Analytical Investigation of Continuous Contact Problem Between Orthotropic Layer and Isotropic Half-Plane

Year 2023, , 154 - 171, 31.12.2023

Erdal Öner , Mine Gül Oktay

https://doi.org/10.53501/rteufemud.1358045

Abstract

Computational contact mechanics is of great importance in mechanical and civil engineering fields, as well as in environmental and medical applications. This branch of mechanics seeks numerical solutions to contact area, pressure, deformation, and stresses in response to the interaction of two bodies. The subject of contact mechanics has contributed significantly to the development of new and interesting fields in mechanics and applied mathematical sciences in recent years. In this study, the problem of continuous contact of the orthotropic layer resting on the isotropic half-plane is analyzed by analytical method. Only the mass force of the orthotropic layer is taken into account in the solution. The orthotropic layer was loaded by a punch with a rigid flat profile. All surfaces are assumed to be frictionless. The theory of elasticity and integral transformation techniques are used to obtain the displacement and stress expressions for the orthotropic layer and the isotropic half-plane. As a result of the study, depending on various dimensionless parameters and orthotropic material types, the contact stress under the punch, the critical separation load causing the initial separation between the orthotropic layer and the isotropic half-plane, and the critical separation distance were obtained as dimensionless

Keywords

Orthotropic layer, Contact stress, Integral equation, Critical separation load, Critical separation distance

Ortotrop Tabaka ile İzotrop Yarım Düzlem Arasındaki Sürekli Temas Probleminin Analitik Olarak İncelenmesi

Abstract

Hesaplamalı temas mekaniği, makine ve inşaat mühendisliği gibi alanların yanı sıra çevre ve tıbbi uygulamalarda da büyük önem taşımaktadır. Mekaniğin bu dalı, iki cismin etkileşimine yanıt olarak temas alanı, basınç, deformasyon ve gerilmelere sayısal çözümler arar. Temas mekaniği konusu, son yıllarda mekanik ve uygulamalı matematik bilimlerinde yeni ve ilginç alanların gelişmesine önemli derecede katkı sağlamıştır. Bu çalışmada izotrop yarım düzlem üzerine oturan ortotrop tabakanın sürekli temasına ilişkin problem analitik yöntemle incelenmiştir. Çözümde sadece ortotrop tabakanın kütle kuvveti hesaba katılmıştır. Ortotrop tabaka rijit düz profile sahip bir panç vasıtasıyla yüklenmiştir. Tüm yüzeylerin sürtünmesiz olduğu varsayılmıştır. Ortotrop tabaka ve izotrop yarım düzlem için yer değiştirme ve gerilme ifadelerinin elde edilmesinde elastisite teorisi ve integral dönüşüm tekniklerinden yararlanılmıştır. Çalışma sonucunda çeşitli boyutsuz parametrelere ve ortotrop malzeme türlerine bağlı olarak panç altındaki temas gerilmesi, ortotrop tabaka ile izotrop yarım düzlem arasında ilk ayrılmaya neden olan kritik ayrılma yükü ve kritik ayrılma uzaklığı boyutsuz olarak elde edilmiştir.

Keywords

Ortotrop tabaka, Temas gerilmesi, İntegral denklem, Kritik ayrılma yükü, Kritik ayrılma uzaklığı

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