A Receding Contact Problem of Two Layers one of Functionally Graded, Loaded by Circular Rigid Block and Resting on a Pasternak Foundation

Year 2024, Volume: 35 Issue: 5, 115 - 132, 01.09.2024

Aleyna Yazıcıoğlu , Ahmet Birinci , Gökhan Adıyaman

https://doi.org/10.18400/tjce.1392997

Abstract

In this study, frictionless receding contact problem of two elastic layers which one is functionally graded material (FGM) resting on a Pasternak foundation is considered. The external load is applied to the homogeneous elastic layer by means of a circular rigid block and the functionally graded layer rests on a Pasternak foundation. The effect of gravity forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. Displacement and stress expressions for the layers are obtained using the theory of elasticity and integral transformation technique. By applying the boundary conditions for the problem, reduced to two integral equations in which the contact stresses and contact lengths are unknown. The system of integral equations is numerically solved by making use of appropriate Gauss Chebyshev integration formulas. The equilibrium conditions are satisfied in the solution and the contact stresses and contact distances related to the problem are obtained for various dimensionless quantities.

Keywords

Contact problem, functionally graded material, Pasternak foundation

Supporting Institution

23. ULUSAL MEKANİK KONGRESİ

References

• Dhaliwal, R.S., Punch Problem for an Elastic Layer Overlying an Elastic Foundation. International Journal of Engineering Science, 8, 273–288, 1970.
• Keer, L.M., Chantarammungkorn K., Loss of contact Between an Elastic Layer and Half-Space. ASME Journal of Applies Mechanics, 39, 1115–1120, 1972.
• Erdogan, F., Gupta, G.D., On the numerical solutions of singular integral equations. Quarterly Journal of Applied Mathematics, 29, 525–534, 1972.
• Ratwani, M., Erdoğan, F., On the Plane Contact Problem for a Frictionless Elastic Layer. International Journal of Solids and Structures, 9,921-936, 1973.
• Cakıroglu, A.O., Elastik Yarım Düzleme Oturan Plakalarda Temas Problemi. PhD Dissertation, K.T.Ü., 1979.
• Aksogan, O., Akaycı, S.S., Becker, A.A., A Comparative Study of the Contact Problem of for an Elastic Layer Supported by two Elastic Quarter Planes J. Fac. Engreg. Architecture Cukurova Univ, 11,25-35, 1996.
• Birinci, A., Erdol, R., Continuous and Discontinuous Contact Problem for a Layered Resting on Simple Supports. Structural Engineering and Mechanics, 12,1,17-34, 2001.
• Birinci, A., Erdol, R., A Frictionless Contact Problem for Two Elastic Layers Supported by a Winkler Foundation. Structural Engineering and Mechanics, 15,331-344, 2003.
• Comez, I., Rijit bir Panç ile Bastırılmış ve Tabanda Tam Olarak Bağlı Ağırlıksız çift Şerit Problemi. PhD Dissertation, K.T.Ü., 2003.
• Comez, I., Birinci, A., Erdol, R., Double receding contact problem for a rigid stamp and two elastic layers. European Journal of Mechanics-A/Solids, 23,2,301-309, 2004.
• El-Borgi, S., Abdelmoula, R., Keer, L., A receding contact plane problem between a functionally graded layer and a homogeneous substrate. Int. J. Solid Struct. 43 (3–4), 658–674, 2006.
• Kahya, V., Ozsahin, T., Birinci, A., Erdol, R., A Receding Contact Problem for an Anisotropic Elastic Medium Consisting of a Layer and a Half Plane. International Journal of Solids and Structures, 44,5695-5710, 2007.
• Yaylacı, M., Birinci, A., İki Elastik Çeyrek Düzleme Oturan Elastik iki Tabakanın Temas Problemi. XVII. National Mechanics Congress Fırat University, Elazığ, 2011.
• Chen, P.J., Chen, S.H M., Contact behaviors of a rigid punch and a homogeneous half space coated with a graded layer. Acta Mech, 223 (3), 563–577, 2012.
• Yan, J., Li, X., Double receding contact plane problem between a functionally graded layer and an elastic layer. Eur. J. Mech. Solid, 53, 143–150, 2015.
• Comez, I., Contact Problem for a Functionally Graded Layer Intended by a Moving Punch. International Journal of Mechanical Sciences, 100, 339-344, 2015.
• Polat, A., Kaya, Y., Ozsahin, T.Ş., Fonksiyonel Derecelendirilmiş Tabakada Sürekli Temas Probleminin Sonlu Elemanlar Yöntemi ile Analizi. XX. National Mechanics Congress Uludağ, Bursa, 2017.
• Valiliev, A.S., Volkov, S.S., Aizikovich, S.M., Mitrin, B.I., Plane contact problem on indentation of a flat punch into a transversely isotropic half-plane with functionally graded transversely-isotropic coating. Z. Angew. Math. Phys., 68 (1), 4, 2017.
• Oner, E., Birinci, A., Investigation of the solution for discontinuous contact problem between a functionally graded (FG) layer and homogeneous half-space. Archive of Applied Mechanics 90, 2799-2819, 2020.
• Arslan, O., Hertz-type frictional contact problem of a bidirectionally graded halfplane indented by a sliding rounded punch. Mech. Mater. 149, 1–11, 2020.
• Zelentsov, V.B., Lapina, P.A., Mitrin, B.I., Eremeyev, V.A., Characterization of the functionally graded shear modulus of a half-space. Mathematics 8 (4), 640, 2020.
• Balcı, N.M., The efect of punch speed on frictional contact mechanics of fnite thickness graded layer resting on the rigid foundation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(6),343, 2020.
• Birinci, A., Eyüpoğlu, A., A double receding contact problem of a functionally graded layer and a homogeneous elastic layer resting on a Winkler foundation. Sigma Journal of Engineering and Natural Sciences, 38(2),667-686, 2021.
• Bakioglu, M., Yanik A., Aldemir, Ü., Contact Analysis of Elastic Layer Supported by a Wedge. European Journal of Science and Technology, 40,1-6, 2022.
• Yaylacı, M., Abanoz, M., Yaylacı, E., Olmez H., Sekban, D.M., Birinci, A., Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods. Archive of Applied Mechanics, 92,1953-1971, 2022.
• Adıyaman, G., Oner, E., Yaylacı, M., Birinci, A., A study on the Contact Problem of a Layer Consisting of Functionally Graded Material (FGM) in the Presence of Body Force. Journal of Mechanics of Materials and Structures, 1,18, 125-141, 2023.
• Adıyaman, G., Tabakalı Ortamlarada Temas Problemlerinin Genel Çözümü ve bu Çözüme İlişkin bir Bilgisayar Programının Geliştirilmesi. PhD Dissertation, K.T.Ü., 2019.
• Eyüpoğlu, A., Winkler Temele Oturan ve Rijit Dairesel Blok Aracılığıyla Yüklenen biri Fonksiyonel Derecelendirilmiş iki Tabakanın Temas Problemi. Master Thesis, K.T.Ü., 2019.