A CONCISE ANALYTICAL TREATMENT OF ELASTIC RESPONSE OF A COOLING TWO-LAYER SOLID CYLINDER WITH DIFFERENT END AND BOUNDARY CONDITIONS

Abstract

Analytical models are developed to estimate the transient elastic response of cooling two-layer solid cylinders with different end and boundary conditions. Such cylinders contain two layers that are in perfect contact. The hot assembly loses energy from its surface to either zero ambient by convection or by a prescribed lower surface temperature. In any case, as the cooling takes place slowly, the problem is amenable to use of the uncoupled theory of elasticity. A generalized plane strain solution is derived and then reduced to the state of plane strain by simply setting the axial strain equal to zero. The results of these solutions revealed that the radial and circumferential stresses remain unchanged by end conditions when the boundaries are free. However, in case of plane strain, the axial stress becomes the dominant stress component and it is much larger than that in free ends. Radially constrained boundaries create very large stresses in the assembly but the corresponding stress state is far away from yielding

Keywords

• Two-layer solid cylinder
• Transient heat conduction
• Cooling
• Thermoelasticity
• Generalized plane strain

İKİ KATMANLI DOLU BİR SİLİNDİRİN ELASTİK DAVRANIŞININ FARKLI UÇ VE SINIR KOŞULLARI İÇİN ANALİTİK OLARAK İNCELENMESİ

Abstract

İki katmanlı dolu silindirlerin zamana bağlı termoelastik davranışlarının farklı uç ve sınır koşulları için belirlenmesi amacıyla analitik modeller geliştirilmiştir. Söz konusu silindirler, aralarında mükemmel temas olan iki katmandan oluşmaktadır. Başlangıçta sıcak olan silindir, yüzeyinden konveksiyon yolu ile sıfır derecelik çevresel sıcaklığa veya önceden daha düşük olarak belirlenen yüzey sıcaklığına ulaşana kadar enerji kaybetmektedir. Tüm durumlarda soğuma yavaş bir biçimde gerçekleştiğinden problemde kuplajsız elastisite teorisinin kullanılması mümkün olmuştur. Genelleştirilmiş düzlemsel şekil değiştirme çözümü elde edilmiş ve bu çözüm, eksenel yöndeki birim şekil değiştirmeyi sıfıra eşitleyerek düzlemsel şekil değiştirme durumuna ait çözüme indirgenmiştir. Bu çözümlere ait sonuçlar, sınır koşullarının serbest olduğu durumlarda radyal ve teğetsel yöndeki gerilmelerin uç koşullarına göre değişmediğini göstermiştir. Ancak düzlemsel şekil değiştirme durumunda, eksenel gerilme baskın gerilme olmakta ve uçların serbest olduğu duruma göre oldukça yüksek değerlere ulaşmaktadır. Kompozit silindirin eksenel ve radyal yönde yer değiştirmesinin kısıtlanması büyük gerilmelere yol açmasına rağmen ilgili gerilme durumu silindirde akmaya yol açmamaktadır.

Keywords

• İki katmanlı dolu silindir
• Zamana bağlı ısı iletimi
• Soğuma
• Termoelastisite
• Genelleştirilmiş düzlemsel şekil değiştirme

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