Tabakalı ve fonksiyonel olarak kademelendirilmiş küresel basınç kapları üzerine analiz

Yıl 2017, Cilt: 23 Sayı: 1, 24 - 35, 01.03.2017

Eray Arslan

Öz

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

Öz

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.

Anahtar Kelimeler

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

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