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On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

  • Research Article - Civil Engineering
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An Erratum to this article was published on 27 October 2015

Abstract

Since the accuracy of results obtained through displacement-based finite element method (FEM) considerably depends on the accuracy of shape functions used to interpolate the displacement field within an element, this paper aims at presenting a new efficient element for static and free vibration analysis of higher-order shear deformable beams using FEM with introducing basic displacement functions (BDFs). First, BDFs are introduced and computed. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions, static and free vibration behavior of the higher-order shear deformable beam is studied using FEM. The accuracy and economy of the method are demonstrated through several numerical examples.

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References

  1. Attarnejad R.: Basic displacement functions in analysis of non-prismatic beams. Eng. Comput. 27(6), 733–745 (2010)

    Article  MATH  Google Scholar 

  2. Budcharoentong D., Neuber V.H.: Finite elements and convergence for dynamic analysis of beams. Comput. Struct. 10, 723–729 (1979)

    Article  MATH  Google Scholar 

  3. Naguleswaran S.: Vibration and stability of an Euler–Bernoulli beam with up to three-step changes in cross-section and in axial force. Int. J. Mech. Sci. 45(9), 1563–1579 (2003)

    Article  MATH  Google Scholar 

  4. Attarnejad R., JandaghiSemnani S., Shahba A.: Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams. Finite Elem. Anal. Des. 46(10), 916–929 (2010)

    Article  MathSciNet  Google Scholar 

  5. Ruta P.: The application of Chebyshev polynomials to the solution of the non-prismatic Timoshenko beam vibration problem. J. Sound Vib. 296, 243–263 (2006)

    Article  MATH  Google Scholar 

  6. Levinson M.: A new rectangular beam theory. J. Sound Vib. 74, 81–87 (1981)

    Article  MATH  Google Scholar 

  7. Bickford W.B.: A consistent higher order beam theory. Dev. Theor. 11, 137–150 (1982)

    Google Scholar 

  8. Wang X.D., Shi G.: Boundary layer solutions induced by displacement boundary conditions of shear deformable beams and accuracy study of several higher-order beam theories. J. Eng. Mech. ASCE 138(11), 1388–1399 (2012)

    Article  Google Scholar 

  9. Wang, M.Z.; Wang, W.: A refined theory of beams. J. Eng. Mech. Suppl. 324–327 (2003) (in Chinese)

  10. Gao Y., Wang M.: The refined theory of rectangular deep beams based on general solutions of elasticity. Sci. China Ser. G 36(3), 286–297 (2006)

    Google Scholar 

  11. Bhimaraddi A., Chandrashekhara K.: Observations on higher-order beam theory. J. Aerosp. Eng. 6(4), 408–413 (1993)

    Article  Google Scholar 

  12. Sayyad A.S.: Comparison of various refined beam theories for the bending and free vibration analysis of thick beams. Appl. Comput. Mech. 5(2), 217–230 (2011)

    Google Scholar 

  13. Li J., Shi C., Kong X., Li X., Wu W.: Free vibration of axially loaded composite beams with general boundary conditions using hyperbolic shear deformation theory. Compos. Struct. 97, 1–14 (2013)

    Article  Google Scholar 

  14. Viola E., Tornabene F., Fantuzzi N.: General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Compos. Struct. 95, 639–666 (2013)

    Article  Google Scholar 

  15. Grover N., Maiti D.K., Singh B.N.: A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates. Compos. Struct. 95, 667–675 (2013)

    Article  Google Scholar 

  16. Carrera E., Miglioretti F., Petrolo M.: Computations and evaluations of higher-order theories for free vibration analysis of beams. J. Sound Vib. 331, 4269–4284 (2012)

    Article  Google Scholar 

  17. Emam S.A.: Analysis of shear-deformable composite beams in postbuckling. Compos. Struct. 94, 24–30 (2011)

    Article  Google Scholar 

  18. Zhang Z., Taheri F.: Dynamic pulsebuckling and postbuckling of composite laminated beam using higher order shear deformation theory. Compos. Part B Eng. 34(4), 391–398 (2003)

    Article  Google Scholar 

  19. Petrolito J.: Stiffness analysis of beams using a higher-order theory. Comput. Struct. 55(1), 33–39 (1995)

    Article  MATH  Google Scholar 

  20. Ravikiran K., Kashif A., Ganesan N.: Static analysis of functionally graded beams using higher order shear deformation theory. Appl. Math. Model. 32, 2509–2525 (2008)

    Article  MATH  Google Scholar 

  21. Attarnejad R.: Basic displacement functions in analysis of non-prismatic beams. Eng. Comput. 27(6), 733–745 (2010)

    Article  MATH  Google Scholar 

  22. Shahba A., Attarnejad R., Hajilar S.H.: Free vibration and stability of axially functionally graded tapered Euler–Bernoulli beams. Shock Vib. 18, 683–696 (2011)

    Article  Google Scholar 

  23. Shahba A., Attarnejad R., Eslaminia M.: Derivation of an efficient non-prismatic thin curved beam element using basic displacement functions. Shock Vib. 18, 1–18 (2011)

    Article  Google Scholar 

  24. Attarnejad, R.; Shahba, A.: Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams a mechanical solution. Meccanica (2010). doi:10.1007/s11012-010-9383-z

  25. Attarnejad, R.; JandaghiSemnani, S.; Shahba, A.: Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams. Finite Elem. Anal. Des. (2010). doi:10.1016/j.finel.2010.06.005

  26. Shahba A., Attarnejad R., JandaghiSemnani S.: Derivation of an efficient element for free vibration analysis of rotating tapered Timoshenko beams using basic displacement functions. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 226(11), 1455–1469 (2011)

    Article  Google Scholar 

  27. Shahba A., Attarnejad R., Semnani S.J., Gheitanbaf H.H.: New shape functions for non-uniform curved Timoshenko beams with arbitrarily varying curvature using basic displacement functions. Meccanica 48, 159–174 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. HosseiniHashemi S., Kalbasi H., Taher H.R.D.: Free vibration analysis of piezoelectric coupled annular plates with variable thickness. Appl. Math. Model. 35, 3527–3540 (2011)

    Article  MathSciNet  Google Scholar 

  29. HosseiniHashemi S., Taher H.R.D., Akhavan H.: Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations. Compos. Struct. 92, 1734–1743 (2010)

    Article  Google Scholar 

  30. Malekzadeh P., Karami G., Farid M.: A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported. Comput. Method Appl. Mech. Eng. 193, 4781–4796 (2004)

    Article  MATH  Google Scholar 

  31. Shu C., Wu W.X., Ding H., Wang C.M.: Free vibration analysis of plates using least square-based finite difference method. Comput. Methods Appl. Mech. Eng. 196, 1330–1343 (2007)

    Article  MATH  Google Scholar 

  32. Sakiama T., Huang M.: Free vibration analysis of rectangular plates with variable thickness. J. Sound Vib. 216, 379–397 (1998)

    Article  Google Scholar 

  33. Ayaz F.: Applications of differential transform method to differential-algebraic equations. Appl. Math. Comput. 152, 649–657 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  34. Heyliger P.R., Reddy J.N.: A higher order beam finite element for bending and vibration problems. J. Sound Vib. 126(2), 309–326 (1988)

    Article  MATH  Google Scholar 

  35. Li X.F.: A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. J. Sound Vib. 318, 1210–1229 (2008)

    Article  Google Scholar 

  36. Yokoyama T.: Free vibration characteristics of rotating Timoshenko beams. Int. J. Mech. Sci. 30(10), 743–755 (1988)

    Article  MATH  Google Scholar 

  37. Eisenberger M.: Dynamic stiffness vibration analysis using a high-order beam model. Int. J. Numer. Methods Eng. 57, 1603–1614 (2003)

    Article  MATH  Google Scholar 

  38. Simsek M., Kocaturk T.: Free vibration analysis of beams by using a third-order shear deformation theory. Sadana 32, 167–179 (2007)

    MATH  Google Scholar 

  39. Izzuddin B.A., Karayannis C.G., Elnashai A.S.: Advanced nonlinear formulation for reinforced concrete beam-columns. J. Struct. Eng. ASCE 120(10), 2913–2934 (1994)

    Article  Google Scholar 

  40. Hurty W.C., Rubinstein M.F.: Dynamics of Structures. Prentice Hall, New Delhi (1967)

    Google Scholar 

  41. Kocaturk, T.; Simsek, M.: Free vibration analysis of Timoshenko beams under various boundary conditions. Sigma J. Eng. Nat. Sci. 1, 30–44 (2005)

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Authors and Affiliations

  1. School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

    Rahmat Kazemi Firouzjaei, Reza Attarnejad, Rohollah Abbasi Shanbehbazari & Fardad Aala

  2. Centre of Numerical Methods in Engineering, University of Tehran, Tehran, Iran

    Reza Attarnejad

  3. Centre of Excellence for Engineering and Management of Infrastructures, School of Civil Engineering, University of Tehran, Tehran, Iran

    Reza Attarnejad

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  1. Rahmat Kazemi Firouzjaei
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  2. Reza Attarnejad
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  3. Rohollah Abbasi Shanbehbazari
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  4. Fardad Aala
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Correspondence to Rahmat Kazemi Firouzjaei.

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Firouzjaei, R.K., Attarnejad, R., Shanbehbazari, R.A. et al. On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element. Arab J Sci Eng 40, 3443–3455 (2015). https://doi.org/10.1007/s13369-015-1814-7

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  • DOI: https://doi.org/10.1007/s13369-015-1814-7

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