مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

تخمین ضریب تمرکز تنش گشودگی دایره ای واقع در ورق ارتوتروپیک با استفاده از مدلی جدید بر پایه روش رگرسیونی

نویسندگان
1 کارشناسی ارشد، دانشکده مکانیک، دانشگاه صنعتی شاهرود، شاهرود
2 دانشیار، دانشکده مکانیک، دانشگاه صنعتی شاهرود، شاهرود
3 گروه مهندسی مکانیک بیوسیستم، دانشگاه فردوسی مشهد، مشهد، ایران
چکیده
یکی از دغدغه‌های طراحان سازه‌های مهندسی، شکست سازه در اثر تمرکز تنش ناشی از ناپیوستگی‌های هندسی در سازه است. لذا با توجه به اینکه صفحات کامپوزیتی دارای گشودگی در اغلب سازه‌های مهندسی کاربرد دارند، مطالعه و بررسی آن‌ها از اهمیت بسیاری برخوردار است. هدف از انجام این مقاله ارائه مدلی جدید بر پایه روش رگرسیونی جهت تخمین ضریب تمرکز تنش در گشودگی دایره‌ای در صفحات ارتوتروپیک می‌باشد. از کاربردهای مهم ارائه توزیع تنش در اطراف گشودگی بر حسب خواص مکانیکی، استفاده از این روابط در تحلیل تنش صفحات ویسکوالاستیک دارای گشودگی با استفاده از روش مدول مؤثر و یا اصل برهمنهی بولتزمن است. در ابتدا با استفاده از مقادیر مختلف خواص مکانیکی کامپوزیت‌ها ، و به کمک حلّی تحلیلی برپایه روش متغیر مختلط، ضریب تمرکرتنش برای تعداد متعددی از این مواد محاسبه شد سپس با استفاده از رگرسیون خطی چندگانه برای گشودگی دایره‌ای رابطه‌ای صریح برای ضریب تمرکز تنش برحسب خواص مکانیکی ارائه ‌شد. نتایج نشان داد که که مدل رگرسیونی قادر به پیش بینی تنش محیطی با حداکثر خطای 1 درصد می‌باشد.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Estimation of stress concentration factor of circular hole in orthotropic plate using a new model based on regression method

نویسندگان English

ali abbasnia 1
Mohammad Jaffari 2
Abbas Rohani 3
1 Department of Mechanical Engineering, Shahrood University, Shahrood, Iran
2 Department of Mechanical Engineering, Shahrood University, Shahrood, Iran
3 Department of bio systems engineering, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده English

One of the concerns of designers of engineering structures is structural failure due to stress concentration caused by geometric discontinuities in the structures. Therefore, by considering that perforated composite plates are used in most engineering structures, their study is very important. The purpose of this paper is to present a new model based on the regression method for estimating stress concentration factor of a circular hole in orthotropic plates. One of the important applications of providing stress distribution around holes in terms of mechanical properties is the use of these relationships in the stress analysis of perforated viscoelastic plate using the effective modulus method or Boltzmann's superposition principle. First, using different values of the mechanical properties of the composites plates, and employing an analytical solution based on the complex variable method, the stress concentration factor of circular hole is calculated for a number of these materials. Then, using multiple linear regression, an explicit expression for the stress concentration factor is given in terms of mechanical properties. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of less than 1%.

کلیدواژه‌ها English

Stress concentration factor
Circular Hole
Multiple Linear Regression
Complex variable method
[1] R. C. J. Howland, On the stresses in the neighborhood of circular hole in a strip under tension, Philosophical Transactions of the Royal Society, Vol. 229, No. 670-680, pp. 49-86, 1930.
[2] N. I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity, 2nd englished. The Netherlands, P. NoordhooffLtd, pp. 1-681, 1962.
[3] G. N. Savin, Stress Concentration Around Holes, New York, Pergamon Press, pp. 1-265, 1961.
[4] S. G. Lenkhnitskii, Anisotropic Plates, 2rd ed., NewYork, Gordonand Breach Science Publishers, pp. 1-534, 1968.
[5] D. S. Sharma, Stress concentration around circular elliptical triangular cutouts in infinite composite plate, Proceedings of the World Congress on Engineering, WCE 2011, London, U.K., July 6 – 8, Vol. 3, 2011.
[6] M. Mohammadi, J. R. Dryden, L. Jiang, Stress concentration around a hole in a radially inhomogeneous plate, Journal of Solids and Structures ,Vol. 48, No. 3, pp. 483–491, 2011.
[7] A. Khechai, A. Tati, A. Guettala, Finite element analysis of stress concentrations and failure criteria in composite plates with circular holes, Frontiers of Mechanical Engineering, Vol. 9, No. 3, pp. 281-294, 2014.
[8] M. Banerjee, N. K. Jain, S. Sanyal, Stress concentration in isotropic and orthotropic composite plates with center circular hole subjected to transverse static loading, International Journal of Mechanical and Industrial Engineering, Vol. 3, No. 1, pp. 109-113, 2013.
[9] P. Dharmin, P. Khushbu, J. Chetan, A review on stress analysis of an infinite plate with cut-outs, International Journal of Scientific and Research Publications, Vol. 2, No. 11, pp. 1-7, 2012.
[10] V. G. Aradhye, S. S. Kulkarni, Experimental investigation of stress concentration factor in an isotropic and orthotropic plate with multiple circular holes, International Journal of Science, Engineering and Technology Research, Vol. 4, No. 11, 2015.
[11] N. M. Abuelfoutouh, Preliminary design of unstiffend composite shells, Symposium of 7th technical Conference of ASC, pp. 693-786, 1993.
[12] L. Zhuang, B. Su, M. Lin, Yi. Liao, Y. Peng, Y. Zhou, D. Luo, Influence of the property of hole on stress concentration factor for isotropic plates, 10th International Conference on Composite Science and Technology, 2015.
[13] A. Kumar, A. Agrawal, R. Ghadai, K. Kalita, Analysis of Stress Concentration in Orthotropic Laminates, Procedia Technology, Vol. 23, No. , pp. 156-162, 2016.
[14] M. Jafari, M. Ghannad, A. Ameri, Study of the stress distribution around circular hole in heterogeneous plate subjected to in-plane loading, Modares Mechanical Engineering, Vol. 15, No. 6, pp. 249-256, 2015. (in Persianفارسی )
[15] M. Jafari, E. Ardalani, Analytical solution to calculate the stress distribution around a triangular hole in finite isotropic plates under in-plane loading, Modares Mechanical Engineering, Vol. 15, No. 5, pp. 165-175, 2015. (in Persianفارسی )
[16] M. Jafari, S. A. Mahmodzade hoseyni, Optimization of Influence Parameter on isotropic plates with Regular polygonal
cutouts using particle swarm Algorithm, Modares Mechanical Engineering, Vol. 15, No. 12, pp. 243-253, 2015. (in Persianفارسی )
[17] M. Jafari, B. Moshiri Aval, Stress analysis of symmetric composite laminates with quasi-rectangular hole subjected to in-plane loading, Modares Mechanical Engineering, Vol. 14, No. 15, pp. 395-404, 2014. (in Persianفارسی )
[18] M. H. Dirikolu, A. Aktas, Analytical and finite element comparisons of stress intensity factors of composite materials, Composite Structures, Vol. 50, No. 1, pp. 99–102, 2000.
[19] M. Karama, L. Toubal, B. Lorrain, Stress concentration in a circular hole in composite plate, Composite Structures, Vol. 68, No. 1, pp. 31–36, 2005.
[20] M. Fakoor, S. Z. Hossein Abadi, R. Rafiee, Extension of maximum tensile stress criterion to mixed mode fracture of orthotropic materials considering t-stress, Modares Mechanical Engineering, Vol. 17, No. 10, pp. 292-300, 2017. (in Persianفارسی )
[21] K. Kaw, Mechanics of Composite Materials, Second Edittion, pp. 6-9, Taylor & Francis Group, 2006.
[22] E. O. Ayorinde, R. F. Gibson, Elastic constants of orthotropic composite materials using plate resonance frequencies, classical lamination theory and an optimized three-mode rayleigh formulation, Compositrcs Engineering, Vol. 3, No. 5, pp. 395-407, 1993.
[23] I. M. Daniel, O. Ishai, Engineering Mechanics of Composite Materials, New York, Oxford university press, Vol. 3, pp. 34-35, 1994.