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Investigation of the Frictionless Contact Problem in A Rigidly Supported Homogeneous Layer by Using FEM

Year 2019, Volume: 9 Issue: 4, 797 - 807, 15.10.2019
https://doi.org/10.17714/gumusfenbil.569047

Abstract

In this study, the continuous contact problem of a homogeneous layer of
constant thickness perfectly bonded to a rigid support on its bottom surface
and loaded a rigid stamp is investigated using the finite element method (FEM).
It is assumed that the all contact surfaces are frictionless.
The homogenous layer is loaded by rigid circular
stamp with external load P. Two-dimensional finite element analysis of the
problem is performed using ANSYS software. Also, normal stresses and shear
stresses are investigated along the depth of the layer for different shear
modulus ratios. Besides, contact length and contact stress between rigid block
and homogenous layer are determined. The obtained results are compared to
analytical solution and they are shown in graphs and tables.

References

  • Abhilash M. N. ve Murthy H., 2014. Finite Element Analysis of 2D Elastic Contacts Involving FGMs, International Journal for Computational Methods in Engineering Science and Mechanics, 15, 253-257
  • Adiyaman, G., Oner E., Yaylaci M. ve Birinci, A., 2016. A Receding Contact Problem between A Functionally Graded Layer and Two Homogeneous Quarter Planes, Acta Mechanica, 227, 1753-1766
  • ANSYS, 2016, Swanson Analysis Systems Inc., Houston PA, USA.
  • Birinci A., Adiyaman G., Yaylaci M. ve Öner, E., 2015. Analysis of Continuous and Discontinuous Cases of A Contact Problem Using Analytical Method and FEM, Latin American Journal of Solids and Structures, 12, 1771-1789
  • Bora P., 2016. İki Rijit Dikdörtgen Blok Ile Yüklenmiş Elastik Yarı Sonsuz Düzlem Üzerine Oturan Iki Elastik Tabakanın Temas Problemi, Ph.D. Thesis, Karadeniz Technical University, Trabzon, Turkey
  • Bussetta A., Marceau D. ve Ponthot J.P., 2012. The Adapted Augmented Lagrangian Method: A New Method for Resolution of The Mechanical Frictional Contact Problem, Computational Mechanics, 49(2), 259-275
  • Chan S.K. ve Tuba I.S., 1971. A Finite Element Method for Contact Problems of Solid Bodies-Part I. Theory and Validation, International Journal of Mechanical Sciences, 13, 615-625
  • Civelek M.B. ve Erdoğan F., 1974. The Axisymmetrical Double Contact Problem for A Frictionless Elastic Layer, International Journal of Solids and Structures, 10(6), 639-659
  • Çömez İ., 2010. Frictional Contact Problem for A Rigid Cylindrical Stamp and An Elastic Layer Resting on A Half Plane, International Journal of Solids and Structures, 47(7-8), 1090-1097.
  • Çömez İ., 2015. Contact Problem for A Functionally Graded Layer Indented by A Moving Punch, International Journal of Mechanical Sciences, 100, 339–344
  • Elhaskawy A. A., 1999. Effect of Friction on Subsurface Stresses in Sliding Line Contact of Multilayered Elastic Solids, International Journal of Solid and Structures, 36, 2903-3915
  • Franke D., Düster A., Nübel V. ve Rank E., 2010. A comparison of The H-, P-, Hp- and Rp Version of The FEM for The Solution of The 2D Hertzian Contact Problem, Computational Mechanics, 45,513-522
  • Giannakopoulos A.E. ve Pallot P., 2000. Two-Dimensional Contact Analysis of Elastic Graded Materials, Journal of The Mechanics and Physics of Solids, 48,1597-1631
  • Kahya V., 1997. Üst Tarafından Rijit Olarak Mesnetlenmiş Elastik Bir Tabaka İle Rijit Bir Blok Arasındaki Sürtünmesiz Değme Problem, Master Thesis, Karadeniz Technical University, Trabzon, Turkey
  • Kaya Y., Polat A. ve Özsahin T.Ş., 2018. Comparison of FEM Solution with Analytical Solution of Continuous and Discontinuous Contact Problem, Sigma Journal of Engineering and Natural Sciences, 36(4), 977-992
  • Nikbakht A., Arezoodar A.F., Sadighi M., Zucchelli A. ve Lari A.F., 2013. Frictionless Elastic Contact Analysis of A Functionally Graded Vitreous Enameled Low Carbon Steel Plate and A Rigid Spherical Indenter, Composite Structures, 96,484-501
  • Öner E., Yaylacı M. ve Birinci A., 2015. Analytical Solution of A Contact Problem and Comparison with The Results from FEM, Structural Engineering and Mechanics, 54(4), 607-622
  • Özşahin T.Ş., Kahya, V. ve Çakıroğlu A., O. 2007. Contact Problem for An Elastic Layered Composite Resting on Rigid Flat Supports, International Journal of Computational and Mathematical Sciences, 1(2), 145-159
  • Polat A., Kaya Y. ve Özsahin T.Ş., 2018. Analytical Solution to Continuous Contact Problem for A Functionally Graded Layer Loaded Through Two Dissimilar Rigid Punches, Meccanica, 53(14), 3565-3577
  • Ratwani M. ve Erdoğan F., 1973. On The Plane Contact Problem for A Frictionless Elastic Layer, International Journal of Solids and Structures, 9, 921-936

Rijit Olarak Mesnetlenmiş Homojen Tabakada Sürtünmesiz Temas Probleminin Sonlu Elemanlar Metodu ile İncelenmesi

Year 2019, Volume: 9 Issue: 4, 797 - 807, 15.10.2019
https://doi.org/10.17714/gumusfenbil.569047

Abstract

Bu çalışmada, alt yüzeyinden rijit olarak mesnetlenmiş
ve rijit bir dairesel blok ile yüklenmiş sabit yükseklikli bir homojen tabakada
sürekli temas problemi sonlu elemanlar yöntemi kullanılarak incelenmiştir.
Bütün yüzeylerin sürtünmesiz olduğu kabul edilmiştir. Homojen tabaka, dış yükü
P olan bir rijit dairesel blok vasıtasıyla yüklenmiştir. Problemin iki boyutlu
sonlu elemanlar analizi ANSYS yazılımı kullanılarak gerçekleştirilmiştir. Ayrıca
farklı yükleme durumları için tabakanın derinliği boyunca normal gerilmeler ve
kayma gerilmeleri incelenmiştir. Bunun yanı sıra  rijit blok ile homojen tabaka arasındaki temas
mesafeleri ve temas gerilmeleri belirlenmiştir. Elde edilen sonuçlar analitik
sonuçlarla kıyaslanarak grafik ve tablo halinde gösterilmiştir.

References

  • Abhilash M. N. ve Murthy H., 2014. Finite Element Analysis of 2D Elastic Contacts Involving FGMs, International Journal for Computational Methods in Engineering Science and Mechanics, 15, 253-257
  • Adiyaman, G., Oner E., Yaylaci M. ve Birinci, A., 2016. A Receding Contact Problem between A Functionally Graded Layer and Two Homogeneous Quarter Planes, Acta Mechanica, 227, 1753-1766
  • ANSYS, 2016, Swanson Analysis Systems Inc., Houston PA, USA.
  • Birinci A., Adiyaman G., Yaylaci M. ve Öner, E., 2015. Analysis of Continuous and Discontinuous Cases of A Contact Problem Using Analytical Method and FEM, Latin American Journal of Solids and Structures, 12, 1771-1789
  • Bora P., 2016. İki Rijit Dikdörtgen Blok Ile Yüklenmiş Elastik Yarı Sonsuz Düzlem Üzerine Oturan Iki Elastik Tabakanın Temas Problemi, Ph.D. Thesis, Karadeniz Technical University, Trabzon, Turkey
  • Bussetta A., Marceau D. ve Ponthot J.P., 2012. The Adapted Augmented Lagrangian Method: A New Method for Resolution of The Mechanical Frictional Contact Problem, Computational Mechanics, 49(2), 259-275
  • Chan S.K. ve Tuba I.S., 1971. A Finite Element Method for Contact Problems of Solid Bodies-Part I. Theory and Validation, International Journal of Mechanical Sciences, 13, 615-625
  • Civelek M.B. ve Erdoğan F., 1974. The Axisymmetrical Double Contact Problem for A Frictionless Elastic Layer, International Journal of Solids and Structures, 10(6), 639-659
  • Çömez İ., 2010. Frictional Contact Problem for A Rigid Cylindrical Stamp and An Elastic Layer Resting on A Half Plane, International Journal of Solids and Structures, 47(7-8), 1090-1097.
  • Çömez İ., 2015. Contact Problem for A Functionally Graded Layer Indented by A Moving Punch, International Journal of Mechanical Sciences, 100, 339–344
  • Elhaskawy A. A., 1999. Effect of Friction on Subsurface Stresses in Sliding Line Contact of Multilayered Elastic Solids, International Journal of Solid and Structures, 36, 2903-3915
  • Franke D., Düster A., Nübel V. ve Rank E., 2010. A comparison of The H-, P-, Hp- and Rp Version of The FEM for The Solution of The 2D Hertzian Contact Problem, Computational Mechanics, 45,513-522
  • Giannakopoulos A.E. ve Pallot P., 2000. Two-Dimensional Contact Analysis of Elastic Graded Materials, Journal of The Mechanics and Physics of Solids, 48,1597-1631
  • Kahya V., 1997. Üst Tarafından Rijit Olarak Mesnetlenmiş Elastik Bir Tabaka İle Rijit Bir Blok Arasındaki Sürtünmesiz Değme Problem, Master Thesis, Karadeniz Technical University, Trabzon, Turkey
  • Kaya Y., Polat A. ve Özsahin T.Ş., 2018. Comparison of FEM Solution with Analytical Solution of Continuous and Discontinuous Contact Problem, Sigma Journal of Engineering and Natural Sciences, 36(4), 977-992
  • Nikbakht A., Arezoodar A.F., Sadighi M., Zucchelli A. ve Lari A.F., 2013. Frictionless Elastic Contact Analysis of A Functionally Graded Vitreous Enameled Low Carbon Steel Plate and A Rigid Spherical Indenter, Composite Structures, 96,484-501
  • Öner E., Yaylacı M. ve Birinci A., 2015. Analytical Solution of A Contact Problem and Comparison with The Results from FEM, Structural Engineering and Mechanics, 54(4), 607-622
  • Özşahin T.Ş., Kahya, V. ve Çakıroğlu A., O. 2007. Contact Problem for An Elastic Layered Composite Resting on Rigid Flat Supports, International Journal of Computational and Mathematical Sciences, 1(2), 145-159
  • Polat A., Kaya Y. ve Özsahin T.Ş., 2018. Analytical Solution to Continuous Contact Problem for A Functionally Graded Layer Loaded Through Two Dissimilar Rigid Punches, Meccanica, 53(14), 3565-3577
  • Ratwani M. ve Erdoğan F., 1973. On The Plane Contact Problem for A Frictionless Elastic Layer, International Journal of Solids and Structures, 9, 921-936
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Alper Polat 0000-0002-6368-5276

Publication Date October 15, 2019
Submission Date May 22, 2019
Acceptance Date September 9, 2019
Published in Issue Year 2019 Volume: 9 Issue: 4

Cite

APA Polat, A. (2019). Rijit Olarak Mesnetlenmiş Homojen Tabakada Sürtünmesiz Temas Probleminin Sonlu Elemanlar Metodu ile İncelenmesi. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 9(4), 797-807. https://doi.org/10.17714/gumusfenbil.569047