نوع مقاله : مقاله پژوهشی
نویسندگان
1 دانشجوی دکتری، مهندسی مکانیک، دانشگاه تربیت مدرس ، تهران.
2 استاد، مهندسی مکانیک، دانشگاه تربیت مدرس، تهرا ن.
چکیده
به دست آوردن مقادیر تنش‌ها در پوسته کروی یک مخزن چند لایه کامپوزیتی جدار نازک به روشی کاملا تحلیلی و بدون نیاز به استفاده از روش‌های عددی در حل معادلات، موضوعی است که تا کنون بررسی نشده است. در این مقاله با استفاده از حلی کاملا تحلیلی به کمک تئوری کلاسیک پوسته‌ها، مقادیر تنش‌ها در هر لایه از پوسته کروی مخزن چند لایه کامپوزیتی جدار نازک به دست آمده است. در این روش حل با استفاده از معادلات تعادل، قانون هوک، روابط کرنش - جابجایی و انحنا – جابجایی، معادلات حاکم بر پوسته دوران یافته عمومی کامپوزیتی استخراج گردیده و سپس معادلات حاکم بر پوسته کروی متقارن به دست آمده‌اند. در ادامه به کمک معادلات سازگاری جابجایی و چرخش، نیروها و تنش‌ها در تقاطع پوسته کروی و استوانه کامپوزیتی استخراج شده‌اند و پس از آن تنش‌های طولی و محیطی در پوسته کروی مخزن کامپوزیتی جدار نازک تحت فشار داخلی در هر لایه به دست آمده‌اند. در نهایت نتایج حل کاملا تحلیلی بر مبنای تئوری کلاسیک پوسته‌ها با نتایج حل عددی اجزاء محدود مقایسه شده و نشان داده شده است مقادیر تنش حاصل از نتایج تحلیلی انطباق خوبی با نتایج حل عددی دارند و می‌توان با استفاده از نتایج این حل تحلیلی مخازن کامپوزیتی را به صورت بهینه طراحی نمود
کلیدواژه‌ها
موضوعات
عنوان مقاله [English]
Analytical solution for stresses in the spherical shell of a thin-wall composite multi-layer vessel under internal pressure by using the classical theory of shells
نویسندگان [English]
- Hossein Farajollahi 1
- Gholamhossein Rahimi 2
1 Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran.
2 Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran.
چکیده [English]
Obtaining stress values in spherical shell of a thin-walled composite multi-layer vessel in a completely analytical way and independent of numerical methods in solving the equations is a subject that has not been investigated so far. In this article, using a fully analytical solution based on classical shell theory, the stress values in each layer of the spherical shell are obtained. In this solution method, by using equilibrium equations, Hooke's law, strain-displacement and curvature-displacement relations, the governing equations of general composite shells of revolution are extracted and then the governing equations of a symmetric spherical shell are obtained. In the following, using displacement and rotation consistency equations, forces and stresses at the intersection of the spherical and cylindrical composite shell are calculated, and then the longitudinal and circumferential stresses due to internal pressure are extracted in each layer. Finally, the results are compared with the results of the finite element numerical solution and it is shown that the stress values obtained from the analytical results are in good agreement with the results of the numerical solution and it is possible to use the results of this analytical solution to make optimally designed composite vessels.
کلیدواژه‌ها [English]
- Analytical Solution
- Classic Theory
- Spherical Shell
- Multi-Layer Composite Vessel
- Thin-Walled
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