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Structural Engineering and Mechanics Volume 66, Number 6, June25 2018 , pages 737-748 DOI: https://doi.org/10.12989/sem.2018.66.6.737 |
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Buckling analysis of tapered BDFGM nano-beam under variable axial compression resting on elastic medium |
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Abbas Heydari and Mahdi Shariati
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| Abstract | ||
| The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices. | ||
| Key Words | ||
| buckling analysis; nonlocal elasticity theory; bidirectional functionally graded material; two-parameter elastic foundation; variable axial compression; tapered nano-beam; multi-span nano-beam | ||
| Address | ||
| Abbas Heydari: Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran Mahdi Shariati: 1) Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran 2) Department of Civil Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia 3) UTM Construction Research Centre, Faculty of Civil Engineering, Institute for Smart Infrastructure and Innovative Construction, UTM, 81310 Johor Bahru, Johor, Malaysia | ||