Non-linear Static Modeling of Moderately Thick Functionally Graded Plate Using Dynamic Relaxation Method
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکمحمدجواد محمودی 1 , وحید محلوجی 2
1 - استادیار، دانشکده مهندسی مکانیک و انرژی، دانشگاه شهید بهشتی، تهران
2 - دانشجوی دکتری، دانشکده مهندسی مکانیک و انرژی، دانشگاه شهید بهشتی، تهران
کلید واژه: Functionally graded plate, Dynamic relaxation method, Mindlin first order shear deformation theory, Elastic large deformation,
چکیده مقاله :
In this paper, nonlinear static analysis of moderately thick plate made of functionally graded materials subjected to mechanical transverse loading is carried out using dynamic relaxation method. Mindlin first order shear deformation theory is employed to consider thick plate. Discretized equations are extracted for geometrically nonlinear behavior analysis.Loading Conditions and boundary conditions of the plate are uniformly distributed transverse load and simply supported at the four edges of the thick plate, respectively. In order to generalize the obtained results, the equations are solved by applying dynamic relaxation method based on central finite deference discretization in the non-dimensional form. The effects of problem parameters such as gradient constant of the functionally graded material and the side to thickness ratio of plate on the results are investigated. According to the obtained results, the need of including elastic large deflection and applying the theory which considers the effects of plate thickness on the plate bending response and also finally the need of employing dynamic relaxation solution method despite the non-linear terms resulted from large deflection of the functionally graded thick plate are discussed.
در این مقاله تحلیل استاتیکی غیرخطی ورق نسبتاً ضخیم ساخته شده از مواد هدفمند تابعی با استفاده از روش آزادسازی دینامیکی صورت گرفته است. این امر به کمک تئوری مرتبه اول برشی میندلین به منظور ضخیم در نظر گرفتن ورق انجام شده است. جهت تحلیل رفتار غیرخطی هندسی معادلات گسسته شده استخراج شده است. شرایط بارگذاری و شرایط مرزی ورق بهترتیب بهصورت بارگستره عرضی یکنواخت و تکیهگاه ساده در چهار لبه ورق ضخیم در نظرگرفته شده است. جهت عمومیت بخشیدن به نتایج بهدستآمده، این معادلات به صورت بدون بعد با اعمال روش آزادسازی دینامیکی بر مبنای تفاضلات محدود مرکزی حل شدهاند. اثر پارامترهای مسأله نظیر ثابت توانی ماده هدفمند تابعی و نسبت ضلع به ضخامت ورق بر نتایج تحلیل مورد بررسی قرار گرفته است. با توجه به نتایج بهدست آمده، لزوم درنظر گرفتن رفتار غیرخطی هندسی و استفاده از تئوری ای که اثرات ضخامت ورق روی پاسخ خمش ورق را درنظر بگیرد و همچنین در نهایت لزوم استفاده از روش حل آزادسازی دینامیکی با وجود جملات غیرخطی ناشی از تغییرشکل زیاد ورق ضخیمهدفمند تابعی بحث شده است.
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[19] Otter J.R.H., Computations for prestressed concrete reactor pressure vessels using dynamic relaxation, Nuclear Structural Engineering, vol. 1, 1965, pp. 61-75.
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