پیشنهاد یک روش ساده اجزای محدود برای تحلیل ارتعاش آزاد و کمانش تیرهای چندلایه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، گروه مهندسی عمران، دانشگاه آزاد اسلامی، واحد لارستان، لارستان، ایران

2 استادیار، گروه مهندسی عمران، دانشگاه فسا

3 دانش آموخته دانشگاه فردوسی مشهد.

4 استادیار، گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه تربت حیدریه

چکیده

در این مقاله یک جزء دو گرهی برپایه‌ی نگره‌ی برشی مرتبه یکم (FSDT ،)برای تحلیل ارتعاش آزاد و کمانش تیرهای چندلایه متقارن پیشنهاد می‌گردد. برای رابطه سازی جزء، میدان جایجایی از درجه سوم و میدان دوران آن نیز از درجه دوم انتخاب می‌شود. همچنین کرنش برشی جزء نیز مقداری ثابت فرض شده است. با نوشتن کارمایه کل تیر و ایستا کردن آن نسبت به کرنش برشی، تابع‌های درون‌یاب برای میدان جابه‌جایی و دوران تیر به صورت صریح محاسبه می‌شود. شایان ذکر است که با کاهش ضخامت تیر، تابع‌های درونیاب جزء پیشنهادی، به تابع‌های درونیاب جزء اولر-برنولی تبدیل می‌شوند و مشکل قفل برشی در آن رخ نمی‌دهد. با بهره جویی از این تابع‌های درون‌یاب، ماتریس سختی تیر محاسبه می‌شود. در ادامه با نوشتن معادلات حاکم بر ارتعاش آزاد تیر، شکل صریح ماتریس جرم انتقالی و دورانی جزء پیشنهادی نیز محاسبه می‌شود. همچنین، با بهره‌جویی از تابع‌های درونیاب، ماتریس سختی هندسی جزء نیز در دسترس قرار می‌گیرد. در پایان با آزمون‌های عددی پرشمار دقت و کارایی جزء پیشنهادی مورد ارزیابی قرار می‌گیرد. برای این منظور، تیرهای چندلایه متقارن با شرط‌های مرزی و نسبت طول به ضخامت گوناگون تحلیل می‌گردد. این آزمون‌ها نشان دهندهی دقت بالای جزء در تحلیل ارتعاش آزاد و کمانش تیرهای چندلایه متقارن نازک و ضخیم می‌باشند. همچنین، نبود مشکل قفل برشی در جزء پیشنهادی نیز به اثبات می‌رسد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A new simple finite element method for free vibration and buckling analysis of symmetrically laminated beams

نویسندگان [English]

  • mohammad karkon 1
  • soliman Ghoohestani 2
  • seyed mohammad saberizadeh 3
  • Majid Yaghoobi 4
1 Civil Engineering Department, Larestan Branch, Islamic Azad University, Larestan, Iran
2 Department of Civil Engineering, Fasa University, Fasa, Iran
3 ferdDepartment of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
4 Assistant Professor, Civil Engineering Department, Engineering Faculty, University of Torbat Heydarieh, Torbat Heydarieh, Iran.
چکیده [English]

In this paper, a new 2-node element is proposed for free vibration and buckling analysis of symmetrically laminated beams. The element’s formulation is based on first order shear deformation theory (FSDT). For this aim, the deflection and rotation field of the element is selected from third and second order functions, respectively. Moreover, the shear strain is assumed to be constant along with the element. By establishing the total strain energy in the element and stationary with respect to shear strain, the explicit form of the shape functions of deflection and rotation fields of the proposed element, are obtained. It should be mentioned, by decreasing the element’s thickness, these shape functions are approach to the Euler-Bernoulli shape’s functions and the shear locking problem does not occurred in the element. By utilizing the obtained shape functions, the explicit form of the stiffness matrix are calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, free vibration and buckling analysis of symmetrically laminated beams with different boundary conditions and aspect ratios, are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.

کلیدواژه‌ها [English]

  • Finite element
  • Laminated beam
  • Free vibration
  • Buckling

مراجع

[1]Y. Ghugal, R. Shimpi, A review of refined shear deformation theories for isotropic and anisotropic laminated beams, Journal of reinforced plastics and composites, 20(3) (2001) 255-272.
[2]K. Chandrashekhara, K. Krishnamurthy, S. Roy, Free vibration of composite beams including rotary inertia and shear deformation, Composite Structures, 14(4) (1990) 269-279.
[3]A. Khdeir, J. Reddy, Free vibration of cross-ply laminated beams with arbitrary boundary conditions, International Journal of Engineering Science, 32(12) (1994) 1971-1980.
[4]K. Chandrashekhara, K.M. Bangera, Free vibration of composite beams using a refined shear flexible beam element, Computers & structures, 43(4) (1992) 719-727.
[5]A. Khdeir, J. Redd, Buckling of cross-ply laminated beams with arbitrary boundary conditions, Composite Structures, 37(1) (1997) 1-3.
[6]A. Chakraborty, D.R. Mahapatra, S. Gopalakrishnan, Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities, Composite Structures, 55(1) (2002) 23-36.
[7]W. Chen, C. Lv, Z. Bian, Free vibration analysis of generally laminated beams via state-space-based differential quadrature, Composite Structures, 63(3-4) (2004) 417.524
[8]M. Murthy, D.R. Mahapatra, K. Badarinarayana, S. Gopalakrishnan, A refined higher order finite element for asymmetric composite beams, Composite Structures, .53-72 )5002( )1(76
[9]M. Aydogdu, Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method, International Journal of Mechanical Sciences, 47(11) (2005) 1740-1755.
[10]M. Aydogdu, Free vibration analysis of angle-ply laminated beams with general boundary conditions, Journal of reinforced plastics and composites, 25(15) (2006) 1571-1583.
[11]M. Aydogdu, Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method, Composites Science and Technology, 66(10) (2006) 12481255.
[12]A. Catapano, G. Giunta, S. Belouettar, E. Carrera, Static analysis of laminated beams via a unified formulation, Composite structures, 94(1) (2011) 75-83.
[13]M. Lezgy-Nazargah, M. Shariyat, S. Beheshti-Aval, A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams, Acta Mechanica, 217(3-4) (2011) 219-242.
[14]M. Lezgy-Nazargah, S. Beheshti-Aval, M. Shariyat, A refined mixed global–local finite element model for bending analysis of multi-layered rectangular composite beams with small widths, Thin-Walled Structures, 49(2) (2011) 351-362.
[15]R.A. Jafari-Talookolaei, M. Abedi, M.H. Kargarnovin, M.T. Ahmadian, An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia, International Journal of Mechanical Sciences, 65(1) (2012) 97-104.
[16]T.P. Vo, H.-T. Thai, Vibration and buckling of composite beams using refined shear deformation theory, International Journal of Mechanical Sciences, 62(1) (2012) 67-76.
[17]J. Li, Z. Wu, X. Kong, X. Li, W. Wu, Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups, Composite structures, 108 (2014) 767-778.
[18]X. Wang, X. Zhu, P. Hu, Isogeometric finite element method for buckling analysis of generally laminated composite beams with different boundary conditions, International Journal of Mechanical Sciences, 104 (2015) .991-091
[19]M. Filippi, A. Pagani, M. Petrolo, G. Colonna, E. Carrera, Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials, Composite Structures, 132 (2015) 1248-1259.
[20]J. Mantari, F. Canales, Free vibration and buckling of laminated beams via hybrid Ritz solution for various penalized boundary conditions, Composite Structures, 152 (2016) 306-315.
[21]F. Canales, J. Mantari, Buckling and free vibration of laminated beams with arbitrary boundary conditions using a refined HSDT, Composites Part B: Engineering, 100 (2016) 136-145.
[22]V. Kahya, Buckling analysis of laminated composite and sandwich beams by the finite element method, Composites Part B: Engineering, 91 (2016) 126-134.
[23]M.Y. Osman, O.M.E. Suleiman, Free vibration analysis of laminated composite beams using finite element method, International Journal of Engineering Research and Advanced Technology (IJERAT), 3(2) (2017) 5-22.
[24]T.-K. Nguyen, N.-D. Nguyen, T.P. Vo, H.-T. Thai, Trigonometric-series solution for analysis of laminated composite beams, Composite Structures, 160 (2017) 142151.
[25]N.-D. Nguyen, T.-K. Nguyen, T.P. Vo, H.-T. Thai, RitzBased Analytical Solutions for Bending, Buckling and Vibration Behavior of Laminated Composite Beams, International Journal of Structural Stability and Dynamics, 18(11) (2018) 1850130.
[26]S. Ghazanfari, S. Hamzehei-Javaran, A. Alesadi, S. Shojaee, Free vibration analysis of cross-ply laminated beam structures using refined beam theories and B-spline basis functions, Mechanics of Advanced Materials and Structures,  (2019) 1-9.
[27]A.S. Sayyad, Y.M. Ghugal, Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures, 171 (2017) 486-504.
[28]A. Moallemi-Oreh, M. Karkon, Finite element formulation for stability and free vibration analysis of Timoshenko beam, Advances in Acoustics and Vibration, 2013 (2013).
[29]M. Petyt, Introduction to finite element vibration analysis, Cambridge university press, 2010.
[30]J.R. Vinson, R.L. Sierakowski, The behavior of structures composed of composite materials, Springer Science & Business Media, 2006.
نشریه مهندسی عمران امیرکبیر
دوره 52، شماره 9
آذر 1399
صفحه 2243-2254

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