT. Interaction of parallel dislocations in a hexagonal crystal, Journal of Applied Physics 33 (1962) 2747–2751.
  • 45. Erdogan F, Gupta GD, Cook TS. Numerical solution of singular integral equations, method of analysis and solution of crack problems, G.C. Sixth (ed.), Noordhoff, Int. Publ. Leyden, (1973) 368-425.
  • 46. Erdogan F, Gupta GD. On the numerical solution of singular integral equations, Quarterly of Applied Mathematics 29 (1972) 525-534.
  • 47. Conner BP. Contact fatigue: Life prediction and palliatives, Ph.D Thesis, Massachusetts Institute of Technology (2002).

Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane

Year 2016, Volume 3, Issue 2, 61 - 72, 31.12.2016
https://doi.org/10.17350/HJSE19030000033

Abstract

A n analytical solution to the frictional sliding contact problem for homogeneous orthotropic materials indented by a semi-circular punch is developed.The principal axes of orthotropy are assumed to be parallel and perpendicular to the contact. Coulomb friction assumption is used to model the friction between the punch and the orthotropic medium. The mixed boundary value problem is reduced into a Fredholm integral equation of the second kind by using Fourier transform technique. The singular integral equation is solved analytically using Jacobi Polynomials for the unknown surface contact stresses. Numerical results show the effect of the orthotropic material parameters, coefficient of friction on the contact stress distribution and load vs. contact length behavior

References

  • 1. Baroumes L, Bouillon E, Christin F. An improved long life duration ceramic matrix composite material for jet aircraft engine applications. 24th International Congress of the Aeronautical Sciences (2004).
  • 2. Esfandiar H, Daneshmand S, Mondali M. Analysis of elastic-plastic behavior of fiber metal laminates subjected to in-plane tensile loading. Int. J. Advanced Design and Manufacturing Technology 5(1), (2011).
  • 3. Itou S. Thermal stress intensity factors of an infinite orthotropic layer with a crack. International Journal of Fracture 103(3), (2000) 279-291.
  • 4. Thompson W. (Lord Kelvin), Note on the integration of the equations of equilibrium of an elastic solid. Cambridge and Dublin Math. J 3, (1848) 87–89.
  • 5. Green G. An essay on the application of mathematical analysis to the theories of electricity and magnetism, Nottingham, England, T. Wheelhouse, (1828) 10-12.
  • 6. Lamé G. Leçons sur la théorie mathématique de l’élasticité des corps solides, (1852).
  • 7. Boussinesq J. Application des potentiels a l’e´tude de l’e´quilibre et du mouvement des solides e´lastiques, Gauthier-Villars, (1885).
  • 8. Hertz H. Vber die beruhrung fester elastischer korper (On the contact of elastic solids). J. Reine Angew. Math. 92, (1882) 156–171 (in German).
  • 9. Cerruti V. A Treatise on the mathematical theory of elasticity in: A.E.H. Love (ed.), Fourth edition, Dover Publications, New York, (1882) 16.
  • 10 Southwell RV. On the concentration of stress in the neighborhood of a small spherical flow. Phil. Mag., Ser. 7,1, (1926) 71.
  • 11. Mindlin RD. Force at a point in the interior of a semi-infinite half space, Journal of Applied Physics 79, (1936) 195–202.
  • 12. Barber JR, Ciavarella M. Contact mechanics in research trends in solid mechanics, (ed. G. Dvorak), International Journal of Solids and Structures, 37, (2000) 29-43.
  • 13. Muskhelishvili NL. Singular integral equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1953. (based on the second Russian edition published in 1946).
  • 14. England AH. Complex variable methods in elasticity, Wiley Interscience, London, 1971.
  • 15. Johnson KL. Contact Mechanics, Cambridge University Press, 1987.
  • 16. Erdogan F. Mixed boundary value problems in mechanics. in: Nemat-Nasser, S. (ed.), Mechanics Today 4, Pergamon Press, (1978) 1–86.
  • 17. Erdogan F. Approximate solutions of systems of singular integral equations, SIAM J. Appl. Math. 17 (1969) 1041–59.
  • 18. Stroh A. Dislocations and cracks in anisotropic elasticity, Philos. Mag. 3(30) (1958) 625–646.
  • 19. Stroh A. Steady state problems in anisotropic elasticity, J. Math. Phys., 41(2) (1962) 77–103.
  • 20. Lekhnitskii SG. Theory of elasticity of an anisotropic elastic body, Holden-Day, San Francisco 1963.
  • 21. Sveklo VA. Boussinesq type problems for the anisotropic half-space, J. Appl. Math. Mech. 28 (1964) 1099–1105.
  • 22. Willis JR. Hertzian contact of anisotropic bodies, J. Mech. Phys. Solids 14 (1966) 163–176.
  • 23. Shi AA, Lin Y, Ovaert TC. Indentation of an orthotropic halfspace by a rigid ellipsoidal indenter, J. Tribol. 125 (2003) 223–231.
  • 24. Kahya V, Birinci A, Erdol R. Frictionless contact problem between two orthotropic elastic layer, International Journal of Computational and Mathematical Sciences 1 (2007) 121– 127.
  • 25. Batra R, Jian W, Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer, Int. J. Solids Struct 45(22) (2008) 5814–5830.
  • 26. Bagault C, Nelias D, Baietto MC, Contact analyses for anisotropic half space: effect of the anisotropy on the pressure distribution and contact area. Journal of Tribology 134 (3) (2012).
  • 27. Ashrafi H, Mahzoon M, Shariyat M. A new mathematical modeling of contact treatment between an orthotropic material and a rigid indenter, Iranian Journal of Materials Science and Engineering 9(1) (2012) 29-41.
  • 28. Dong X-Q, Zhou Y-T, Wang L-M, Ding S-H, Park J-B. Stress state of two collinear stamps over the surface of orthotropic materials, Arch Appl. Mech (2014)
  • 29. Ramirez G, Heyliger P. Frictionless contact in a layered piezoelectric half-space, Smart Mater. Struct 12 (2003) 612–625.
  • 30. Ramirez G. Frictionless contact in a layered piezoelectric medium characterized by complex eigenvalues, Journal of Smart Materials and Structures, 15(5) (2006) 1287-1295.
  • 31. Zhou YT , Lee, KY. Exact solutions of a new, 2D frictionless contact model for orthotropic piezoelectric materials indented by a rigid sliding punch, Philosophical Magazine 92(15) (2012) 1937–1965.
  • 32. Zhou YT, Lee KY, Frictional contact of anisotropic piezoelectric materials indented by flat and semi-parabolic stamps, Arch Appl. Mech. 83 (2013) 73–95.
  • 33. Krenk S. On the elastic constants of plane orthotropic elasticity, Journal of Composite Materials 13 (1979) 108- 116.
  • 34. Cinar A, Erdogan F. The crack and wedging problem for an orthotropic strip, International Journal of Fracture (1982) 83–102.
  • 35. Ozturk M, Erdogan F. Mode I crack problem in an inhomogeneous orthotropic medium, International Journal of Engineering, Sci. 35(9) (1997) 869-883.
  • 36. Ozturk M, Erdogan F. The mixed mode crack problem in an inhomogeneous orthotropic medium, International Journal of Fracture 98, (1999) 243–261.
  • 37. Guler MA. Contact stresses in an orthotropic medium: a closed-form solution, International Journal of Mechanical Sciences 87 (2014) 72–88
  • 38. Guler MA, Erdogan F. Contact mechanics of graded coatings, International Journal of Solids and Structures 41, (2004) 3865–3889.
  • 39. Guler MA, Erdogan F. Contact mechanics of two deformable elastic solids with graded coatings, Mechanics of Materials, 38(2006) 633–647.
  • 40. Guler MA, Erdogan F. The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings, International Journal of Mechanical Sciences49(2) (2007) 161–182.
  • 41. Kucuksucu A, Guler MA, Avci A. Closed-form solution of a frictional sliding contact problem for an orthotropic elastic half-plane indented by a wedge-shaped punch, Key Engineering Materials 618 (2014) 203-225.
  • 42. Bakırta I. The contact problem of an orthotropic nonhomogeneous elastic half space, International Journal of Engineering Science, 22 (1984) 347-359.
  • 43. Erdogan F. Fracture materials and contact problems in materials involving graded coatings and interfacial zones, Final Technical Reports, Lehigh University, (2001).
  • 44 Chou YT. Interaction of parallel dislocations in a hexagonal crystal, Journal of Applied Physics 33 (1962) 2747–2751.
  • 45. Erdogan F, Gupta GD, Cook TS. Numerical solution of singular integral equations, method of analysis and solution of crack problems, G.C. Sixth (ed.), Noordhoff, Int. Publ. Leyden, (1973) 368-425.
  • 46. Erdogan F, Gupta GD. On the numerical solution of singular integral equations, Quarterly of Applied Mathematics 29 (1972) 525-534.
  • 47. Conner BP. Contact fatigue: Life prediction and palliatives, Ph.D Thesis, Massachusetts Institute of Technology (2002).

Details

Primary Language English
Journal Section Research Article
Authors

Aysegul KUCUKSUCU This is me
Department of Mechanical Engineering, TOBB University of Economics and Technology Ankara 06560, Turkey


Mehmet Ali GULER This is me
Department of Mechanical Engineering, TOBB University of Economics and Technology Ankara 06560, Turkey

Publication Date December 31, 2016
Application Date
Acceptance Date
Published in Issue Year 2016, Volume 3, Issue 2

Cite

Bibtex @ { hjse860016, journal = {Hittite Journal of Science and Engineering}, eissn = {2148-4171}, address = {Hitit Üniversitesi Mühendislik Fakültesi Kuzey Kampüsü Çevre Yolu Bulvarı 19030 Çorum / TÜRKİYE}, publisher = {Hitit University}, year = {2016}, volume = {3}, number = {2}, pages = {61 - 72}, doi = {10.17350/HJSE19030000033}, title = {Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane}, key = {cite}, author = {Kucuksucu, Aysegul and Guler, Mehmet Ali} }
APA Kucuksucu, A. & Guler, M. A. (2016). Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane . Hittite Journal of Science and Engineering , 3 (2) , 61-72 . DOI: 10.17350/HJSE19030000033
MLA Kucuksucu, A. , Guler, M. A. "Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane" . Hittite Journal of Science and Engineering 3 (2016 ): 61-72 <https://dergipark.org.tr/en/pub/hjse/issue/59669/860016>
Chicago Kucuksucu, A. , Guler, M. A. "Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane". Hittite Journal of Science and Engineering 3 (2016 ): 61-72
RIS TY - JOUR T1 - Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane AU - AysegulKucuksucu, Mehmet AliGuler Y1 - 2016 PY - 2016 N1 - doi: 10.17350/HJSE19030000033 DO - 10.17350/HJSE19030000033 T2 - Hittite Journal of Science and Engineering JF - Journal JO - JOR SP - 61 EP - 72 VL - 3 IS - 2 SN - -2148-4171 M3 - doi: 10.17350/HJSE19030000033 UR - https://doi.org/10.17350/HJSE19030000033 Y2 - 2022 ER -
EndNote %0 Hittite Journal of Science and Engineering Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane %A Aysegul Kucuksucu , Mehmet Ali Guler %T Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane %D 2016 %J Hittite Journal of Science and Engineering %P -2148-4171 %V 3 %N 2 %R doi: 10.17350/HJSE19030000033 %U 10.17350/HJSE19030000033
ISNAD Kucuksucu, Aysegul , Guler, Mehmet Ali . "Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane". Hittite Journal of Science and Engineering 3 / 2 (December 2016): 61-72 . https://doi.org/10.17350/HJSE19030000033
AMA Kucuksucu A. , Guler M. A. Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane. Hittite J Sci Eng. 2016; 3(2): 61-72.
Vancouver Kucuksucu A. , Guler M. A. Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane. Hittite Journal of Science and Engineering. 2016; 3(2): 61-72.
IEEE A. Kucuksucu and M. A. Guler , "Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane", Hittite Journal of Science and Engineering, vol. 3, no. 2, pp. 61-72, Dec. 2016, doi:10.17350/HJSE19030000033