The new version of Differential Quadrature Buckling Analyses of FGM Rectangular Plates Under Non-Uniform Distributed In-Plane Loading
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکمحمد مهدی نجفی زاده 1 , رضا کاظمی مهرآبادی 2
1 - استادیار، دانشگاه آزاد اسلامی واحد اراک.
2 - کارشناس ارشد، مهندسی مکانیک، دانشگاه آزاد اسلامی واحد اراک.
کلید واژه: Buckling, FGM materials, Isotropic plate, The new version of DQ,
چکیده مقاله :
In this paper the buckling coefficient of FGM rectangular plates calculated by the new version of differential quadrature method (DQM). At the first the governing differential equation for plate has been calculated and then according to the new version of differential quadrature method (DQM) the existence derivatives in equation , convert to the amounts of function in the grid points inside of the region is solved .With doing this , The equation will be converted to an eigen value problem and the buckling coefficient is obtained . In the solving of this problem two kinds of loading for all edges are simply supported or clamped are considered and also the effect of power law index over the buckling coefficient is considered . For the case Isotropic the results are compared well with finite element and finite difference results.This fact indicates that the new version of DQ method can be employed for obtaining buckling loads of plates subjected to non–uniform distributed loading for other boundary conditions.
در این مقاله ضریب کمانش صفحات مستطیل شکلی که از مواد FGM ساخته شده‌اند، به کمک روش مربعات دیفرانسیلی اصلاح شده، محاسبه می‌شود. ابتدا معادله حاکم بر کمانش ورق محاسبه و سپس بر اساس روش مربعات دیفرانسیلی اصلاح شده، مشتقات موجود در معادله تبدیل به مقادیر تابع، در نقاط شبکه داخل ناحیه، حل می‌گردند. در ادامه، معادله تبدیل به یک مسئله مقدار ویژه خواهد شد که با محاسبه مقادیر ویژه، ضریب کمانش به‌دست می‌آید. درحل مسئله دو نوع حالت بارگذاری برای شرایط مرزی تکیه‌گاه ساده و گیردار مورد بررسی قرار می‌گیرد. همچنین اثر ثابت قانون توانی بر ضریب کمانش، مورد بررسی قرار می‌گیرد. در ادامه، درحالتی که جنس ورق ایزوتروپیک باشد، نتایج این روش با نتایج به‌دست آمده از راه حلهای تفاضلات متناهی و المان محدود مقایسه و بررسی می شود. این حقیقت نشان می‌دهد که روش مربعات دیفرانسیلی اصلاح شده برای به‌دست آوردن بارهای کمانش صفحات مستطیلی تحت نیروهای توزیع شده غیر یکنواخت برای شرایط مرزی مختلف روش بسیار مناسبی می باشد.
[1] Bellman RE, Casti J., Differential quadrature and long-term integration, J. Mathematical Analysis and Applications, Vol. 34, 1971, pp. 235-238.
[2] Wang X, Gu H, Liu B., on buckling analysis of beam and frame structures by differential quadrature element method, Proceedings of Engineering Mechanics, Vol. 1, 1996, pp. 382-385.
[3] Liu GR, Wu TY., Vibration analysis of beam using the generalized differential quadrature rule and domain decomposition, J. Sound and Vibration, Vol. 246, 2001, pp. 461-481.
[4] Bert CW, Devarakonda KK., Buckling of rectangular plates subjected to nonlinearly distributed in-plane loading, Int. J. Solids Structures, Vol. 40, 2003, pp. 4097–4106.
[5] Sherbourne AN, Pandey MD., differential quadrature method in the buckling analysis of beams and composite plates, Computers and Structures, Vol. 40, 1991, pp. 903–913.
[6] Bert CW, Wang X, Striz AG., Differential quadrature for static and free vibration analyses of anisotropic plates. Int. J. Solids Structures, Vol. 30(13), 1993, pp. 1737–44.
[7] Wang X, Bert CW., A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates, J Sound & Vibration, Vol. 162(3), 1993, pp. 566–72.
[8] Wang X, Gu H, Liu B., On buckling analysis of beams and frame structures by the differential quadrature element method, Proc Eng Mech, Vol. 1, 1996, pp.382–5.
[9] Wang X, Differential quadrature for buckling analysis of laminated Plates, Comput Struct, Vol. 57(4), 1995, pp.715–9.
[10] Wang X, Tan M, Zhou Y., Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method, Thin-Walled Structures, Vol. 41, 2003, pp.15–29.
[11] Wang X., Shi X., Applications of differential quadrature method for solutions of rectangular plates subjected to non-uniformly distributed in-plane loadings, (unpublished manuscript).
[12] Wang. X., Xinfeng W., Differential quadrature buckling analyses of rectangular plates subjected to non–uniform distributed in–plane loadings, Thin-walled structures, Vol. 44, 2006, pp. 837-843.
[13] Koizumi M., FGM activities in Japan, Composites, Vol. 28 (1-2), 1997, pp. 1-4.
[14] Reddy J. N., Wang C. M., Kitipornachi, axisymmetric bending of functionally graded circular annular plates, Eur. J. Mech A/Solid, Vol. 20, 2001, pp. 841-855.
[15] Brush D.O., Almroth B.O., Buckling of bars, plates and shells, McGraw Hill, New York, 1975.
[16] Xinwei W., Feng L., Xinfeng W. and Lifei G., New approaches in application of differential quadrature method to fourth – order differential equations, Communication In Methods In Engineering, Vol. 21, 2005, pp. 61-71.
[17] Praveen G.N., Reddy J.N., Nonlinear Transient thermoelastic analysis of functionally graded Ceramic-metal plates, Int. J. solids and structures, Vol. 35(33), 1998, pp. 4457-4476.
[18] Van der Neut A., Buckling caused by thermal stresses, High temperature effects in aircraft structures, AGARDograph, Vol. 28, 1958, pp.215–47.
[19] Benoy M.B., An energy solution for the buckling of rectangular plates under non-uniform in-plane loading, Aeronaut J, Vol. 73, 1969, pp. 974–7.
[20] Young WC, Budynas RG., Roarks formulas for stress & strain, 7th ed., New York, USA, McGraw-Hill, 2002.
