فرمول‌بندی الاستیک پوسته‌های متقارن محوری ناهمگن با انحنای دلخواه و ضخامت متغیر با نظریه برشی مرتبه اول

نوع مقاله : مقاله پژوهشی

نویسنده

استادیار، گروه مهندسی مکانیک، دانشگاه اراک، اراک، ایران

چکیده

تحلیل الاستیک پوسته­های متقارن محوری با استفاده از نظریه برشی مرتبه اول در این مقاله ارائه شده است. ابتدا با در نظر گرفتن پوسته متقارن با انحنای دلخواه و ضخامت متغیر، فرمول‌بندی عمومی پوسته با استفاده از روش انرژی ارائه شده است. در ادامه با در نظر گرفتن سیلندر با ضخامت ثابت و همچنین ضخامت متغیر به عنوان پوسته­های متقارن محوری، به بررسی روش های حل و ارائه نتایج پرداخته شده است. با ارائه نتایج عددی تحلیل حاضر با حل کلاسیک مقایسه شده است. ماده ناهمگن، تاثیر شرایط مرزی بر روی رفتار سیلندر، فشار غیر یکنواخت، انحنای دلخواه و ضخامت متغیر از مزیت های تحلیل ارائه شده می­باشد. ناهمگنی به صورت تغییرات در ضخامت و به صورت تابع توانی در نظر گرفته شده است. طیف وسیعی از پوسته­ها با در نظر گرفتن انحنای دلخواه و ضخامت متغیر با فرمول‌بندی ارائه شده قابل تحلیل می­باشند. کاربرد­های بسیار این گونه پوسته­ها در صنعت مانند صنعت هوا فضا وجود دارد. با تحلیل حاضر توانایی رسیدن به ضخامت بهینه و همچنین خواصی مانند مقاومت گرمایی با استفاده از مواد ناهمگن وجود دارد.

کلیدواژه‌ها

موضوعات


[1]  Timoshenko S., Strength of Materials, Pt. 2: Advanced Theory and Problems: R. E. Krieger Publishing Company, 1983.
[2]  Rahimi GH, Ghannad M, Esmaeilzadeh Khadem S, General Solution of Plane Elasticity of Axisymmetric Functionally Graded Thick Cylinderical Shells, Modares Mechanical Engineering, Vol. 10, No. 3, pp. 13, 1389. In Persian
[3]  Tutuncu N., Ozturk M., Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, Vol. 32, No. 8, pp. 683-686, 2001.
[4]  Reddy J. N., Arciniega R. A., Shear Deformation Plate and Shell Theories: From Stavsky to Present, Mechanics of Advanced Materials and Structures, Vol. 11, No. 6, pp. 535-582, 2004.
[5]  Ghannad M, RAHIMI G, ESMAEILZADEH KS., General Solution of Shear Deformation of Axisymmetric Functionally Graded Thick Cylinderical Shells, Modares Mechanical Engineering, Vol. 10, No. 4, pp. 14, 1389. In Persian
[6]  Khoshgoftar M. J., Rahimi G. H., Arefi M., Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure, Mechanics Research Communications, Vol. 51, No. 0, pp. 61-66, 7//, 2013.
[7]  Dai HL, Rao YN, Dai T., A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000–2015. Composite Structures, Vol. 15, No.152, pp. 199-225, 2016.
[8]  E. Asadi, W. Wang, M. S. Qatu, Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories, Composite Structures, Vol. 94, No. 2, pp. 494-500, 2012.
[9]  Eipakchi H., Khadem S., G. Rahimi S., Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure, Journal of Engineering Mechanics, Vol. 134, No. 8, pp. 601-610, 2008.
[10]             Arefi M., Rahimi G. H., The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clamped–clamped FG cylinder under mechanical and thermal loads, International Journal of Pressure Vessels and Piping, Vol. 96–97, pp. 30-37, 2012.
[11]             Zozulya V. V., A high-order theory for functionally graded axially symmetric cylindrical shells, Archive of Applied Mechanics, Vol. 83, No. 3, pp. 331-343, 2013.
[12]             Kang J. H., Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory, Acta Mechanica, Vol. 188, No. 1-2, pp. 21-37, 2007.
[13]             Wu C., Liu C., Stress and Displacement of Thick Doubly Curved Laminated Shells, Journal of Engineering Mechanics, Vol. 120, No. 7, pp. 1403-1428, 1994.
[14]             Santos H., Mota Soares C. M., Mota Soares C. A., Reddy J. N., A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials, Composite Structures, Vol. 91, No. 4, pp. 427-432, 12//, 2009.
[15]             Bahtui A., Eslami M. R., Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications, Vol. 34, No. 1, pp. 1-18, 1//, 2007.
[16]             Khoshgoftar M. J., Ghorbanpour Arani A., Arefi M., Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures, Vol. 18, No. 11, 2009.
[17]             Jabbari M., Bahtui A., Eslami M. R., Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders, International Journal of Pressure Vessels and Piping, Vol. 86, No. 5, pp. 296-306, 2009.
[18]             Shao Z. S., Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length, International Journal of Pressure Vessels and Piping, Vol. 82, No. 3, pp. 155-163, 2005.
[19]             Dai HL, Rao YN., Dynamic thermoelastic behavior of a double-layered hollow cylinder with an FGM layer. Journal of Thermal Stresses, Vol. 36, No.9, pp. 962-984, 2013.
[20]             Zhang W., Hao Y. X., Yang J., Nonlinear dynamics of FGM circular cylindrical shell with clamped–clamped edges, Composite Structures, Vol. 94, No. 3, pp. 1075-1086, 2012.
[21]             Amabili M., Reddy J. N., A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells, International Journal of Non-Linear Mechanics, Vol. 45, No. 4, pp. 409-418, 2010.
[22]             Tornabene F., Viola E., Free vibration analysis of functionally graded panels and shells of revolution, Meccanica, Vol. 44, No. 3, pp. 255-281, 2009/06/01, 2009.
[23]             Arefi M, Rahimi GH., Three-dimensional multi-field equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity. Acta Mechanica, Vol. 223, No.1, pp. 63-79, 2012.
[24]             Arefi M., Size-dependent bending behavior of three-layered doubly curved shells: Modified couple stress formulation. Journal of Sandwich Structures & Materials, Vol. 0, No.0, pp. 1-40, 2018.
[25]             Arefi M., Analysis of a doubly curved piezoelectric nano shell: nonlocal electro-elastic bending solution. European Journal of Mechanics-A/Solids, Vol. 1, No.70, pp. 226-37, 2018.
[26]             Arefi M, Bidgoli EM., Electro-elastic displacement and stress analysis of the piezoelectric doubly curved shells resting on Winkler's foundation subjected to applied voltage. Mechanics of Advanced Materials and Structures, Vol. 0, No.0, pp. 1-14, 2018.
[27]             Arefi M., Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell. STEEL AND COMPOSITE STRUCTURES, Vol. 27, No.4, pp. 479-93, 2018.
[28]             Arefi M., A complete set of equations for piezo-magnetoelastic analysis of a functionally graded thick shell of revolution. Latin American Journal of Solids and Structures, Vol. 11, No.11, pp. 2073-92, 2014.