Finite Element Solution of the Contact Problem

Year 2018, Volume: 13 Issue: 1, 113 - 117, 01.03.2018

Pembe Merve Karabulut Murat Yaylacı Ahmet Birinci

Abstract

In this paper,
continuous and discontinuous contact problems for an elastic layer loaded by
symmetrical distributed loads whose lengths are 2a on an elastic semi-infinite
plane is solved using finite element method. The elastic layer also subjected
to uniform vertical body force because of effect of the gravity. Thickness in z
direction is taken to be unit. It is assumed that the contact surfaces are
frictionless, only normal tractions can be transmitted through the contact
areas. The contact along the interface between elastic layer and half plane is
continuous if the value of load factor is less than a critical value. In
continuous and discontinuous contact cases, the stress distribution on the
contact interface are plotted for different dimensionless quantities. The
finite element model of the problem is constituted using ANSYS software and
analysis of the problem is carried out. Finally, the results obtained from the
finite element solution are verified by comprasion with the analytical results.

Keywords

Mechanic, Continuous contact, Discontinuous contact, Elasticity, Half plane, Finite element analysis

References

• 1. 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 Mechanica Sciences, 13(7): 615-625. 2. Keer, L. M., Dundurs, J. and Tsai, K. C. (1972). Problems involving a receding contact between a layer and a half space. Journal of Applied Mechanics, 39(4): 1115-1120. 3. Erdogan, F. and Gupta, G. D. (1972). Numerical solution of singular integral equations. Quarterly of Applied Mathematics, 29(4): 525-&. 4. Ratwani, M. and Erdogan, F. (1973). On the plane contact problem for a frictionless elastic layer. International Journal of Solids and Structures, 9(8): 921-936. 5. Francavilla, A. and Zienkiewicz, O. C. (1975), A note on numerical of elastic contact problems. International Journal for Numerical Methods in Engineering, 9(4): 913-924. 6. Adams, G. G., Bogy, D. B. (1977), The plane symmetric contact problem for dissimilar elastic semi-infinite strips of different widths. Journal of Applied Mechanics-ASME, 44(4): 604-610. 7. Civelek, M. B., Erdogan, F. and Cakiroglu, A.O. (1978). Interface seperation for an elastic layer loaded by a rigid stamp. International Journal of Engineering Science, 16(9): 669-679. 8. Gecit, M. R. (1986). Axisymmetric contact problem for a semi-infinite cylinder and a half space. International Journal of Engineering Science, 24(8): 1245-1256. 9. Abdou, M. A. (1999). Integral equation and contact problem for a system of impressing stamps. Applied Mathematics and Computation, 106(2-3): 141-148. 10. Francavilla, A. and Zienkiewicz, O. C. (1975). A note on numerical computation of elastic contact problems. International Journal for Numerical Methods in Engineering, 9(4): 913-924. 11. Cakiroglu, A. O. and Cakiroglu, F.L. (1991). Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane. International Journal of Engineering Science, 29: 93-111. 12. Jing, H. -S. and Liao, M. -L. (1990). An improved finite element scheme for elastic contact problems with friction. Mathematical and Computer Modeling, 15: 143-154. 13. Gorrido, J. A., Foces, A. and Paris, F. (1991). BEM applied to receding contact problems with friction. Mathematical and Computer Modeling, 15, 143-154. 14. Gorrido, J. A., Foces, A. and Paris, F. (1991). BEM applied to receding contact problems with frictions. Mathematical and Computer Modeling, 15(3-5), 143-153. 15. Gorrido, J. A. and Lorenzana, A. (1998). Receding contact problem involving large displacements using the BEM. Engineering Analysis with Boundary Elements, 21(4), 295-303. 16. El-Borgi, S., Abdelmaula, R. and Keer, L. (2006). A receding contact plane problem between a functionally graded layer and a homogeneous substrate. International Journal of Solids and Structures, 43(3-4): 658-674. 17. 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. 18. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011). A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. Mechanics of Materials, 43(12), 787-798. 19. Long, J. M. and Wang, G. F. (2013). Effects of surface tensionon axisymmetric Hertzian contact problem. Mechanics of Materials, 56: 65-70. 20. Gun, H. and Gao, X. W. (2014). Analysis of frictional contact problems for functionally graded materials using BEM. Engineering Analysis with Boundary Elements, 38: 1-7. 21. Li, X. -Y., Zheng, R. -F. and Chen, W. -Q. (2014). Fundemental solutions to contact problems of a magneto-electro-elastic half space intended by a semi-infinite punch. International Journal of Solids and Structures, 51(1): 164-178. 22. El-Borgi, S., Usman, S. and Guler, M. A. (2014). A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate. International Journal of Solids and Structures, 51(25-26): 4462-4476. 23. Adiyaman, G., Yaylaci, M. and Birinci, A. (2015). Analytical and finite element solution of a receding contact problem. Structural Engineering and Mechanics, 54: 69-85. 24. Oner, E., Yaylaci, M. and Birinci, A. (2015). Analytical solution of a contact problem and comprasion with the results from FEM. Structural Engineering and Mechanics, 54: 607-622. 25. Birinci, A., Adiyaman, G., Yaylaci, M. and Oner, E. (2015). Analysis of continuous and discontinuous cases of a contact problem using analytical method and FEM. Latin American Journal of Engineering Science, 12: 1771-1789. 26. 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: 143-150. 27. Comez, I. (2015). Contact problem for a functionally graded layer intended by a moving punch. International Journal of Mechanical Sciences, 100: 339-344. 28. Liao, X. and Wang, G. G. (2015). Non-lineer dimentional variation analysis for sheet metal assemblies by contact modeling. Finite Elements in Analysis and Design, 44: 34-44.