Analytical and numerical approaches for calculating the static deflection of functionally graded beam under mechanical load

  • Authors

    • Hayder Z. Zainy University of Kufa-Faculty of Engineering-Mechanical Engineering Department
    • Luay S.Al-Ansari University of Kufa – Faculty of Engineering – Mechanical Engineering Department
    • Ali M.Al-Hajjar University of Kufa – Faculty of Engineering – Mechanical Engineering Department
    • Mahdi M.S.Shareef The Islamic University- Engineering College- Refrigeration and Air-Conditioning Techniques Department
    2018-12-05
    https://doi.org/10.14419/ijet.v7i4.20515
  • FG Beam, Static Deflection, Finite Element Method, ANSYS Software, Trapezoidal Method, Simpson Method, Power Law Model, Cantilever Beam, Simply Supported Beam.

  • Functionally graded material is a new type of composite material and it is used in several smart applications. The static deflec-tion of the FG beam under mechanical and/or thermal load is a complex phenomenon because of the complexity of material properties. The power law model is used to described the material properties of FG beam. The analytical approach depending on the compound beam theory is derived in order to find the equivalent cross section area of FG beam and then calculate the static deflection for new beam. This approach can be achieved analytically when the power law index equals 1 and achieved by numerical integrals (Trapezoidal and Simpson Method) for any value of power law index. The numerical approach ( Finite Element Method using ANSYS software) used in this work depends on the laminate theory , compound beam theory in order to build three different models. The validation of these methods were done by comparing the results with the results of Alexraj et. al. [9]. The comparison among the five methods were done and analysis to choose the suitable method.

     

     

  • References

    1. [1] F.-G. Y. a. R. E. Miller, "A New Finite Element for Laminated Composite Beams," Computer and Structures , vol. 31, no. 5, pp. 737-745, 1989. https://doi.org/10.1016/0045-7949(89)90207-1.

      [2] T. Lidstrom, "An Analytical Energy Expression for Equilibrium Analysis of a 3-D Timoshenko Beam," Computer and Structures, vol. 52, no. 1, pp. 95-101, 1993. https://doi.org/10.1016/0045-7949(94)90259-3.

      [3] Chakraborty, "A New Beam Nite Element for the Analysis of Functionally Graded Materials," International Journal of Mechanical Sciences, pp. 519-539, 2003.

      [4] M. ÅžimÅŸek, "Static Analysis of Functionally Graded Material Beam Under a Uniformly Distributed Load bb Ritz Method," International Journal of Engineering and Applied Sciences (IJEAS), vol. 1, no. 3, pp. 1-11, 2009.

      [5] C. A. Almeida, "Geometric Nonlinear Analyses of Functionally Graded Beams Using a Tailored Lagrangian Formulation," Mechanics Research Communications, vol. 38, pp. 553-559, 2011. https://doi.org/10.1016/j.mechrescom.2011.07.006.

      [6] M. A. Elshafei, "FE Modeling and Analysis of Isotropic and Orthotropic Beams Using First Order Shear Deformation Theory," Materials Sciences and Applications, vol. 4, pp. 77-102, 2013. https://doi.org/10.4236/msa.2013.41010.

      [7] A. Daneshmehr, "Investigation of Elastoplastic Functionally Graded Euler-Bernoulli Beam," Journal of Basic and Applied Scientific Research Subjected to Distributed Transverse Loading, vol. 2, pp. 10628-10634, 2012.

      [8] R. Mehta, "Static and Dynamic Analysis of Functionally Graded Beam," Indian Journal of research, vol. 2, no. 7, 2013.

      [9] S. Alexraj, N. Vasiraja and P.Nagaraj, “STATIC BEHAVIOUR OF FUNCTIONALLY GRADED MATERIAL BEAM USING FINITE ELEMENT METHOD", IEEE, 2013. https://doi.org/10.4236/msa.2013.41010.

      [10] M.A. Benatta, I. Mechab, A. Tounsi and E.A. Adda Bedia “Static Analysis of Functionally Graded Short Beams Including Warping and Shear Deformation Effects", Computational Materials Science vol. 44, P.P. 765–773, 2008.

      [11] X.-F. Li," A Unified Approach for Analyzing Static and Dynamic Behaviors of Functionally Graded Timoshenko and Euler–Bernoulli Beams", Journal of Sound and Vibration Vol. 318, P.P.1210–122, 2008.

      [12] Neethu Charndran and M.G. Rajendran “Study on Flexural Behavior of Cantilever Beam Made of Functionally Graded Material", International Journal of Mechanical And Production Engineering, Vol. 2, Issue- 3, 2014.

      [13] M. Sitar, F. Kosel and M. Brojan ," Large Deflections of Nonlinearly Elastic Functionally Graded Composite Beams", archives of civil and mechanical engineering Vol. 14,P.P. 700 – 709, 2014.

      [14] S.Tharaknath. M.Tech, S.Govindaraji, T.Anbu, G.purushothaman and C.kannadhasan," Analysis of Fgm Beam Under a Udl Load", Journal of Mechanical and Civil Engineering, Volume 11, Issue 5, P.P. 83-86, 2014.

      [15] Thuc P. VO, Huu-Tai Thai, Trung-Kien Nguyen, Fawad Inam and Jaehong Lee," Static Behavior of Functionally Graded Sandwich Beams Using a Quasi-3D Theory", Composites: Part B, Vol. 68, P.P.59-74, 2015.

      [16] M. Filippi, E. Carrera and A.M. Zenkour," Static Analyses of FGM Beams by Various Theories and Finite Elements", Composites: Part B, Vol. 72, P.P.1-9, 2015.

      [17] M. Filippi, A. Pagani, M. Petrolo, G. Colonna and E. Carrera," Static and Free Vibration Analysis of Laminated Beams by Refined Theory Based on Chebyshev Polynomials", Composites: Part B, Vol. 132, P.P. 1248–1259, 2015.

      [18] Waleed M. Soliman M. Adnan Elshafei and M. A. Kamel," Static Analysis of Isotropic, Orthotropic and Functionally Graded Material Beams", Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 2458-9403 Vol. 3 Issue 5, May – 2016.

      [19] J.L.Mantaria and F.G.Canales," A Unified Quasi-3D HSDT for the Bending Analysis of Laminated Beams", Aerospace Science and Technology, Vol. 54, P.P. 267–275, 2016.

      [20] J.L.Mantaria and F.G.Canales," Finite Element Formulation of Laminated Beams with Capability to Model the Thickness Expansion ", Composites: Part B, Vol. 101, P.P. 107–115, 2016.

      [21] Manish Bhandari and Dr. Kamlesh Purohit, "Analysis of Functionally Graded Material Plate under Transverse Load for Various Boundary Conditions", Journal of Mechanical and Civil Engineering, Volume 10, Issue 5, PP 46-55, 2014.

      [22] Reddy JN. Mechanics of laminated composites plates: theory and analysis. Boca Raton: CRC Press; 1997.

      [23] E. J. Hearn," Mechanics of Materials I: An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials", third edition, Butterworth-Heinemann, 2000.

      [24] Ferdinand L.Singer and Andrew Pytel, “Strength of Materials", third edition, Hrper & Row Publishers, New York, 1980.

  • Downloads

  • How to Cite

    Z. Zainy, H., S.Al-Ansari, L., M.Al-Hajjar, A., & M.S.Shareef, M. (2018). Analytical and numerical approaches for calculating the static deflection of functionally graded beam under mechanical load. International Journal of Engineering & Technology, 7(4), 3889-3896. https://doi.org/10.14419/ijet.v7i4.20515