Frictionless Contact Problem Between Two Orthotropic Elastic Layers
A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.
[1] Weitsman, Y., ''A tensionless contact between a beam and an elastic half space'', International Journal of Engineering Science, vol. 10, pp. 73-81, 1972. [2] Ratwani, M., Erdogan, F., ''On the plane contact problem for a frictionless elastic layer'', International Journal of Solids and Structures, vol. 9, pp. 921-936, 1973. [3] Erdogan, F., Ratwani, M., ''The contact problem for an elastic layer supported by two quarter planes'', Journal of Applied Mechanics, vol. 41, no. 96, pp. 673-678, 1974. [4] Civelek, M.B., Erdogan, F., ''The axisymmetric double contact problem for a frictionless elastic layer'', International Journal of Solids and Structures, vol. 10, pp. 639-659, 1974. [5] Gecit, M.R., ''A tensionless contact without friction between an elastic layer and an elastic foundation'', International Journal of Solids and Structures, vol. 16, pp. 387-396, 1980. [6] Gecit, M.R., ''Axisymmetric contact problem for an elastic layer and an elastic foundation'', International Journal of Engineering Science, vol. 19, pp. 747-755, 1981. [7] Dempsey, J.P., Zhao, Z.G., Li, H., ''Plane contact of an elastic layer supported by Winkler foundation'', Journal of Applied Mechanics, vol. 57, pp. 974-980, 1990. [8] Birinci, A., Erdol, R., ''A frictionless contact problem for two elastic layers supported by a Winkler foundation'', Structural Engineering and Mechanics, vol. 15, no. 3, pp. 331-344, 2003. [9] Civelek, M.B., Erdogan, F., ''The frictionless contact problem for an elastic layer under gravity'', Journal of Applied Mechanics, vol. 42, no. 97, pp. 136-140, 1975. [10] Civelek, M.B., Erdogan, F., ''Interface separation in a frictionless contact problem for an elastic layer'', Journal of Applied Mechanics, vol. 43, no. 98, pp. 175-177, 1976. [11] Civelek, M.B., Erdogan, F., Cakiroglu, A.O., ''Interface separation for an elastic layer loaded by a rigid stamp'', International Journal of Engineering Science, vol. 16, pp. 669-679, 1978. [12] Cakiroglu, A.O., Cakiroglu, F.L., ''Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane'', International Journal of Engineering Science, vol. 29, no. 1, pp. 99-111, 1991. [13] Birinci, A., Erdol, R., ''Continuous and discontinuous contact problem for a layered composite resting on simple supports'', Structural Engineering and Mechanics, vol. 12, no. 1, pp. 17-34, 2001. [14] Gecit, M.R., Gokpinar, S., ''Frictionless contact between an elastic layer and a rigid rounded support'', The Arabian Journal for Science and Engineering, vol. 10, no. 3, pp. 243-251, 1985. [15] Gecit, M.R., Yapici H., ''Contact problem for an elastic layer resting on rigid flat supports'', The Arabian Journal for Science and Engineering, vol. 11, no. 3, pp. 235-242, 1986. [16] Kahya, V., Birinci, A., Erdol, R., ''Frictionless contact problem between an elastic layer bonded to a rigid support and a rigid stamp'', Mathematical and Computational Applications, vol. 6, no 1, pp. 13-22, 2001. [17] Erdogan, F., Gupta, G.D., ''On the numerical solution of singular integral equations'', Quarterly Journal of Applied Mathematics, vol. 29, pp. 525-534, 1972.
[1] Weitsman, Y., ''A tensionless contact between a beam and an elastic half space'', International Journal of Engineering Science, vol. 10, pp. 73-81, 1972. [2] Ratwani, M., Erdogan, F., ''On the plane contact problem for a frictionless elastic layer'', International Journal of Solids and Structures, vol. 9, pp. 921-936, 1973. [3] Erdogan, F., Ratwani, M., ''The contact problem for an elastic layer supported by two quarter planes'', Journal of Applied Mechanics, vol. 41, no. 96, pp. 673-678, 1974. [4] Civelek, M.B., Erdogan, F., ''The axisymmetric double contact problem for a frictionless elastic layer'', International Journal of Solids and Structures, vol. 10, pp. 639-659, 1974. [5] Gecit, M.R., ''A tensionless contact without friction between an elastic layer and an elastic foundation'', International Journal of Solids and Structures, vol. 16, pp. 387-396, 1980. [6] Gecit, M.R., ''Axisymmetric contact problem for an elastic layer and an elastic foundation'', International Journal of Engineering Science, vol. 19, pp. 747-755, 1981. [7] Dempsey, J.P., Zhao, Z.G., Li, H., ''Plane contact of an elastic layer supported by Winkler foundation'', Journal of Applied Mechanics, vol. 57, pp. 974-980, 1990. [8] Birinci, A., Erdol, R., ''A frictionless contact problem for two elastic layers supported by a Winkler foundation'', Structural Engineering and Mechanics, vol. 15, no. 3, pp. 331-344, 2003. [9] Civelek, M.B., Erdogan, F., ''The frictionless contact problem for an elastic layer under gravity'', Journal of Applied Mechanics, vol. 42, no. 97, pp. 136-140, 1975. [10] Civelek, M.B., Erdogan, F., ''Interface separation in a frictionless contact problem for an elastic layer'', Journal of Applied Mechanics, vol. 43, no. 98, pp. 175-177, 1976. [11] Civelek, M.B., Erdogan, F., Cakiroglu, A.O., ''Interface separation for an elastic layer loaded by a rigid stamp'', International Journal of Engineering Science, vol. 16, pp. 669-679, 1978. [12] Cakiroglu, A.O., Cakiroglu, F.L., ''Continuous and discontinuous contact problems for strips on an elastic semi-infinite plane'', International Journal of Engineering Science, vol. 29, no. 1, pp. 99-111, 1991. [13] Birinci, A., Erdol, R., ''Continuous and discontinuous contact problem for a layered composite resting on simple supports'', Structural Engineering and Mechanics, vol. 12, no. 1, pp. 17-34, 2001. [14] Gecit, M.R., Gokpinar, S., ''Frictionless contact between an elastic layer and a rigid rounded support'', The Arabian Journal for Science and Engineering, vol. 10, no. 3, pp. 243-251, 1985. [15] Gecit, M.R., Yapici H., ''Contact problem for an elastic layer resting on rigid flat supports'', The Arabian Journal for Science and Engineering, vol. 11, no. 3, pp. 235-242, 1986. [16] Kahya, V., Birinci, A., Erdol, R., ''Frictionless contact problem between an elastic layer bonded to a rigid support and a rigid stamp'', Mathematical and Computational Applications, vol. 6, no 1, pp. 13-22, 2001. [17] Erdogan, F., Gupta, G.D., ''On the numerical solution of singular integral equations'', Quarterly Journal of Applied Mathematics, vol. 29, pp. 525-534, 1972.
@article{"International Journal of Architectural, Civil and Construction Sciences:51883", author = "V. Kahya and A. Birinci and R. Erdol", title = "Frictionless Contact Problem Between Two Orthotropic Elastic Layers ", abstract = "A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented. ", keywords = "Frictionless contact, Initial separation, Orthotropicmaterial, Singular integral equation.", volume = "1", number = "1", pages = "7-7", }
