THE CONTACT MECHANIC FOR FUNCTIONALLY GRADED LAYER RESTING ON HALF PLANE

Öz

In this study, a contact mechanic of a functionally graded (FG) layer resting on a half plane and pressed with distributed load from the top was considered according to theory of elasticity. The problem is solved under the assumptions that all surfaces are frictionless, the effect of gravity forces is neglected. The problem is reduced a system of integral equation in which the contact pressure are unknown functions by using integral transform technique and applying boundary conditions on equilibrium equations, constitutive equations and strain-displacement equations. The numerical solution of the integral equation was carried out with Gauss-Jacobi integration formulation taking into account the equilibrium condition and contact lengths and stresses have been found. In addition, in this study, the effect of the Application width of distributed load and the functional change of material properties on the stress distribution will be investigated. 

Anahtar Kelimeler

• Contact mechanics,Functionally graded layer,Theory of elasticity,Integral equation

YARIM DÜZLEM ÜZERİNE OTURAN FONKSİYONEL DERECELENDİRİLMİŞ TABAKANIN DEĞME MEKANİĞİ

Öz

Bu çalışmada, yarım düzlem üzerine oturan ve üstten yayılı yükler ile bastırılan fonksiyonel derecelendirilmiş (FD) bir tabakanın eksenel simetrik değme mekaniği elastisite teorisine göre ele alınmıştır. Değme yüzeyleri sürtünmesiz olup, kütle kuvvetlerinin etkisi ihmal edilmiştir. Denge denklemlerine, bünye denklemlerine ve şekil değiştirme-yer değiştirme bağıntılarına sınır şartları uygulanıp problemde integral dönüşüm teknikleri kullanılarak değme gerilmelerinin bilinmeyen olduğu integral denklemine indirgenmiştir. İntegral denklemin sayısal çözümü, denge şartı da dikkate alınarak, Gauss-Jacobi integrasyon formülasyonuyla gerçekleştirilmiş, değme uzunlukları ve değme gerilmeleri bulunmuştur. Ayrıca çalışmada, yayılı yükün uygulama genişliği ve malzeme özelliklerinin fonksiyonel değişiminin tabakada oluşacak gerilme dağılışlarına etkisi incelenmiştir.    

Anahtar Kelimeler

• Değme mekaniği,Fonksiyonel derecelendirilmiş tabaka,Elastisite teorisi,İntagral denklem

Kaynakça

1. Abanoz, M., Yaylacı, M., Birinci, A., 2019. Contact problems between a functionally graded layer and a rigid support. Journal of Structural Engineering & Applied Mechanics, 2 (1), 25-35.
2. Adıyaman, G., Birinci, A., Öner, E., Yaylacı, M., 2016. A receding contact problem between a functionally graded layer and two homogeneous quarter planes. Acta Mechanica, 227, 1753–1766.
3. Adıyaman, G., Öner, E., Birinci, A., 2017. Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation. Acta Mechanica, 228, 303–317.
4. Avcar, M., Mohammed, WKM., (2017). Winkler zemin ve fonksiyonel derecelendirilmiş malzeme özelliklerinin kirişin frekans parametrelerine etkilerinin incelenmesi. Mühendislik Bilimleri ve Tasarım Dergisi, 5,(3), 573-580.
5. Çömez, İ., 2009. Rijit Dairesel Bir Pançla Bastırılan Elastik Tabaka ve Yarım Düzlemin Sürtünmeli Değme Problemi. Doktora Tezi. Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon, Türkiye, 128s.
6. Çömez, İ., El-Borgi, S., Kahya, V., Erdöl, R., 2016. Receding contact problem for two layer functionally graded media ındented by a rigid punch. Acta Mechanica, 227, 2493-2504.
7. Çömez, İ., El-Borgi, S., 2017. Contact problem of a graded layer supported by two rigid punches. Archives of Mechanics, 11, 1-11.
8. Çömez, İ., Güler, M.A., 2017. The contact problem of a rigid punch sliding over a functionally graded bilayer, Acta Mechanica, 228, 2237–2249.

9. El-Borgi, S., Abdelmoula, R., Keer L., 2006. A receding contact problem between a functionally graded layer and a homogeneous substrate. International Journal of Solids and Structures, 43, 658-674.
10. El-Borgi, S., Usman, S., Güler, 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, 4462-4476.
11. Erdoğan, F., Gupta, G.D., 1972. On the numerical solution of singular integral equations. Quarterly Journal Of Applied Mathematics, 29, 525-534.
12. Erdogan, F., Gupta, G.D., Cook, T.S., 1973. Numerical solution of singular ıntegral equations, in methods of analysis and solution of crack problems, Noordhoff, Groningen.
13. Ke, L., Wang, Y., 2006. Two-Dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. International Journal of Solids and Structures, 43, 5779-5798.
14. Koizumi, M., 1993. Functionally gradient materials the concept of FGM, Ceramic Transactions, 34, 3-10.
15. Krenk, S., 1975. On quadrate formulas for singular ıntegral-equations of 1st and 2nd kind. Quarterly of Applied Mathematics, 33, (3), 225-232.
16. Turan, M., Adiyaman, G., Kahya, V., Birinci, A., 2016. Axisymmetric analysis of a functionally graded layerresting on elastic substrate. Structural Engineering and Mechanics, 58, 423-442.
17. Yamanouchi, M., Koizumi, M., Hirai, T., Shiota I., Proceedings of the First International Symposium on Functionally Gradient Materials, Japan, 1990.