TEMAS PROBLEMLERİNDE SONLU ELEMANLAR YÖNTEMİNİN DOĞRULUĞUNUN İNCELENMESİ

Yıl 2018, Cilt: 6 Sayı: 3, 511 - 519, 28.09.2018

Murat Yaylacı Cemalettin Terzi

https://doi.org/10.21923/jesd.407121

Cited By: 3

Öz

Bu
çalışmada, ANSYS ve ABAQUS yazılımları kullanılarak rijit bir panç ile bir
elastik yarım düzlem üzerine bağlanmış birbirine bağlı iki tabakanın simetrik
temas problemi dikkate alındı. Tabakalar farklı elastik sabit ve yüksekliklere
sahiptir. Dış yük üst elastik tabakaya rijit bir panç vasıtasıyla uygulandı. Bu
problem iki elastik tabaka arasında ve rijit panç arasındaki temasın
sürtünmesiz olduğu ve yerçekimi kuvvetinin etkisinin ihmal edildiği
varsayımıyla çözüldü. Sayısal uygulamalar sonlu eleman yöntemine dayanan ANSYS
ve ABAQUS yazılımları ile çözüldü. Temas uzunlukları ve temas gerilmeleri
farklı yük, malzeme ve geometri parametrelerine göre elde edildi ve sonuçlar
tablo ve grafikler halinde verildi. Bu sonuçlar literatürdeki (Adıbelli, 2010)
ilgili temas probleminin analitik sonuçlarıyla karşılaştırılarak doğrulandı. 

Anahtar Kelimeler

Temas Mekaniği, Temas Mesafeleri, Temas Gerilmeleri, Sonlu Elemanlar Yöntemi.

INVESTIGATION OF THE ACCURACY OF FINITE ELEMENTS METHOD IN CONTACT PROBLEMS

Öz

In this study, the
symmetrical contact problem of two bonded layers resting on an elastic half
plane with a rigid punch had been considered according to Finite Element Method
using ANSYS and ABAQUS software. These elastic layers have different elastic
constants and heights. The external load had been applied to the upper elastic
layer by means of a rigid stamp. This problem had been solved under the
assumptions that the contact between two elastic layers, and between the rigid
stamp are frictionless, the effect of gravity force had been neglected.
Numerical practices had been performed by ANSYS and ABAQUS software based on
FEM. The contact length and contact stress had been obtained according to different
parameters of load, material and geometry and results had been presented in
tables and graphics. These results had been confirmed by comparing the
analytical results of the related contact problem in the literature.

Anahtar Kelimeler

Contact Mechanics, Contact Length, Contact Stress, Finite Element Method

Kaynakça

• ABAQUS. 2017. ABAQUS/Standard: User's Manual. Dassault Systèmes Simulia, Johnston, RI
• Adıbelli, H., 2010. Elastik Yarım Düzleme Oturan Simetrik Yüklü Yapışık Çift Tabakada Değme Ve Çatlak Problemi. Doktora Tezi, Karadeniz Teknik Üniversitesi, Trabzon.
• ANSYS. 2013. Swanson Analysis Systems Inc., Houston, PA, USA.
• Bathe, K.J., Chaudhary, A., 1985. A Solution Method for Planar and Axisymmetric Contact Problems. International Journal for Numerical Methods in Engineering, 21, 65-88.
• Belgacem, F.B., Hild, P., Laborde, P., 1998. The Mortar Finite Element Method for Contact Problems. Mathematical Computational, 28(4–8), 263–271.
• Birinci, A., Adıyaman, G., Yaylacı, M., 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(9), 1771-1789.
• Chan, S.K., Tuba, I.S., 1971. A Finite Element Method for Contact Problems of Solid Bodies-I. Theory and Validation. International Journal Mechanical Science, 13, 615-625.
• Chidlow, S.J., Teodorescu, M., 2013 Two-Dimensional Contact Mechanics Problems Involving Inhomogeneously Elastic Solids Split Into Three Distinct Layers. International Journal of Engineering Science, 70, 102–123.
• Çömez, İ., Birinci, A., and Erdöl, R., 2004. Double Receding Contact Problem for a Rigid Stamp and Two Elastic Layers. European Journal of Mechanics A/Solids, 23, 301–309.
• Fredriksson, B., 1976. Finite Element Solution of Surface Nonlinearities in Structural Mechanics With Special Emphasis to Contact and Fracture Mechanics Problems. Computational Structural, 6, 281-290.
• Gladwell, G.M.L., 1980. Contact Problems in the Classical Theory of Elasticity, Sijthoff and Nordhoff.
• Gun, H., Gao, X.W., 2014. Analysis of Frictional Contact Problems for Functionally Graded Materials Using BEM. Engineering Analysis Boundary Element, 38, 1–7.
• Guyot, N., Kosior, F., Maurice, G., 2000. Coupling of Finite Elements and Boundary Elements Methods for Study of the Frictional Contact Problem. Computational Methods Applied Mechanical Engineering, 181(1–3), 147–159.
• Hertz, H., 1881. Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik,92, 156-171.
• Hertz, H., 1896. Miscellaneous Papers on the Contact o1 Elastic Solids. Translation by D. E. Jones. McMillan, London.
• Johnson, K.L., 1985. Contact Mechanics, Cambridge University Press, Cambridge, U.K.
• Klarbring, A., Orkman, G., 1992. Solution of Large Displacement Contact Problems with Friction Using Newton's Method for Generalized Equations. International Journal. Numerical Methods in Engineering, 34, 249-269.
• Long, J.M., Wang, G.F., 2013. Effects of Surface Tension on Axisymmetric Hertzian Contact Problem. Mechanics of Materials, 56, 65–70.
• Oden, J.T., Pires, E.B., 1984. Algorithms and Numerical Results for Finite Element Approximations of Contact Problems with Non-Classical Friction Laws. Computational Structure, 19, 137-147.
• Okamoto, N., Nakazawa, M., 1979. Finite Element Incremental Contact Analysis with Various Frictional Conditions. International Journal for Numerical Methods in Engineering, 14, 337-357.
• Öner, E., Birinci, A., 2014. Continuous Contact Problem for Two Elastic Layers Resting on an Elastic Half-Infinite Plane. Journal of Mechanics of Materials and Structures, 9 (1), 105-119.
• Oysu, C., 2007. Finite Element and Boundary Element Contact Stress analysis with Remeshing Technique. Applied Mathematical Model, 31, 2744–2753.
• Özşahin, T.S., Kahya, V., Birinci, A., Cakiroğlu, A.O., 2007 Contact Problem for an Elastic Layered Composite Resting on Rigid Flat Supports. International Journal of Computational and Mathematical Sciences, 1, 154-159.
• Schwarzer, N., Djabella, H., Richter, F., Arnell, R.D., 1995. Comparison Between Analytical and FEM Calculations for The Contact Problem of Spherical Indenters on Layered Materials, Thin Solid Films, 270, 279–282.
• Solberg, J.M., Jones, R.E., Papadopoulos, P., 2007. A Family of Simple Two-Pass Dual Formulations for the Finite Element Solution of Contact Problems. Comput. Methods Applied Mechanical Engineering 196 (4–6), 782–802.
• Soldatenkov, I.A., 2013. The Periodic Contact Problem of the Plane Theory Of Elasticity. Taking Friction, Wear and Adhesion into Account. Pmm-J. Appl. Mathematical Mechanic, 77, 245–255.
• Yang, Y.Y., 2013. Solutions of Dissimilar Material Contact Problems Engineering Fracture Mechanics, 100, 92–107.
• Zhang, H.W., Xie, Z.Q., Chen, B.S., Xing, H.L., 2012. A Finite Element Model for 2D Elastic-Plastic Contact Analysis of Multiple Cosserat Materials. European Journal of Mechanics A/Solids. 31, 139-151.
• Zhu, C., 1995. A Finite Element-mathematical Programming Method for Elastoplastic Contact Problems with Friction. Finite Elem. Anal. Des. 20 (4), 273–282.