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COMPARISON OF FEM SOLUTION WITH ANALYTICAL SOLUTION OF CONTINUOUS AND DISCONTINUOUS CONTACT PROBLEM

Yıl 2018, Cilt: 36 Sayı: 4, 977 - 992, 01.12.2018

Öz

The continuous and discontinuous contact problem of a homogeneous layer loaded with three rigid flat blocks and resting on the elastic semi-infinite plane was investigated in this study by using the finite element method (FEM). All surfaces are assumed to be frictionless. The homogenous layer was loaded by means of three rigid flat blocks whose external loads are Q and P (per unit thickness in 𝑧 direction). Two dimensional finite element analysis of the problem was performed using ANSYS package program. Analyzes were performed for loading conditions which are Q=P, Q=2P, Q=4P, Q=8P and Q=10P, and different values of block widths, distances between blocks and shear modulus. The initial separation loads and initial separation distances between the homogeneous layer and the elastic semi-infinite plane were determined for continuous contact condition. The length of the separation zone was obtained for discontinuous contact condition. In addition to these, normal stress distributions between the layer and the semi-infinite plane were determined for continuous and discontinuous contact conditions. As a result of the study, the analytical results, and the results of the finite element method were shown by comparing as graphs and tables.

Kaynakça

  • [1] Hertz H., (1895) Gessammelte Worke. Leipzig, Germany.
  • [2] Sneddon I.N., (1972) The Use of Integral Transforms, McGraw-Hill, New York.
  • [3] Adıyaman G., Birinci A., (2013) İki Çeyrek Düzlem Üzerine Oturan Elastik Bir Tabakanın Sürtünmesiz ve Ayrılmalı Temas Problemi, XVIII. Ulusal Mekanik Kongresi, Manisa.
  • [4] Öner E., (2011) The continuous contact problem for two elastic layers loaded by means of a rigid circular punch and resting on an elastic half infinite plane, A Master Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [5] Ozsahin T.S. and Taskıner O., (2013) Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches, Mathematical Problems in Engineering, Article ID 137427, 14 pages.
  • [6] Bora P., (2016) The contact problem for two elastic layers loaded by means of two rigid rectangle blocks and resting on an elastic half infinite plane, A Phd Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [7] Ueda S. and Mukai T., (2002) The Surface Crack Problem for A Layered Elastic Medium with A Functionally Graded Nonhomogeneous Interface, JSME International Journal Series a Solid Mechanics and Material Engineering, vol. 45, no. 3, pp. 371-378.
  • [8] Matysiak S.J., (2003) Edge Crack in An Elastic Layer Resting on Winkler Foundation, Engineering Fracture Mechanics, vol. 70, no. 17, pp. 2353-2361.
  • [9] Dong C.Y., Lo S.Y. and Cheung Y.K., (2004) Numerical Solution for Elastic Half Plane Inclusion Problems by Different Integral Equation Approaches, Engineering Analysis with Boundary Elements, vol. 28, pp. 123-130.
  • [10] Elsharkawy A.A., (1999) Effect of Friction on Subsurface Stresses in Sliding Line Contact of Multilayered Elastic Solids, International Journal of Solids and Structures, vol. 36, pp. 3903-3915.
  • [11] Giannakopoulos A.E. and Pallot P., (2000) Two-Dimensional Contact Analysis of Elastic Graded Materials, Journal of the Mechanics and Physics of Solids, vol. 48, pp.1597-1631.
  • [12] Çömez İ., (2009) Receding contact problem of two elastic layers supported by two elastic quarter planes, A Phd Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [13] Keer L.M., Dundurs J. and Tasi K.C., (1972) Problems Involving a Receding Contact Between a Layer and a Half-Space, Journal of Applied Mechanics, vol. 39, pp.1115–1120.
  • [14] Kahya V., Ozsahin T.S., Birinci A. and Erdol R., (2007) A Receding Contact Problem for An Anisotropic Elastic Medium Consisting of A Layer And A Half Plane, International Journal of Solids and Structures, vol. 44, no. 17, pp.5695–5710.
  • [15] Adibelli H., Çömez İ. and Erdöl R., (2013) Receding Contact Problem for A Coated Layer And A Half-Plane Loaded By A Rigid Cylindrical Stamp, Archives of Mechanics, vol. 65, pp.219-236.
  • [16] Yan J. and Mi C., (2017) On the Receding Contact between An Inhomogeneously Coated Elastic Layer and A Homogeneous Half-Plane, Mechanics of Materials, vol. 112, pp. 18-27.
  • [17] Yaylaci M., Oner E. and Birinci A., (2014) Comparison Between Analytical and ANSYS Calculations for A Receding Contact Problem, Journal of Engineering and Mechanics, vol. 140, no. 9, 04014070.
  • [18] Chan S.K. and Tuba I. S., (1971) A Finite Element Method for Contact Problems of Solid Bodies—Part I. Theory and Validation, International Journal of Mechanical Sciences, vol. 13, pp. 615-625.
  • [19] Klarbring A., (1986) A Mathematical Programming Approach to Three-Dimensional Contact Problems with Friction, Computer Methods in Applied Mechanics and Engineering, vol. 58, no. 2, pp.175-200.
  • [20] Bostan V. and Han W., (2006) A Posteriori Error Analysis for Finite Element Solutions of A Frictional Contact Problem, Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 9-12, pp. 1252–1274.
  • [21] Roncevic B. and Siminiati D., (2010) Two Dimensional Receding Contact Problem Analysis with NX-NASTRAN, Advanced Engineering, vol. 4, pp. 1846-5900.
  • [22] Adiyaman G., Yaylaci M. and Birinci A., (2015) Analytical and Finite Element Solution of a Receding Contact Problem, Structural Engineering And Mechanics, vol. 54, no. 1, pp.69-85.
  • [23] Yaylacı M., (2017) Comparıson Between Numerıcal and Analytıcal Solutions for the Receding Contact Problem, Sigma Journal of Engineering and Natural Sciences, vol. 35, no. 2, pp.333-346.
  • [24] Oner E., Yaylacı M. and Birinci A., (2015) Analytical solution of a contact problem and comparison with the results from FEM, Structural Engineering and Mechanics, vol. 54, no. 4.
  • [25] Kaya Y., Polat A. and Özşahin T.Ş., Analysis Of Continuous Contact Problem Of Homogeneous Plate Bonded A Rigid Support By Using Finite Element Method, 2nd International Conference On Advanced Engineering Technologies (ICADET 2017), 21-23 October 2017 Bayburt, Turkey.
  • [26] Birinci A., Adıyaman G., Yaylacı M. and 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, vol. 12, pp.1771-1789.
  • [27] Polat A., Kaya Y. and Ozsahin T.S., (2018) Analysis of Frictionless Contact Problem for A Layer on An Elastic Half Plane Using FEM, Düzce Üniversitesi Bilim ve Teknoloji Dergisi, vol. 6, no. 2, pp. 357-368.
  • [28] Polat A., Kaya Y. and Ozsahin T.S., (2018) Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches, Meccanica, vol. 53, no. 14, pp. 3565-3577.
  • [29] Erdogan F. and Gupta G., (1972) On The Numerical Solutions of Singular Integral Equations, Quarterly of Applied Mathematics, vol. 29, pp. 525-534.
  • [30] ANSYS, (2015) Swanson Analysis Systems Inc., Houston PA, USA.
  • [31] Biswas P.K. and Banerjee S., (2013) ANSYS Based FEM Analysis for Three And Four Coil Active Magnetic Bearing-A Comparative Study, International Journal of Applied Science and Engineering, vol. 11, no. 3, pp. 277-292.
Yıl 2018, Cilt: 36 Sayı: 4, 977 - 992, 01.12.2018

Öz

Kaynakça

  • [1] Hertz H., (1895) Gessammelte Worke. Leipzig, Germany.
  • [2] Sneddon I.N., (1972) The Use of Integral Transforms, McGraw-Hill, New York.
  • [3] Adıyaman G., Birinci A., (2013) İki Çeyrek Düzlem Üzerine Oturan Elastik Bir Tabakanın Sürtünmesiz ve Ayrılmalı Temas Problemi, XVIII. Ulusal Mekanik Kongresi, Manisa.
  • [4] Öner E., (2011) The continuous contact problem for two elastic layers loaded by means of a rigid circular punch and resting on an elastic half infinite plane, A Master Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [5] Ozsahin T.S. and Taskıner O., (2013) Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches, Mathematical Problems in Engineering, Article ID 137427, 14 pages.
  • [6] Bora P., (2016) The contact problem for two elastic layers loaded by means of two rigid rectangle blocks and resting on an elastic half infinite plane, A Phd Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [7] Ueda S. and Mukai T., (2002) The Surface Crack Problem for A Layered Elastic Medium with A Functionally Graded Nonhomogeneous Interface, JSME International Journal Series a Solid Mechanics and Material Engineering, vol. 45, no. 3, pp. 371-378.
  • [8] Matysiak S.J., (2003) Edge Crack in An Elastic Layer Resting on Winkler Foundation, Engineering Fracture Mechanics, vol. 70, no. 17, pp. 2353-2361.
  • [9] Dong C.Y., Lo S.Y. and Cheung Y.K., (2004) Numerical Solution for Elastic Half Plane Inclusion Problems by Different Integral Equation Approaches, Engineering Analysis with Boundary Elements, vol. 28, pp. 123-130.
  • [10] Elsharkawy A.A., (1999) Effect of Friction on Subsurface Stresses in Sliding Line Contact of Multilayered Elastic Solids, International Journal of Solids and Structures, vol. 36, pp. 3903-3915.
  • [11] Giannakopoulos A.E. and Pallot P., (2000) Two-Dimensional Contact Analysis of Elastic Graded Materials, Journal of the Mechanics and Physics of Solids, vol. 48, pp.1597-1631.
  • [12] Çömez İ., (2009) Receding contact problem of two elastic layers supported by two elastic quarter planes, A Phd Thesis, Institute of Natural Sciences Karadeniz Technical University, Trabzon.
  • [13] Keer L.M., Dundurs J. and Tasi K.C., (1972) Problems Involving a Receding Contact Between a Layer and a Half-Space, Journal of Applied Mechanics, vol. 39, pp.1115–1120.
  • [14] Kahya V., Ozsahin T.S., Birinci A. and Erdol R., (2007) A Receding Contact Problem for An Anisotropic Elastic Medium Consisting of A Layer And A Half Plane, International Journal of Solids and Structures, vol. 44, no. 17, pp.5695–5710.
  • [15] Adibelli H., Çömez İ. and Erdöl R., (2013) Receding Contact Problem for A Coated Layer And A Half-Plane Loaded By A Rigid Cylindrical Stamp, Archives of Mechanics, vol. 65, pp.219-236.
  • [16] Yan J. and Mi C., (2017) On the Receding Contact between An Inhomogeneously Coated Elastic Layer and A Homogeneous Half-Plane, Mechanics of Materials, vol. 112, pp. 18-27.
  • [17] Yaylaci M., Oner E. and Birinci A., (2014) Comparison Between Analytical and ANSYS Calculations for A Receding Contact Problem, Journal of Engineering and Mechanics, vol. 140, no. 9, 04014070.
  • [18] Chan S.K. and Tuba I. S., (1971) A Finite Element Method for Contact Problems of Solid Bodies—Part I. Theory and Validation, International Journal of Mechanical Sciences, vol. 13, pp. 615-625.
  • [19] Klarbring A., (1986) A Mathematical Programming Approach to Three-Dimensional Contact Problems with Friction, Computer Methods in Applied Mechanics and Engineering, vol. 58, no. 2, pp.175-200.
  • [20] Bostan V. and Han W., (2006) A Posteriori Error Analysis for Finite Element Solutions of A Frictional Contact Problem, Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 9-12, pp. 1252–1274.
  • [21] Roncevic B. and Siminiati D., (2010) Two Dimensional Receding Contact Problem Analysis with NX-NASTRAN, Advanced Engineering, vol. 4, pp. 1846-5900.
  • [22] Adiyaman G., Yaylaci M. and Birinci A., (2015) Analytical and Finite Element Solution of a Receding Contact Problem, Structural Engineering And Mechanics, vol. 54, no. 1, pp.69-85.
  • [23] Yaylacı M., (2017) Comparıson Between Numerıcal and Analytıcal Solutions for the Receding Contact Problem, Sigma Journal of Engineering and Natural Sciences, vol. 35, no. 2, pp.333-346.
  • [24] Oner E., Yaylacı M. and Birinci A., (2015) Analytical solution of a contact problem and comparison with the results from FEM, Structural Engineering and Mechanics, vol. 54, no. 4.
  • [25] Kaya Y., Polat A. and Özşahin T.Ş., Analysis Of Continuous Contact Problem Of Homogeneous Plate Bonded A Rigid Support By Using Finite Element Method, 2nd International Conference On Advanced Engineering Technologies (ICADET 2017), 21-23 October 2017 Bayburt, Turkey.
  • [26] Birinci A., Adıyaman G., Yaylacı M. and 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, vol. 12, pp.1771-1789.
  • [27] Polat A., Kaya Y. and Ozsahin T.S., (2018) Analysis of Frictionless Contact Problem for A Layer on An Elastic Half Plane Using FEM, Düzce Üniversitesi Bilim ve Teknoloji Dergisi, vol. 6, no. 2, pp. 357-368.
  • [28] Polat A., Kaya Y. and Ozsahin T.S., (2018) Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches, Meccanica, vol. 53, no. 14, pp. 3565-3577.
  • [29] Erdogan F. and Gupta G., (1972) On The Numerical Solutions of Singular Integral Equations, Quarterly of Applied Mathematics, vol. 29, pp. 525-534.
  • [30] ANSYS, (2015) Swanson Analysis Systems Inc., Houston PA, USA.
  • [31] Biswas P.K. and Banerjee S., (2013) ANSYS Based FEM Analysis for Three And Four Coil Active Magnetic Bearing-A Comparative Study, International Journal of Applied Science and Engineering, vol. 11, no. 3, pp. 277-292.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Articles
Yazarlar

Yusuf Kaya Bu kişi benim 0000-0002-1894-1146

Alper Polat Bu kişi benim 0000-0002-6368-5276

Talat Şükrü Özşahin Bu kişi benim 0000-0002-1179-6556

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 17 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 36 Sayı: 4

Kaynak Göster

Vancouver Kaya Y, Polat A, Özşahin TŞ. COMPARISON OF FEM SOLUTION WITH ANALYTICAL SOLUTION OF CONTINUOUS AND DISCONTINUOUS CONTACT PROBLEM. SIGMA. 2018;36(4):977-92.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/