تحلیل کمانش مکانیکی پوسته های استوانه ای جدار ضخیم مدرج تابعی با استفاده از تئوری تغییر شکل برشی مرتبه سوم

نویسندگان

دانشگاه صنعتی بابل

چکیده

استوانه ای جدار ضخیم با استفاده از تانسور مرتبه دوم پیولا-کیرشهف به دست آمده و از آنها در راستای ضخامت انتگرال گرفته می شود. معادلات حاکم به دست آمده، با استفاده از تئوری تغییر شکل برشی مرتبه سوم بر حسب مولفه های تغییر مکان توسعه داده شده و به صورت تحلیلی حل شده اند. فرض می شود که خواص ماده در راستای ضخامت مطابق قانون توزیع توانی بر حسب کسر حجمی مواد تشکیل دهنده به آرامی تغییر کند، در حالی که ضریب پواسون ماده ثابت در نظر گرفته شده است. همچنین معادلات کمانش به دست آمده، با استفاده از روش نیمه عددی کوادریچر تفاضلی گسسته سازی شده و به یک سیستم معادلات خطی همگن تبدیل می شوند. نتایج به دست آمده از روش تحلیلی با جوابهای حاصله از روش اجزا محدود به دست آمده از نرم افزار تجاری انسیس و نتایج ارائه شده در کار دیگر محققان مقایسه گردیده و صحت و درستی آنها بررسی شده است. اثر پارامتر های مختلف شامل شرایط تکیه گاهی، کسر حجمی مواد تشکیل دهنده، شرایط مختلف بارگذاری و نسبت های هندسی بر رفتار کمانشی پوسته استوانه ای جدار ضخیم ساخته شده از مواد مدرج تابعی مورد بررسی قرار گرفته است.

کلیدواژه‌ها


عنوان مقاله [English]

MECHANICAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED THICK CYLINDRICAL SHELLS USING THIRD ORDER SHEAR DEFORMATION THEORY

نویسندگان [English]

  • Reza Akbari Alashti
  • Seysd Ali Ahmadi
چکیده [English]

In this paper, buckling analysis of thick cylindrical shells using the third order shear deformation theory is carried out. The governing differential stability equations are obtained based on the second Piola-Kirchhoff tensor and are integrated across the thickness of the shell. These equations are developed in terms of components of the displacement field using third order shear deformation theory and solved analytically. It is assumed that material properties of the shell vary smoothly through the thickness according to a power law distribution of the volume fraction of constituent materials, while the Poisson’s ratio is assumed to be constant. Also governing equations are discretized and reduced to a linear system of homogenous equations using differential quadrature method. The results obtained by the present work are compared with finite element solutions and results reported in the literature and the accuracy of this method is shown. Effects of various parameters including the boundary conditions, volume fraction, different loading conditions and geometric ratios on the buckling behavior of functionally graded thick cylindrical shells are investigated.

کلیدواژه‌ها [English]

  • Mechanical buckling
  • critical load
  • Functionally Graded Material
  • thick cylindrical shell
  • third order shear deformation
 
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