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Structural Engineering and Mechanics
  Volume 48, Number 2, October25 2013 , pages 195-205

Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity
Bekir Akgoz and Omer Civalek

    The buckling problem of linearly tapered micro-columns is investigated on the basis of modified strain gradient elasticity theory. Bernoulli-Euler beam theory is used to model the non-uniform micro column. Rayleigh-Ritz solution method is utilized to obtain the critical buckling loads of the tapered cantilever micro-columns for different taper ratios. Some comparative results for the cases of rectangular and circular cross-sections are presented in graphical and tabular form to show the differences between the results obtained by modified strain gradient elasticity theory and those achieved by modified couple stress and classical theories. From the results, it is observed that the differences between critical buckling loads achieved by classical and those predicted by non-classical theories are considerable for smaller values of the ratio of the micro-column thickness (or diameter) at its bottom end to the additional material length scale parameters and the differences also increase due to increasing of the taper ratio.
Key Words
    buckling; strain gradient theory; size effect; Rayleigh-Ritz method; non-uniform micro-column
Bekir Akgoz and Omer Civalek : Civil Engineering Department, Division of Mechanics, Akdeniz University, Antalya, Turkey

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