Analytical solutions to orthotropic variable thickness disk problems

Abstract

An analytical model is developed to estimate the mechanical response of nonisothermal, orthotropic, variable thickness disks under a variety of boundary conditions. Combining basic mechanical equations of disk geometry with the equations of orthotropic material, the elastic equation of the disk is obtained. This equation is transformed into a standard hypergeometric differential equation by means of a suitable transformation. An analytical solution is then obtained in terms of hypergeometric functions. The boundary conditions used to complete the solutions simulate rotating annular disks with two free surfaces, stationary annular disks with pressurized inner and free outer surfaces, and free inner and pressurized outer surfaces. The results of the solutions to each of these cases are presented in graphical forms. It is observed that, for the three cases investigated the elastic orthotropy parameter turns out to be an important parameter affecting the elastic behavior

Keywords: Orthotropic disk, Variable thickness, Thermoelasticity, Hypergeometric equation

Keywords

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Ortotropik değişken kalınlıklı disk problemlerinin analitik çözümleri

Öz

Bu çalışmada eş ısıl olmayan, ortotropik, değişken kesitli disklerin, farklı sınır koşulları altında mekanik davranışlarını tahmin edebilmek için analitik bir model geliştirilmiştir. Disk geometrisi için temel mekanik denklemleri, ortotropik malzeme denklemleri ile birleştirilerek elastik denklem elde edilmiştir. Bu denklem uygun bir dönüşüm tekniği ile standart hipergeometrik diferansiyel denkleme dönüştürülmüş ve bunun analitik çözümü hipergeometrik fonksiyonlar cinsinden bulunmuştur. Çözümü tamamlayan sınır koşulları, iki ucu serbest dönen, iç veya dış yüzeyden basınçlandırılmış durağan değişken kesitli disklerin benzetişimini sağlayacak şekilde seçilmiştir. Elde edilen sonuçlar grafiksel olarak sunulmuştur. Sonuçlar göstermiştir ki makalede incelenen her üç problem için de elastik ortotropi parametresi diskin elastik davranışını etkileyen en önemli parametre olarak ortaya çıkmıştır.

Anahtar Kelimeler: Ortotropik diskler, Değişken kesit, Termo elastisite, Hipergeometrik denklem

Anahtar Kelimeler

• Ortotropik diskler, Değişken kesit, Termo elastisite, Hipergeometrik denklem

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