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Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method

Author

Listed:
  • Bekir Akgöz

    (Division of Mechanics, Department of Civil Engineering, Akdeniz University, Antalya 07070, Turkey)

  • Ömer Civalek

    (Division of Mechanics, Department of Civil Engineering, Akdeniz University, Antalya 07070, Turkey
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan)

Abstract

In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of changes in the cross-section and Young’s modulus, size dependency, and non-classical boundary conditions are examined in detail. It is observed that the size effect becomes more pronounced for smaller sizes and differences between the classical and non-classical buckling loads increase by increasing the taper ratios.

Suggested Citation

  • Bekir Akgöz & Ömer Civalek, 2022. "Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4429-:d:982659
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    References listed on IDEAS

    as
    1. Ashraf M. Zenkour & Zahra S. Hafed & Ahmed F. Radwan, 2020. "Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    2. Youssef Boutahar & Nadhir Lebaal & David Bassir, 2021. "A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams," Mathematics, MDPI, vol. 9(12), pages 1-16, June.
    3. Francesco Paolo Pinnola & Raffaele Barretta & Francesco Marotti de Sciarra & Antonina Pirrotta, 2022. "Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    4. Renyu Ge & Feng Liu & Chao Wang & Liangliang Ma & Jinping Wang, 2022. "Calculation of Critical Load of Axially Functionally Graded and Variable Cross-Section Timoshenko Beams by Using Interpolating Matrix Method," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
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