بررسی تنش الاستیک در یک استوانه‌ی جداره ضخیم ساخته شده از مواد خواص گرادیانی دوبعدی با مدل ماده جدید

نوع مقاله: مقاله مکانیک

نویسندگان

دانشکده مهندسی مکانیک، دنشگاه سمنان

چکیده

در این مقاله تحلیل الاستیک تنش در یک استوانه‌ی جداره ضخیم با طول کوتاه و ساخته شده از مواد خواص گرادیانی دوبعدی که خواص مواد در آن بر اساس مدل موری – تاناکا ارائه شده، انجام شده است. بارهای اعمالی بر این استوانه به صورت فشار خارجی یا فشار داخلی بوده است و از روش المان محدود که المان‌های آن توابع درونیاب درجه سوم لاگرانژی دارند، برای حل مساله استفاده شده است. همچنین اعتبار سنجی مساله به کمک مقایسه با مساله‌ی ساده‌تری که تحلیل تنش به روش بدون مش پتروف-گلرکین در آن صورت گرفته، انجام پذیرفته است. با توجه به نتایج، مقادیر تنش بدست آمده در اثر فشار خارجی بیشتر از مقادیر تنش در اثر فشار داخلی می‌باشد. همچنین تنش موثر نرمال در راستای خط مرکزی شعاعی بر اساس توزیع درصد حجمی فاز فلزی با تغییر nz ، تغییرات چشمگیری دارد و تنش موثر نرمال در نقطه‌ی مرکزی دیواره‌ی استوانه با افزایش مقادیر nr زیاد می شود. در پایان، بیشینه تنش موثر نرمال برای تمامی درصد حجمی‌های ممکن روی دیواره‌ی استوانه مورد بررسی قرار گرفته است. نتایج نشان می‌دهد که کمترین مقدار برای بیشینه‌ی تنش موثر نرمال در هر دو حالت فشار داخلی و خارجی مربوط به nr برابر 20 و nz برابر 1/. می‌باشد. به عبارت دیگر دیواره‌ی سیلندر ساخته شده از سرامیک دوم (سیلیکون نیتراید) دارای کمترین مقدار تنش موثر نرمال خواهد بود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Axisymmetric Elastic stress investigation of a 2D- FGM thick hollow cylinder with new material model

نویسندگان [English]

  • Amir Najibi
  • Ramezanali Hajighorbani
چکیده [English]

In this paper elastic mechanical stress analysis for a 2D- FGM thick hollow cylinder with finite length have been conducted in which the material properties distributions are following a new developed material model according to the Mori- Tanaka scheme. This cylinder is subjected to internal or external non-uniform pressure loading and finite element method with third order Lagrange shape functions have been utilized to analyze the problem. Verification has been performed with a simplified study in which the results have been extracted by utilizing MLPG method. The results show that the stresses obtained from external pressure loading is higher than its counterpart stresses related to the internal pressure. Furthermore, normalized effective stresses according to the metallic volume fraction along the horizontal center line have significant change by nz variation. Also, normalized effective stresses on the center point of the cylinder wall have been increased by increasing of nr. Finally, it has been demonstrated that the minimum value of the maximum normalized effective stresses for both internal and external pressure loading are related to material distribution of nr=20 and nz=0.1. It means that the ceramic 2 (Si3N4) rich cylinder wall has the lowest value of normalized effective stress.

کلیدواژه‌ها [English]

  • 2D-FGM
  • Thick hollow cylinder with finite length
  • Mori-Tanaka
  • Elastic stress
 

[1] Reddy J.N., Chin C.D., Thermomechanical Analysis of Functionally Graded Cylinders and Plates, J. Therm. Stresses, Vol. 21, pp- 593–626, (1998).

 [2] Tutuncu, Naki; Ozturk, Murat “ Exact solutions for stresses in functionally graded pressure vessels”, Composites Part B: Engineering, Vol. 32, No. 8, pp- 683-686, (2001).

[3] Jabbari, M., Sohrabpour, S., Eslami, M. R., “Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads” International Journal of Pressure Vessels and Piping, Vol. 79, No. 7, pp- 493-497, (2002).

[4] Jabbari, M., Sohrabpour, S., Eslami, M. R.,” General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Nonaxisymmetric Steady-State Loads”, Journal of Applied Mechanics, Transactions ASME, Vol. 70, No. 1, pp- 111-118, (2003).

[5] Chen, B., Tong, L., “Thermomechanically Coupled Sensitivity Analysis and Design Optimization of Functionally Graded Materials”, Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 18-20, pp- 1891-1911, (2005).

  [6] 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).

[7] Ching, H.K., Yen, S.C., “Meshless Local Petrov- Galerkin Analysis for 2D Functionally Graded Elastic Solids under Mechanical and Thermal loads”, Composites Part B: Engineering, Vol. 36, No. 3, pp- 223-240, (2005).

[8] Oral, A., Anlas, G., “Effects of Radially Varying Moduli on Stress Distribution of Nonhomogeneous Anisotropic Cylindrical Bodies”, International Journal of Solids and Structures, Vol. 42, No. 20, pp- 5568-5588, (2005).

[9] Shi, Zh., Zhang, T., Xiang, H., “ Exact Solutions of Heterogeneous Elastic Hollow Cylinders”, Composite Structures, Vol. 79, No. 1, pp-140-147, (2007).

 [10] Shao, Z. S., Wang, T. J.,” Three-Dimensional Solutions for the Stress Fields in Functionally Graded Cylindrical Panel with Finite Length and Subjected to Thermal/Mechanical Loads”, International Journal of Solids and Structures, Vol. 43, No. 13, pp- 3856-3874, (2006).

[11] Xiang, H., Shi, Zh., Zhang, T., “Elastic Analyses of Heterogeneous Hollow Cylinders”, Mechanics Research Communications, Vol. 33, No. 5, pp- 681-691, (2006).

[12] Tutuncu, N., “Stresses in Thick-Walled FGM Cylinders with Exponentially-Varying Properties”, Engineering Structures, Vol. 29, No. 9, pp- 2032-2035, September 2007.

[13] Akis, T., Eraslan, A. N., “The Stress Response and Onset of Yield of Rotating FGM Hollow Shafts”, Acta Mechanica, Vol. 187, No. 1-4, pp- 169-187, (2006).

[14] Eraslan, A.N., Akis, T., “On the Plane Strain and Plane Stress Solutions of Functionally Graded Rotating Solid Shaft and Solid Disk Problems”, Acta Mechanica, Vol. 181, No. 1-2, pp- 43-63, (2006).

[15] Tokovyy, Yu. V., Ma, Ch., Ch., “Analysis of 2D Non-Axisymmetric Elasticity and Thermoelasticity Problems for Radially Inhomogeneous Hollow Cylinders”, Journal of Engineering Mathematics, Thermo-mechanics of Non-Homogeneous Structures, Vol. 61, No. 2-4, p 171-184, (2008).

 [16] Asemi, K., Salehi, M., Akhlaghi, M., “Elastic Solution of a Two-Dimensional Functionally Graded Thick Truncated Cone with Finite Length under Hydrostatic Combined Loads”, Acta. Mech., Vol 217, pp-119-134 (2010).

[17] Najibi, A., Shojaeefard, M.H., “Elastic Mechanical Stress Analysis in a 2D-FGM Thick Finite Length Hollow Cylinder with Newly Developed Material Model”, Acta Mechanica Solida Sinica, Vol 29(2), pp-178-191 (2016).

 [18] Mori T, Tanaka T, “Average Stresses in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions”, Acta Metallurgica, Vol. 21, pp- 571-574, (1973).

[19] Reiter, T., Dvorak, G. J., Tvergaard, V., “Micromechanical Models for Graded Composite Materials”, Journal of the Mechanics and Physics of Solids, Vol. 45, No. 8, pp- 1281-1302, (1997)

[20] Kim J.H., Paulino G.H., Iso-parametric Graded Finite Elements for Non-Homogeneous Isotropic and Orthotropic Materials. ASME J. Appl. Mech. vol. 69 (4), pp. 502–514, (2002).

[21] Ching H.K., Yen S.C., Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads, Composites: Part B, 2005, 36, 223–240.

HMSO, London, pp. 1-8, (1996).

[22] Nemat-Alla M., Ahmed Kh.I.E., Hassab-Allah I., Elastic–Plastic Analysis of Two-Dimensional Functionally Graded Materials under Thermal Loading, Int. J. Solids & Structures vol. 46, pp. 2774–2786, (2009).

[23] Noda N., Thermal Stresses in Functionally Graded Materials. J. Therm. Stresses, vol. 22, pp. 477–512, (1999).