THE CONTACT MECHANIC FOR FUNCTIONALLY GRADED LAYER RESTING ON HALF PLANE

Year 2019, Volume: 7 Issue: 3, 639 - 646, 15.09.2019

Müjgen Yaylı Murat Yaylacı Ahmet Birinci

https://doi.org/10.21923/jesd.533618

Abstract

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. 

Keywords

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

YARIM DÜZLEM ÜZERİNE OTURAN FONKSİYONEL DERECELENDİRİLMİŞ TABAKANIN DEĞME MEKANİĞİ

Abstract

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.    

Keywords

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

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