Tabakalı ve fonksiyonel olarak kademelendirilmiş küresel basınç kapları üzerine analiz

İç ya da dış basınca maruz kalan tabakalı ve fonksiyonel olarak kademelendirilmiş küresel basınç kapları için iki ayrı analitik model sunulmuştur. Her bir tabakasında elastisite modülü ve akma gerilmesinin kademeli bir şekilde değiştiği varsayılan n tabakalı basınç kabı için çift tekrarlamalı (rekursif) bir algoritma kullanılmıştır. Fonksiyonel olarak kademelendirilmiş basınç kabı için ise aynı mekanik özelliklerin radyal doğrultuda bir güç fonksiyonuna bağlı olarak değiştiği kabul edilmiştir. Bu heterojen (ve bunlara ilaveten homojen) basınç kaplarının aynı yük koşulları altındaki elastik davranışları karşılaştırılmıştır. Elastik limit yükü (von Mises akma kretierine göre) ile kademelendirme parametresi (fonksiyonel olarak kademelendirilmiş kap için) ve tabaka sayısı (tabakalı kap için) arasındaki ilişkiler incelenmiştir. Sonuç olarak, iki tabakalı basınç kabında ulaşılan elastik limit yükü ile kademelendirilmiş kabın elastik limit yükü arasındaki farkın %70 civarında olduğu fakat bu farkın 32 tabakalı kapta %2'ye inebildiği gözlenmiştir. Diğer bir yandan, kademelendirilmiş basınç kabında akma, yüke ve kademelendirme parametresine bağlı olarak iç ya da dış yüzeyde oluşabilirken, tabakalı basınç kabında akma (r-1)'inci arayüz koordinatında gerçekleşmektedir.

Anahtar Kelimeler:

Heterojen küresel basınç kabı, FKM, Tabakalı malzeme, Elastik limit, Von Mises akma kriteri

Analysis on multi-layered and functionally graded spherical pressure vessels

Analytical models are presented for both multi-layered and functionally graded thick walled spherical pressure vessels that are subjected to uniform internal or external pressure. A double recursive algorithm is used for the n-layered vessel of which the modulus of elasticity and yield stress are assumed to change stepwise from one layer to another. In the model intended for the continuously graded one, these properties are assumed to vary in radial direction according to a power law. The elastic behaviors under the same loading conditions for such heterogeneous vessels, and the homogeneous ones alike, have been compared. The relationships between the elastic limit load (according to the yield criterion of von Mises) and the grading indices or number of layers have been investigated. As a result, it has been observed that although the difference between elastic limit load of the functionally graded and that of 2-layered pressure vessels is 70%, this difference decreases to 2% for the 32-layered one. Moreover, yielding may emerge at the inner or outer surfaces of the graded vessel depending on the load and grading parameter however it occurs at (r-1)th interface coordinate in the multi-layered one.

Keywords:

Heterogeneous spherical pressure vessel, FGM, Multi-layered material, Elastic limit, Von Mises yield criterion,

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