Discontinuous Contact Problem of Elastic Two Layers Loaded With Two Rigid Rectangular Blocks

Yıl 2022, , 266 - 278, 31.12.2022

Pınar Bora , Talat Şükrü Özşahin

https://doi.org/10.29132/ijpas.1038088

Öz

In this study, unlike the literature, the discontinuous contact problem of two elastic layers resting on a loaded elastic semi-infinite plane with two rigid rectangular blocks is analyzed analytically.P and Q loads are.transferred to the layers through blocks. Sheet weights were included in the problem. When the load value λ applied to the system exceeds the critical load value λcr, discontinuities occur on the contact surfaces. The problem is reduced to a singular integral equation using Fourier integral transform techniques in case of discontinuous contact. Singular integral equation is solve using Gauss-Chebyshev integral formulation. These discontinuities have been examined for the change in distance between blocks, block widths and changes in load ratios. Moreover, the swelling rates occurring during the separations are presented in graphics. In addition, the results obtained have been solved and compared with the help of ANSYS package program using the Finite Element Method.

Anahtar Kelimeler

Discontinuous Contact, Elasticity, Integral Equations, Finite Element Analysis

İki Rijit Dikdörtgen Blok ile Yüklenen Elastik İki Tabakanın Süreksiz Temas Problemi

Öz

Anahtar Kelimeler

Süreksiz temas, elastisite, Sonlu Elemanlar Analizi, integral denklemler

Kaynakça

• Abhilash, M.N. and Murthy, H. (2014). Finite Element Analysis of 2-d Elastic Contacts Involving FGMs. Int J Comput Methods Eng Sci Mech, 15(3), 253–57.
• Adiyaman, G. and Birinci, A. (2018). A General Solution for the Receding Contact Problem of a Functionally Graded Layer Resting on a Winkler Foundation. Journal of Structural Engineering & Applied Mechanics, 1(3), 136–46.
• Adiyaman G., Öner E. and Birinci A. (2017). Continuous and Discontinuous Contact Problem of a Functionally Graded Layer Resting on a Rigid Foundation. Acta Mechanica, 228(9), 1–15.
• Adıbelli, H., Comez, I. and Erdol, R. (2013). Receding Contact Problem for a Coated Layer and a Half-Plane Loaded by a Rigid Cylindrical Stamp. Arch. Mech., 65(3), 219–36.
• Argatov, I. (2013). Contact Problem for a Thin Elastic Layer with Variable Thickness: Application to Sensitivity Analysis of Articular Contact Mechanics. Appl. Math. Model.,. 37, 8383–93.
• Bendine, K. and Polat, A. (2020). Numerical Modelling of Piezoelectric Based Energy Harvesting from The Bridge Structure. International Journal of Pure and Applied Sciences, 6(2), 130–39. doi: 10.29132/ijpas.796480.
• Birinci, A., Adiyaman, G., Yaylaci, M. and Öner, E. (2015). Analysis of Continuous and Discontinuous Cases of a Contact Problem Using Analytical Method and FEM. Latin Am. J. Solids Struct., 12, 1771–89.
• 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. Institute of Natural Sciences Karadeniz Technical University, Trabzon.
• Çakıroğlu, A.O. and Çakıroğlu, F. L. (1991). Continuous and Discontinuous Contact Problems for Strips on an Elastic Semi-Infinite Plane. International Journal of Engineering Science, 29(1), 99–111.
• Comez, I., Birinci, A. and Erdol, R. (2004). Double Receding Contact Problem for a Rigid Stamp and Two Elastic Layers. European Journal of Mechanics, A/Solids, 23(2), 301–9.
• Çömez, I. and Guler, M. A. (2017). The Contact Problem of a Rigid Punch Sliding over a Functionally Graded Bilayer. Acta Mechanica, 228, 2237–49.
• Comez, I. (2013). Contact Problem of a Functionally Graded Layer Resting on a Winkler Foundation. Acta Mechanica, 224(11), 2833–43.
• Çömez, I. (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), 1090–97.
• Dag, S., Guler, M.A., Yildirim, B. and Ozatag, A. C. (2009). Sliding Frictional Contact between a Rigid Punch and a Laterally Graded Elastic Medium. International Journal of Solids and Structures, 46(22–23), 4038–53.
• El-Borgi, S., Abdelmoula, R. and Keer, L. (2006). A Receding Contact Plane Problem between a Functionally Graded Layer and a Homogeneous Lower-layer. Int. J. Solids Struct., 43, 658–74.
• Erdogan, F. and Gupta, G. D. (1972). On the Numerical Solution of Singular Integral Equations. Quarterly Applied Mathematics, 30, 525-534.
• Erdoğan F. and Ratwani, M. (1974). The Contact Problem for an Elastic Layer Supported by Two Elastic Quarter Planes. ASME Journal of Aplied Mechanics, 41, 673–77.
• Etli, S. (2021). Analytical Evaluation of Behavior of Composite Columns Under Axial Load. International Journal of Pure and Applied Sciences, 7(3), 526–36. doi: 10.29132/ijpas.991166.
• Giannakopoulos, A.E.,and Pallot, P. (2000). Two-Dimensional Contact Analysis of Elastic Graded Materials. Journal of the Mechanics and Physics of Solids, 48(8), 1597–1631.
• Güler, M.A. , Kucuksucu, A., Yilmaz, K.B. and Yildirim, B. (2017). On the Analytical and Finite Element Solution of Plane Contact Problem of a Rigid Cylindrical Punch Sliding over a Functionally Graded Orthotropic Medium. Int. J. Mech. Sci., 120, 12–29.
• 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, 44(17), 5695–5710.
• Kaya, Y. and Polat, A. (2019). Analytical Solution of Continuous Contact Problem in Functionally Graded Layer Resting on Rigid Plane 3 Rd International Conference on Advanced Engineering Technologies. (October).
• Kaya, Y., Polat, A. and Özşahin, T. Ş. (2020). Analytical and Finite Element Solutions of Continuous Contact Problem in Functionally Graded Layer. European Physical Journal Plus, 135(1). doi: 10.1140/epjp/s13360-020-00138-9.
• Keer, L. M., Dondurs, J. and Tsai, K. C. (1972). Problems Involving a Receding Contact between a Layer and a Half Space. Journal of Applied Mechanics Transactions ASME, 39(4), 1115–20.
• Keer, Leon M., and Chantaramungkorn, K. (1972). Loss of Contact between an Elastic Layer and Half-Space. Journal of Elasticity, 2(3), 191–97. doi: 10.1007/BF00125527.
• Gecit, M.R. and Erdogan, F. (1978). Frictionless Contact Problem for an Elastic Layer under Axisymmetric Loading. International Journal of Solids and Structures, 14(9), 771–85.
• Oner, E., Adiyaman, G. and Birinci, A. (2017). Continuous Contact Problem of a Functionally Graded Layer Resting on an Elastic Half-Plane. Arch. Mech., 69(1), 53–73.
• Oner, E. and Birinci, A. (2014). Continuous Contact Problem for Two Elastic Layers Resting on an Elastichalf-Infinite Plane. J. Mech. Mater. Struct., 9(1), 105–19.
• Ozsahin, T. S. (2007). Frictionless Contact Problem for a Layer on an Elastic Half Plane Loaded by Means of Two Dissimilar Rigid Punches. Structural Engineering and Mechanics, 25(4), 383–403.
• Polat, A., Kaya, Y., and Özsahin, T. Ş. (2018). Analytical Solution to Continuous Contact Problem for a Functionally Graded Layer Loaded through Two Dissimilar Rigid Punches. Meccanica, 53(19), 1–13.
• Polat, A., Kaya, Y., Bendine, K. and Özşahin, T. Ş. (2019). Frictionless Contact Problem for a Functionally Graded Layer Loaded through Two Rigid Punches Using Finite Element Method. Journal of Mechanics, 35(5), 591–600.
• Polat, A., Kaya, Y. and Ozsahin, T. Ş. (2018). Analysis of Frictionless Contact Problem for a Layer on an Elastic Half Plane Using FEM. Duzce Univ J Sci Technology, 6(2), 357–68.
• Polat, A. and Kaya, Y. (2018). Comparison of Fem Solution With Analytical Solution Of. (December).
• Rhimi, M., El-Borgi, S. and Lajnef, N. (2011). A Double Receding Contact Axisymmetric Problem between a Functionally Graded Layer and a Homogeneous Lower-layer. Mechanics of Materials, 43(12), 787– 798.
• Urquhart, E.E. and Pindera, M. J. (1994). Incipient Separation Between a Frictionless Flat Punch and an Anisotropic Multilayered Half Plane. International Journal of Solids and Structures, 31(18), 2445–61.
• Volkov, S., Aizikovich, A., Wang, Y.S. and Fedotov, I. (2013). Analytical Solution of Axisymmetric Contact Problem about Indentation of a Circular Indenter into a Soft Functionally Graded Elastic Layer. Acta Mechanica Sinica, 29(2), 196–201.
• Yan, J. and Li, X. (2015). Double Receding Contact Plane Problem between a Functionally Graded Layer and an Elastic Layer. European Journal of Mechanics - A/Solids, 53, 143–50.
• Yang, J. and Ke, L. L. (2008). Two-Dimensional Contact Problem for a Coating-Graded Layer-Lower-layer Structure under a Rigid Cylindrical Punch. International Journal of Mechanical Sciences, 50(6), 985–94.
• Yaylaci M., Oner E. and Birinci A. (2014). Comparison between Analytical and ANSYS Calculations for a Receding Contact Problem. Journal of Engineering Mechanics-ASCE, 140(9), 10.
• Zhupanska, O. I. (2011). Contact Problem for Elastic Spheres: Applicability of the Hertz Theory to Non-Small Contact Areas. International Journal of Engineering Science, 49(7), 576–88.