Kama ile Destekli Elastik Tabakanın Temas Analizi

Year 2022, Issue: 40, 1 - 6, 30.09.2022

Mehmet Bakioğlu , Arcan Yanık , Ünal Aldemir

https://doi.org/10.31590/ejosat.1172175

Abstract

Bu çalışmada düzlemde kama ile destekli elastik tabakanın temas analizi yapılmıştır. Bu problem kapalı formda integral denklemleri ile formüle edilmiştir. Temas bölgesinin uzunluğu, kama ve tabakalar arasındaki basınç ile tabaka ve panç arasındaki basınç problemin bilinmeyenleridir. Bu problemde hem malzeme hem de tabaka elastik kabul edilmiştir. Bu problem dik açılı iki kama tarafından destekli bir tabaka olarak tanımlanabilir. Tabakanın kalınlığı üst yüzeyin çok büyük yarıçaplı bir çember olduğu varsayımı ile sonlu olarak kabul edilmiştir. Problemin çözümü için tekil integral denklemleri kullanılmıştır. Bu formülasyonun yararları şöyle açıklanabilir ; problem basit bir şekilde kuvvetlerin bir çok panç tarafından etki ettirildiği durum için genelleştirilebilir. Çözüm temas gerilmesini direkt olarak verir ve tekil integral denklemlerinin çözümü sayısal çözüm tekniği bakımından uygun bir yoldur. Bu problemin uygulaması rayların birleşim bölgeleri ile temas eden tren tekerleği örneğidir. Denge koşullarını göz önüne alarak çekirdeklerdeki ıraksak terimlerin birbirini sadeleştirdiği gösterilmiştir. Sayısal örnek olarak teker ve ray arasındaki temas problemi rayların birbiri arasında aralıklı hali için incelenmiştir.

Keywords

temas problemi, kama, elastik tabaka, basınç, uygulamalı mekanik

Contact Analysis of Elastic Layer Supported by a Wedge

Abstract

In this paper the contact analysis of elastic layer supported by a wedge is considered in plane. The problem is formulated with closed formed integral equations. The length of the contact region, the pressure between the wedge and the layers, and the pressure between the layer and the punch are unknowns. Both the material and layer are elastic in this problem. This problem can be defined as a layer supported over two wedges with perpendicular angle. The upper surface of the layer is assumed as circle with a large radius. The thickness of the layer is finite. Singular integral equations are used in the formulation of the problem. The benefits of this formulation are the following: the problem can easily be generalized for the case of forces acting through many rigid punches. The solution gives the contact stress directly and the solution of the singular integral equations is an appropriate way in terms of numerical solution technique. The application of this problem is the train wheel that is contacted to the connection part of the rails. It is shown that the divergent terms at the kernels cancel each other by considering the equilibrium conditions. As a numerical example, the contact problem between the wheel and rails is investigated.

Keywords

contact problem, wedge, elastic layer, pressure, applied mechanics

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