آمار

تعداد نشریات8
تعداد شماره‌ها425
تعداد مقالات5,551
تعداد مشاهده مقاله6,577,623
تعداد دریافت فایل اصل مقاله5,603,219
soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. (1398). Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material. نشریه مهندسی عمران امیرکبیر, 4(1), 91-102. doi: 10.22060/ajce.2019.15195.5525
masoumeh soltani; behrooz asgarian; Firooz Jafarzadeh. "Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material". نشریه مهندسی عمران امیرکبیر, 4, 1, 1398, 91-102. doi: 10.22060/ajce.2019.15195.5525
soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. (1398). 'Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material', نشریه مهندسی عمران امیرکبیر, 4(1), pp. 91-102. doi: 10.22060/ajce.2019.15195.5525
soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material. نشریه مهندسی عمران امیرکبیر, 1398; 4(1): 91-102. doi: 10.22060/ajce.2019.15195.5525

Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material

AUT Journal of Civil Engineering
مقاله 8، دوره 4، شماره 1، خرداد 2020، صفحه 91-102    اصل مقاله (1.87 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22060/ajce.2019.15195.5525
نویسندگان
masoumeh soltani* 1؛ behrooz asgarian2؛ Firooz Jafarzadeh3
1Department of civil engineering, faculty of engineering, University of Kashan, kashan, Iran
2Department of Civil Engineering, University of Khajeh Nasireddin Tousi
3Department of Civil Engineering, Faculty of Engineering, Shahr-e-Qods Branch, Islamic Azad University
چکیده
This paper addresses the linear buckling behavior of tapered Timoshenko beams made of axially functionally graded material (AFGM). Material properties of the non-prismatic Timoshenko beam vary continuously along the length of the member according to power law as well as exponential law. Based on Timoshenko beam assumption and using small displacements theory, the linear equilibrium equations are adopted from the energy principle for functionally graded non-uniform Timoshenko beams related to constant compressive axial load. The resulting system of stability equations are strongly coupled due to the presence of transverse deflection and angle of rotation. The differential equations are then uncoupled and lead to a single homogeneous differential equation where only bending rotation is present. The finite difference method (FDM) is then selected to numerically solve the resulting second-order differential equation with variable coefficients and determine the critical buckling loads. Two numerical examples are finally conducted to demonstrate the performance and efficiency of this mathematical procedure. The obtained results are contrasted with accessible numerical and analytical benchmarks.
کلیدواژه‌ها
Critical Buckling Load؛ Functionally Graded Material؛ Tapered Timoshenko Beam؛ Finite Difference Method
مراجع
  1. Irie T., Yamada G., Takahashi I. (1980), “Vibration and stability of non- uniform Timoshenko beam subjected to a follower force”, Journal of Sound and Vibration; 70: 503-512.
  2. Lee S.Y, Lin S.M. (1995), “Vibrations of elastically restrained non-uniform Timoshenko beams”, Journal of Sound and Vibration; 184(3): 403-415.
  3. Esmailzadeh E., Ohadi A.R. (2000), “Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads”, Sound and Vibration; 236(3): 443-456.
  4. Chen C.N. (2002), “DQEM vibration analysis of non-prismatic shear deformable beams resting on elastic foundations”, Sound and Vibration; 255(5): 989-999.
  5. Aucoello N.M., Ercolano A. (2002), “A general solution for dynamic response of axially loaded non-uniform Timoshenko beams”, Solids and Structures; 41(18-19): 4861-4874.
  6. Ruta P. (2006), “The application of Chebyshev Polynomials to the solution of the non-prismatic Timoshenko beam vibration problem”, Sound and Vibration; 296(1-2): 243-263.
  7. Wickowski Z., Colubiewski M. (2007), “Improvement in accuracy of the finite element method in analysis of stability of Euler-Bernouli and Timoshenko beam”, Thin-walled Structures; 45: 950-954.
  8. Ozdemir Ozgumus O., Kaya M.O. (2008), “Flapwise bending vibration analysis of a rotating double-tapered Timoshenko beam”, Archive of Applied Mechanics; 78(5): 379-392.
  9. Zhu B., Leung A.Y.T. (2009), “Linear and nonlinear vibration of non- uniform beams on two-parameter foundations using p-elements”,  Computers and Geotechnics; 36: 743-750.
  10. Soufyana A. (2009), “Exponential stability analysis of the linearized non-uniform Timoshenko beam”. Nonlinear Analysis: Real world Application; 10: 1016-1025.
  11. Attarnejad R., Shahba A., Jandaghi Semnani S. (2011), “Analysis of non- prismatic Timoshenko beams using basic displacement functions”. Advances in Structural Engineering; 14(2): 319-332.
  12. Chakraborty A., Gopalakrishnan S., Reddy J.N. (2003), “A new beam finite element for the analysis of functionally graded materials”, International Journal Mechanical Science; 45: 519–39.
  13. Simsek M., Kocatürk T. (2009), “Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load”, Composite Structures; 90: 465–73.
  14. Li X.F., Kang Y.A., Wu J. X. (2013), “Exact frequency equations of free vibration of exponentially graded beams”, Applied Acoustic; 74: 413–420.
  15. Pradhan K.K., Chakraverty S. (2013), “Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method”, Composite Part B; 51: 175–184.
  16. Arefi M. (2015), “Nonlinear electromechanical stability of functionally graded circular plate integrated with functionally graded piezoelectric layers under radial compressive”, Latin American Journal of Solids and Structures; 12(9): 1653-1665.
  17. Shvartsman B., Majak J. (2016), “Numerical method for stability analysis of functionally graded beams on elastic foundation”, Applied Mathematical Modelling; 44: 3713–3719.
  18. Soltani M. (2017), “Vibration characteristics of axially loaded tapered Timoshenko beams made of functionally graded materials by the power series method”, Numerical Methods in Civil Engineering; 2(1): 1-14.
  19. Pradhan K. K., Chakraverty S. (2017), “Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions”, Journal of the Brazilian Society of Mechanical Sciences and Engineering; 39(9): 3295-3313.
  20. Khaniki H.B., Rajasekaran S. (2018), “Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory”, Materials Research Express; 5-055703.
  21. Li X., Li L., Hu Y. (2018), “Instability of functionally graded micro-beams via micro-structure-dependent beam theory”, Applied Mathematics and Mechanics (English Edition); 39: 923-952.
  22. Soltani M., Asgarian B. (2019) “Finite  element  formulation  for  linear stability analysis of axially functionally graded non-prismatic Timoshenko beam”. International Journal of Structural Stability and dynamics, 19(2): 1950002 (33 pages).
  23. Shahb A., Attarnejad R., Tavanaie Marvi M., Hajilar S., (2011) “Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions”, Composites: Part B; 42(4): 801-808.
آمار
تعداد مشاهده مقاله: 855
تعداد دریافت فایل اصل مقاله: 726


سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب