IJE TRANSACTIONS A: Basics Vol. 22, No. 4 (November 2009) 405-416   

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A.R. Saidi*, S.R. Atashipour and E. Jomehzadeh

Department of Mechanical Engineering, Shahid Bahonar University of Kerman
P.O. Box 76175-133, Kerman, Iran
saidi@mail.uk.ac.ir - atashipour@yahoo.com - jomehzadeh@graduate.uk.ac.ir

* Corresponding Author
( Received: October 07, 2008 – Accepted in Revised Form: February 19, 2009 )

Abstract    In this paper, exact closed-form solutions for displacement and stress components of thick-walled functionally graded (FG) spherical pressure vessels are presented. To this aim, linear variation of properties, as an important case of the known power-law function model is used to describe the FG material distribution in thickness direction. Unlike the pervious studies, the vessels can have arbitrary inner to outer stiffness ratio without changing the function variation of FGM. After that, a closed-form solution is presented for displacement and stress components based on exponential model for variation of properties in radial direction. The accuracy of the present analyses is verified with known results. Finally, the effects of non-homogeneity and different values of inner to outer stiffness ratios on the displacement and stress distribution are discussed in detail. It can be seen that for FG vessels subjected to internal pressure, the variation of radial stress in radial direction becomes linear as the inner stiffness becomes five times higher than outer one. When the inner stiffness is half of the outer one, the distribution of the circumferential stress becomes uniform. For the case in which the external pressure is applied, as the inner to outer shear modulus becomes lower than 1/5, the value of the maximum radial stress is higher than external pressure.


Keywords    Thick-Walled Pressure Vessels, Functionally Graded Materials, Linearly-Varying Properties, Exponentially-Varying Properties


چکیده    در اين مقاله، براي جابجايي و ميدان تنش مخازن جدار ضخيم كروي ساخته شده از مواد هدفمند پاسخ بسته عرضه شده است. بدين منظور، تغييرات خطي خواص، به عنوان مهم ترين حالت خاص از مدل معروف تابع تواني، برای تشريح توزيع مواد سازنده در راستاي ضخامت استفاده شده است. در اين مطالعه بر خلاف مطالعات مشابه، بدون محدوديت تغيير حالت خطي توزيع مواد، نسبت سفتي سطح داخل مخزن به سطح خارج مي تواند مقادير متفاوتي داشته باشد. سپس، برپاية مدل تابع نمايي تغييرات خواص در راستاي شعاعي، براي مؤلفه هاي ميدان تنش و جابجايي پاسخ بسته عرضه شده و صحت تحليل ها با نتايج موجود بررسي شده است. در پايان، تِأثيرات ناهمگني و مقادير مختلف نسبت سفتي سطوح مخزن بر توزيع تنش و جابه جايي بررسي شده است. نتایج نشان داد كه در مخازن FG كروي تحت فشار داخلي، هرگاه نسبت سفتي سطح داخلي به سطح خارجي حدوداً برابر 5 باشد، توزيع تنش شعاعي در راستاي شعاعي تقريباً خطي است. هنگامي كه سفتي سطح داخلی تقريباً نصف سفتي سطح خارج باشد، توزيع تنش حلقوي يكنواخت است. براي حالتي كه تنها فشار خارجي وجود داشته باشد، هرگاه نسبت مدول برشي سطح داخل به سطح خارج كمتر از 5/1 باشد، مقدار بیشترین تنش شعاعي در داخل جدارة مخزن، بيشتر از مقدار فشار خارجي خواهد بود.


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