رفتار ورق‌های چهارگوش تحت بار دفعی: تحلیل ابعادی

نوع مقاله : مکانیک جامدات

نویسندگان

1 استادیار گروه مهندسی مکانیک، دانشگاه ایوانکی

2 گروه مهندسی مکانیک، دانشگاه ایوانکی

3 دانشیار، دانشگاه گیلان

چکیده

در این مقاله، از یک روش تحلیل بی‌بعد جهت ارائه دو رابطه تجربی بر اساس اعداد بی‌بعد به‌منظور پیش‌بینی نسبت بیشترین خیز دائمی ورق‌های تک‌لایه چهارگوش به ضخامت آن تحت بارگذاری دینامیکی با توزیع یکنواخت و محلی استفاده شده است. در اعداد بی‌بعد پیشنهادی، اثر هندسه ورق، شدت بار اعمالی، خواص مکانیکی ورق، حساسیت ماده به نرخ کرنش و شعاع بارگذاری در نظر گرفته شده است. جهت صحت‌سنجی مدل‌های تجربی از هشت سری آزمایش و 267 داده موجود در ادبیات تحقیق در طول چهل سال گذشته استفاده شده است. نتایج حاصل از مدل‌سازی نشان داد که تطابق خوبی بین نتایج پیش‌بینی مدل و مقادیر تجربی وجود دارد به‌طوری‌که درمجموع 117 داده تجربی برای بارگذاری یکنواخت، به ترتیب 94% (110 داده) و 98% (115 داده) از کل نقاط تجربی در محدوده خطای کمتر از 10% و 20% قرار دارند. همچنین، درمجموع 150 داده تجربی موجود برای بارگذاری محلی، به ترتیب 83% (124 داده) و 97% (146 داده) از کل نقاط تجربی در این دو محدوده قرار گرفتند. نتایج همچنین نشان داد که متغیر در نظر گرفتن کمیت‌های ماده با ضخامت در معادله کوپر-سیموندز موجب بهبود دقت پیش‌بینی مدل‌های تجربی می‌گردد به‌طوری‌که تنها 6% و 12% از داده‌های برای دو بارگذاری یکنواخت و محلی در محدوده 10% خطا قرار نمی‌گیرند.

کلیدواژه‌ها


عنوان مقاله [English]

The Behavior of Quadrangular Plates under Impulsive Loading: a Dimensional Analysis

نویسندگان [English]

  • Tohid Mirzababaie Mostofi 1
  • Mostafa Sayah Badkhor 2
  • Hashem Babaei 3
1 Faculty of Mechanical Engineering, University of Eyvanekey
2 Faculty of Mechanical Engineering, University of Eyvanekey
3 Faculty of Mechanical Engineering, University of Guilan
چکیده [English]

In this paper, a non-dimensional analysis approach has been used to propose two empirical equations based on dimensionless numbers to predict the maximum transverse permanent deflection-thickness ratio of single-layered quadrangular plates under uniformly and locally distributed dynamic loading. In the presented dimensionless numbers, the effect of plate geometry, the impulse of the applied load, the mechanical properties of the plate, the strain-rate sensitivity, and the loading radius have been considered. To validate the empirical models, eight series of conducted experiments and 267 data points in the state of the art over the past forty years have been used. The obtained results show good agreement between the model prediction results and the experimental values so that in the total of 117 experimental data for uniform loading, 94% (110 data) and 98% (115 data) of the data points were distributed in the ±10% and ±20% error range, respectively. Besides, in the total of 150 experimental data for localized loading, 83% (124 data) and 97% (146 data) of data points were distributed in these two ranges, respectively. The results also showed that assuming the material constants as variables based on the plate thickness, in the Cooper-Symonds constitutive equation improves the prediction accuracy of the empirical models so that only 6% and 12% of the data for uniform and localized loading respectively, are not within the 10% error range.

کلیدواژه‌ها [English]

  • Uniform loading
  • Localized loading
  • Non-dimensional analysis
  • Empirical model
  • Quadrangular plate
[1] Jones, N., Uran, T.O., Tekin, S.A. “The dynamic plastic behavior of fully clamped rectangular plates”, Int. J. Solids Struct., Vol. 6, No. 12, pp.  1499-1512, 1970.##
[2] Jones, N. “A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections”, Int. J. Solids Struct., Vol. 7, No. 8, pp. 1007-1029, 1971.##
[3] Olson, M., Nurick, G., Fagnan J. “Deformation and rupture of blast loaded square plates-predictions and experiments”, Int. J. Impact Eng., Vol. 13, No. 2 pp. 279-291, 1993.##
[4] Nurick, G., Conolly, A. “Response of clamped single and double stiffened rectangular plates subjected to blast loads”, WIT Transactions on The Built Environment, Vol. 8, Institute of Technology, and Mott MacDonald Group, UK., 1970.##
[5] Nurick, G., Shave, G. “The deformation and tearing of thin square plates subjected to impulsive loads—an experimental study”, Int. J. Impact Eng., Vol. 18, No. 1 pp. 99-116, 1996.##
[6] Jacob, N., Yuen, S.C.K., Nurick, G., Bonorchis, D., Desai, S., Tait, D. “Scaling aspects of quadrangular plates subjected to localised blast loads—experiments and predictions”, Int. J. Impact Eng., Vol. 30, No. 8-9 pp. 1179-1208, 2004.##
[7] Yuen, S.C.K., Nurick, G. “Experimental and numerical studies on the response of quadrangular stiffened plates. Part I: subjected to uniform blast load”, Int. J. Impact Eng., Vol. 31 No. 1, pp. 55-83, 2005.##
[8] Bonorchis, D., Nurick, G. “The effect of welded boundaries on the response of rectangular hot-rolled mild steel plates subjected to localised blast loading”, Int. J. Impact Eng., Vol. 34, No. 11, pp. 1729-1738, 2007.##
[9] Nurick, G., Pearce, H., Martin, J. “Predictions of transverse deflections and in-plane strains in impulsively loaded thin plates”, Int. J. Mech. Sci., Vol. 29, No. 6, pp. 435-442, 1987.##
[10] Nurick, G., Martin J. “Deformation of thin plates subjected to impulsive loading—a review part II: experimental studies”, Int. J. Impact Eng., Vol. 8, No. 2, pp. 171-186, 1989.##
[11] Nurick, G., Martin J. “Deformation of thin plates subjected to impulsive loading—a review: Part i: Theoretical considerations”, Int. J. Impact Eng., Vol. 8 No. 2, pp. 159-170, 1989.##
[12] Chen W. “A new bound solution for quadrangular plates subjected to impulsive loads”; 3rd Int. offshore polar Eng. Con, Int. Society Offshore Polar Eng., 1993.##
[13] Shen, W.Q., Jones, N. “Dynamic response and failure of fully clamped circular plates under impulsive loading”, Int. J. Impact Eng., Vol. 13, No. 2, pp. 259-278, 1993.##
[14] Li, Q., Jones, N. “On dimensionless numbers for dynamic plastic response of structural members”, Arch. Appl. Mech., Vol. 70, No. 4, pp. 245-254, 2000.##
[15] Park, B.-W., Cho, S.-R. “Simple design formulae for predicting the residual damage of unstiffened and stiffened plates under explosion loadings”, Int. J. Impact Eng., Vol. 32, No. 10, pp. 1721-1736, 2006.##
[16] Jones, N. “Dynamic inelastic response of strain rate sensitive ductile plates due to large impact, dynamic pressure and explosive loadings”, Int. J. Impact Eng., Vol. 74, pp. 3-15 2014.##
[17] Mostofi, T.M., Babaei, H., Alitavoli M. “Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behaviour of fully clamped thin quadrangular plates”, Thin-Walled Struct., Vol. 109, pp. 367-376, 2016.##
[18] Mostofi, T.M., Golbaf, A., Mahmoudi, A., Alitavoli, M., Babaei, H. “Closed-form analytical analysis on the effect of coupled membrane and bending strains on the dynamic plastic behaviour of fully clamped thin quadrangular plates due to uniform and localized impulsive loading”, Thin-Walled Struct., Vol. 123, pp. 48-56, 2018.##
[19] Yuen, S.C.K., Nurick, G., Langdon, G., Iyer, Y. “Deformation of thin plates subjected to impulsive load: Part III–an update 25 years on”, Int. J. Impact Eng., Vol. 107, pp. 108-117, 2017.##
[20] Johnson, W. “Impact Strength of Materials”, Edward Arnold, London, Google Scholar, 1972.##
[21] Zhao, Y.-P. “Suggestion of a new dimensionless number for dynamic plastic response of beams and plates”, Arch. Appl. Mech., Vol. 68, No. 7-8, pp. 524-538, 1998.##
[22] Jones, N. “Structural Impact”, Cambridge University Press, 1989.##
[23] Jones, N. “Influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively loaded rigid-plastic beams”, Int. J. Mech. Sci., Vol. 9, No. 12, pp. 777-796, 1967.##
[24] Mostofi, T.M., Babaei, H., Alitavoli, M. “The influence of gas mixture detonation loads on large plastic deformation of thin quadrangular plates: Experimental investigation and empirical modelling”, Thin-Walled Struct., Vol. 118, pp. 1-11, 2017.##
[25] Mostofi, T.M., Babaei, H., Alitavoli, M., Lu, G., Ruan, D. “Large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load”, Int. J. Impact Eng., Vol. 125, pp. 93-106, 2019.##
[26] Babaei, H., Mirzababaie Mostofi, T., Armoudli, E. “On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading”, Proc. Inst. Mech. Eng-Part E J. Process Mech. Eng., Vol. 231, No. 5, pp. 939-50, 2017.##
[27] Mirzababaie Mostofi, T., Babaei, H., Alitavoli, M. “Experimental and theoretical study on large ductile transverse deformations of rectangular plates subjected to shock load due to gas mixture detonation”, Strain, Vol. 53, No. 4, e12235.##
[28] Babaei, H., Mostofi, T.M., Namdari-Khalilabad M, Alitavoli, M., Mohammadi, K. “Gas mixture detonation method, a novel processing technique for metal powder compaction: Experimental investigation and empirical modeling. Powder Tech.”, Vol. 315, pp. 171-81, 2017.##
[29] Babaei, H., Mostofi, T.M., Alitavoli, M., “Experimental and theoretical study of large deformation of rectangular plates subjected to water hammer shock loading”, Proc. Inst. Mech. Eng-Part E J. Process Mech. Eng., Vol. 231, No. 3, pp. 490-6, 2017.##
[30] Babaei H, Mostofi TM, Alitavoli M, Saeidinejad A. “Experimental investigation and dimensionless analysis of forming of rectangular plates subjected to hydrodynamic loading”, J. Appl. Mech. Tech. Phys., Vol. 58, No. 1, pp. 139-47,2017.##
[31] Babaei, H., Mirzababaie Mostofi, T. “New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading”, Proc. Inst. Mech. Eng-Part L J. Mater. Des. Appl., Vol. 234, No. 2., pp. 231-45, 2020.##
[32] Rezasefat, M., Mirzababaie Mostofi, T., Babaei, H., Ziya-Shamami, M., Alitavoli, M. “Dynamic plastic response of double-layered circular metallic plates due to localized impulsive loading”, Proc. Inst. Mech. Eng-Part L J. Mater. Des. Appl., Vol 233. No. 7, pp. 1449-71, 2019.##
[33] Rezasefat, M., Mostofi, T.M., Ozbakkaloglu, T. “Repeated localized impulsive loading on monolithic and multi-layered metallic plates”, Thin-Walled Struct., Vol. 144, 106332, 2019.##
[34] Babaei, H., Mostofi, T.M., Sadraei, S.H. “Effect of gas detonation on response of circular plate-experimental and theoretical”, Struct. Eng. Mech., Vol. 56, No. 4, pp. 535-48, 2015.##
[35] Babaei, H., Mostofi, T.M., Alitavoli, M., Darvizeh, A. “Empirical modelling for prediction of large deformation of clamped circular plates in gas detonation forming process”, Exp. Tech., Vol. 40, No. 6, pp. 1485-94, 2016.##
[36] Babaei, H., Mostofi, T.M., Alitavoli, M. “Study on the response of circular thin plate under low velocity impact”, Geomech. Eng., Vol. 9, No. 2, pp. 207-18, 2015.##
[37] Babaei, H., Mostofi, T.M., Namdari, M., Alitavoli, M. “Experimental investigation and a model presentation for predicting the behavior of metal and alumina powder compaction under impact loading”, Journal of Modares Mechanical Engineering, Vol. 15, No. 5, pp. 357-366, 2015.##
[38] Mostofi, T.M., Babaei, H., Alitavoli, M., Hosseinzadeh, S. “On dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile”, Thin-Walled Struct., Vol. 112, pp. 118-124, 2017.##
[39] Jones, N., Jones, C. “Inelastic failure of fully clamped beams and circular plates under impact loading, Proceedings of the Institution of Mechanical Engineers”, Part C: J. Mech. Eng. Sci., Vol. 216, No. 2, pp. 133-149, 2002.##